Online Prac CAT # 03 Solution
Content
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1.
Ans.(3). If we look up paragraph 3, we can understand that the author has a grudge against tacking the story up with the gameplay. Why does he think so? Because as he explains further, the storyline moved previously with one motivator, which was "fun". Even in the newer version of the game, this inducement could have done its part. There was no actual need for the added narrative. Now, the answer to question would require us to understand what is "blatant". It means something that is completely obvious or vehemently loud. The reason why the storyline justifies this adjective is that according to the author it is the most visible feature because of its uselessness. Thus, option (3) is correct because it encompasses all the major points. Option (1) misses out the unsuccessfulness of the storyline. Option (2) is an innocuous one and could have been chosen given there was a lack of better choice. Option (4) is not supported by the author. He may have mentioned that the narrative was redundant but he never says that it shifts the focus away. These are two different things. Option (5) is not even close as it is talking of improving the gameplay, when the question asks about the fallacies of the move.
2.
Ans. (1). Harrowing means "causing pain, or trouble". Option (2) is incorrect because intertwining means overlapping which isn't the intended meaning. Option (5) is wrong because levels is not what the author meant by courses. Among options (1), (3) and (4) option (1) is a better choice because when one is talking about the difficulty of the game what one means is that it is troublesome, and not traumatic or agonizing. These are higher degrees which should be avoided.
3.
Ans.(1). Read the first line of the passage and it becomes clear that the author loves the newer version (Marble Saga) over the older one (Marble Mania). Also, throughout the passage, he maintains this tone. Options (3) and (4) are wrong as they ask for the removal of the narrative for the making of the choice. This, as is evident from the passage is not a necessary condition. Of course, the improvement of the controls is an enhancement in the later version, but this is mentioned as a sideline benefit.
4.
Ans.(1). The passage uses disarming as "Marble Saga Kororinpa is disarming in its simplicity". Here, the clear meaning is that Marble Saga has won over the critic's heart with its simplicity. Even the meaning of the word "disarming" is "to win over".
5.
Ans.(3). Option (3) best rounds up what the author has in mind. Options (1) and (2) are incorrect because they compare the newer version with the older one; this is not required. Option (5) misses out the negative feedback. Option (4) is a close one but it forgets to mention the game's "already great formula".
6.
Ans.(5). The third reason given in the passage about the acceptance of relativism talks of accepting different reasons or logics in view of different cultures. So, option (1) is ruled out. Options (2) and (3) can be deduced from the first paragraph. Option (4) implies the same as the other three and says that there is no singular benchmark for absolute truth. Hence, the answer is option (5).
7.
Ans.(5). A doctrine is selfrefuting if its truth implies its falsehood .Option(1) plays on the definition of relativism, since the truth value of a particular statement is relative, it can at the same time be true or false with respect to different statements hence it clearly implies that relativism itself is false, at least relative to some standpoints. Option (2) is a clear example of self refutation given in the passage. Option (3) is stated in the opening paragraphs of the passage.
8.
Ans.(4). Options (1), (2) and (3) can be inferred from the second ,third and fourth reasons for acceptance of cognitive relativism. Media here refers to the broader term that reflects all medium of expression, viz. Drama, Literature, etc. Option (5) is stated in the seventh and eighth paragraph. Option (4) is the only one that is not supported by the passage.
9.
Ans (4). Option(1) is not correct as this is the view of critics and not that of realists themselves. Option (2) is also wrong as it describes the perspective of certain 'sophisticated' relativists and not that of all relativists on the whole. Option (3) is wrong as the passage says "cognitive relativism is a thought to undermine………..",i.e. , not the view of realists themselves. Option (4) is right as it has been explicitly stated in the passage.
10.
Ans.(2). Option (1) fails because it brands all unintelligent people to be the degrader of relativism. Option (3) speaks about who do not represent relativism, while the paragraph was talking about who represent relativism incorrectly. Option (4) is close but covers only one part of the paragraph and leaves out what this activity leads to. Option (5) is incorrect as it intends to state information contrary to the paragraph.
11.
Ans.(4). If we look at the given statement in the passage, we clearly see that author agrees to it as being an issue, but an overrated one and not as serious as is made out to be. Option (1) is given nowhere in the passage. Option (2) though has been given in the passage but is not the right answer because it does not relate to the question. It is just a justification of how other issues have been overshadowed by global warming. Option (3) shows how activists exaggerate things and does not convey the meaning of given, it is simply an example to prove it. Option (5) clearly does not fit in.
12.
Ans.(3). Immediately before the last statement, the author has said that popular media has given 300 problems arising out of global warming. Last line is a mockery of this and means that just the way people believed pope when he said witches caused deaths due to cold, similarly people today believe global warming as being the "witch" that is causing all the problems. Although author believes that activists sometimes misguide people he does not relate it to people's belief about witches. Nowhere has the author talked about superstition as being one of the major problems. Hence, option (4) is rejected.
13.
14.
Ans.(2) At first glance option(5) seems to be right as all others have been mentioned in the passage but on reading again we find that though the author has talked of countereffects of global warming, nowhere does he say that the two will balance out each other's effects. Option (1) finds mention in the last line of paragraph 3. Option (3) has been justified in the last paragraph. Option (4) can be inferred from paragraph 4. Ans.(4) This is the correct answer as in the last two paragraphs, the author talks of investing funds wisely and equally in all the major problems than just focusing on global warming. This is on the same lines as options (3) and (5) but is more appropriate as it justifies them both. Thus, (4) is an all inclusive answer. Options (1) and (2) are the assertions made by author as reasons causing the exaggeration of issue. He does not talk of eradicating them.
15.
Ans.(2). Arrant actually means "without qualification; used informally as (often pejorative) an intensifier". Clearly, option (2) is the correct one. We can solve this question by looking up the context in which this word has been used in the passage.
16.
Ans.(1). It is clear that all options are mentioned in the passage except option (1). This is contrary to what the passage says that 'Chickens and eggs raised on small, sustainable farms seem relatively expensive' in paragraph 2.
17.
Ans.(4). The line has to mean that after eating your first egg sandwich, the taste that lingers in the mouth is one that you remember and hence in every next purchase, you try to have something like it or better than it. So, the eggs that you purchase, you try to have the ones that can provide the best possible taste. This is mentioned in option (4). All other options can be true if we visualise the line alone. But if taken in the context of the passage, only option (4) fits in.
18.
Ans.(3). The author is thrilled in the first paragraph to witness eggs being sold at $6. This reveals that this is a high price and yet there are people who are buying the eggs. This goes to show that there is a change in the buying pattern of the consumers. This change becomes evident as we read the next few paragraphs. Thus, option (3)is the best answer.
19.
Ans.(3). Paragraph 1 states that the author viewed $6 eggs as a rarity. He felt thrilled to see this. The answer to why he felt thrilled can be given by answering why he considered the eggs as a rarity. He did that because he had never seen so expensive eggs being sold. This eliminates options (2), (4) and (5). Option (1) is cancelled out because the inability to sell eggs at $4 or $5 was not a discovery for the author as the option makes us believe.
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20.
Ans.(4). Only option (4) is incorrect as the passage says "humane standards for the animals" which means treating animals considerately and kindly, not humanly.
21.
Ans.(2). The passage undoubtedly talks about winemaking, but in clear reference to the state of Burgundy. Even from the first paragraph one can deduce the author's motive that he wishes to examine the role played by Burgundy in the making of wine. Only option (2) speaks about this.
22.
Ans.(2). If all the grapes from differnet vineyards could provide similar (best) quality of the grapes they could be used to create a similar (best) quality of wine. Thus, option (2) seems the most plausible answer. Options (1) and (3) are redundant as they state something that the passage states. Option (4) has the flaw that the advantage enlisted has nothing to do with the development of winemaking.
23.
Ans.(3). This question can be answered only by understanding the text that follows this line in the passage. On reading it we can ascertain that the author is speaking about the experience a person has after drinking Burgundy wine. The person savours the taste for the first time but then cannot experience it again because of the wine being present there everytime. Thus, there is a clear indication to overabundance of wines, and hence option (3) is correct.
24.
Ans.(4). Ethereral as used in the passage can correspond to an experience which is outofordinary, or simply something higher than earthly things. All options except option (4) refer to something that is out of ordinary. Option (4) erroneously links commonsense to ethereal.
25.
Ans.(2). Option (1) finds a mention in paragraph 4. Option (3) is there in paragraph 2 and option (4) is there in the next to last paragraph. Option (2) is incorrect as the passage states that Gamay grape was considered to be unfit for human consumption and hence was not grown. Pinot Noir was grown for making wine. Gamay grape was not the reason for growing Pinot Noir.
26.
Ans.(2). The argument in option (2) is essentially that the proposed creation of a Censor Board makes no sense because sitcoms show the same content. The argument relies explicitly on an analogy between movies and sitcoms. Thus, the two must be similar in all respects relevant to the argument. Otherwise, the argument is unconvincing. Option (2) affirms that sitcoms are in fact detrimental, thereby solidifying the analogy between the two. (1), (3) and (4) each in its own way supports the bare assertion that the proposed Censor Board might not be effective. However, none of these answer choices confirms the argument's essential reasoning. (5) actually weakens the argument, by providing a reason why sitcoms and movies are not relevantly similar.
27.
Ans.(5). A typical weekend IPL match generates more revenue than a typical Art Exhibition. Hence, increasing the number of weekend IPL matches is the surest way, among the five choices, for Detro to maximize revenues, especially if the number of days per year that the stadiums are used for Art Exhibitions would at least remain the same, as (5) implies. Options (1) and (2) are incorrect for essentially the same reason. By increasing the admission fee, Detro might either enhance or reduce its total revenues, depending on the decrease in attendance (if any) due to the fee increase. Besides, neither plan would add to the number of days during which one or the other type of event takes place. Hence, neither is as likely to succeed as the one that option (5) suggests. (3) is the worst of the five choices, and the easiest one to eliminate; replacing an event with one that generates significantly less revenue can only serve to reduce revenues. Option (4) suggests a course of action that is unlikely to be as effective as the one that option (5) suggests. Increasing the number of weekend exhibitions might boost revenues. However, since a weekend art exhibition generates less revenue than a weekend IPL match, the boost would be less than if the number of weekend IPL matches were increased instead.
28.
Ans.(1). The argument relies on the unstated assumption that no other event since the fest could have caused the outbreak instead. Statement (1) provides some evidence that the students who have reported Psoriasis symptoms in fact contracted it at least one week ago. Accordingly, (1) helps support the claim that it was the swim in the contaminated water during the trip two weeks ago that caused the outbreak. (4) has no effect on the argument. It is the time after contact that symptoms begin to occur, not the duration of those symptoms, that is key to identifying the source of spread. (2) actually weakens the claim, by providing another possible explanation for the outbreak. Specifically, (2) provides for the possibility that the outbreak can be attributed to the water in the swimming pool of the school rather than the dip at the picnic. (3) provides some support for the argument, insofar as it helps to explain why only one of those reporting symptoms has tested positive so far. Additional statistical information would be required to assess whether (5) supports the argument. For example, assume for the moment that several studentsincluding the 63 later reporting Psoriasis symptoms attended the trip. In this event (5) would strengthen the teacher's claim, by providing an explanation for how the picnic bath could have been contaminated if only a small percentage of attendees have reported Psoriasis symptoms. Or assume on the other hand that the only students attending the trip were the 63 later reporting Psoriasis symptoms. In that case all who took a bath showed symptoms for Psoriasis and hence, teacher’s assertion will be repealed.
29.
Ans.(5). The argument relies on the unstated assumption that Tamil Nadu's Karanatakan population either remained stable or increased during 2007. However, (5) provides that this population actually declined in 2007, despite the influx of Karanatakans. Given that the number of Karanatakans residing in Tamil Nadu decreased while the crime rate increased, (5) reduces the likelihood that it was Karanatakans who were responsible for the increase in violent crime in 2007. (1) would appear to weaken the argument, by providing ostensible evidence that Tamil Nadu citizens are more likely than Karanatakans to commit violent crimes. However, (1) does not account for the possibility that in Karanataka far more violent criminals go unapprehended than in Tamil Nadu. In fact, the argument's explicit reference to "reported" violent crimes underscores this possibility, which prohibits us from drawing any firm conclusion as to which group is more likely responsible for violent crimes. (2) provides no information useful in evaluating the argument. Whether (2) strengthens the argument depends on additional considerations as well, such as: the total population of Karanataka compared to Tamil Nadu; whether the Karanatakan population increased or decreased in each state during the year; and whether the crime rate in Karanataka increased or decreased during 2007. (3) actually strengthens the argument. By providing evidence that number of Karanatakans residing in Tamil Nadu increased in 2007, (3) makes it more likely that Karanatakans were responsible for the increase in violent crime that year. (4) actually strengthens the argument, by affirming the essential premise that the number of violent crimes in Karanataka increased dramatically during 2007.
30.
Ans.(1). According to the passage, the total aluminium demand for packaging has been decreasing, while the amount of aluminium packaging recycled for the same purpose has been increasing. These two facts, considered together, lend strong support to the conclusion that manufacturers have substituted recycled aluminiumpackaging for "fresh" aluminium to meet their demand for aluminium packaging. (2) is not strongly inferrable from the passage, because without any numbers, it is impossible to compare the total amount of recycled packaging to the total amount of "fresh" packaging. (3) is incorrect because the passage provides no information for the inference that all recycled aluminium packaging has been used to meet the aluminium packaging demands of manufacturers. (4) is not a strong option. The only information in the passage about the demand for packaging material involves aluminium packaging. It is impossible to draw any strong conclusions about the demand for nonaluminium packaging material. In (5), just because the amount of recycled aluminium packaging has increased, it is unfair to conclude that the amount of aluminium from products has also increased.
31.
Ans.(2). It is clear that in protectionist policies one country would protect its own jobs whatever the type of job may be. Thus, global is incorrect. Since, the paragraph is not worried about the type of job, we can even cancel out options (3), (4) and (5). Ans.(1). Since we are talking of a grave situation, option (1) clearly is the best choice. Option (2) is in opposite context. Option (3) though might seem true with respect to protectionism but does not fit in because nowhere has the authenticity of situation been questioned. Option (4) is not right because such a situation already occurred in 1930. Option (5) is close but ponderous (heavy; or having a great mass and weight and unwieldiness) is not of the required level that is expected from an occurence that causes end of globalization.
32.
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33.
Ans.(4). Selfish in this option cannot fit because it would be redundant to speak "selfish protectionist" when protectionism has the meaning of selfish built in. Tender will be inept because the speaker is condemning protectionism. Fearsome implies something that is dreadful or frightening. Fearful might have been an apt choice. Mediocre doesn't explain anything. Only shortsighted seems correct as the speaker warns that decisions like these may hamper growth in the future.
34.
Ans.(3). Since we are talking of a threat against globalization, options (2) and (4) are ruled out. Options (1) and (5) talk of temporary hindrance, but option (3) says choke off; i.e. ,complete devastation and thus option (3) most aptly defines the threat.
35.
Ans.(2). Since we are talking of resisting protectionism, (1) and (5) are rejected as instead of tackiling it, they would further promote it. Options (3) and (4) are general words and do not fully bring out the graveness of the need to work together. Hence option (2) is the right answer.
36.
Ans.(3). Options (1) and (4) that mention "special mark" presupposing that it has been introduced are incorrect as it is nowhere in the first part of the paragraph. Option (5) is close but is incorrect because had it been in the paragraph, the construction would have looked like, "Its not just this attitude that is mysterious. Its also their special mark". There is an also missing there. Option (2) is wrong because long eyelashes and sombre face does not prepare the donkeys for long journeys. Only option (3) gives a link between the two parts.
37.
Ans.(2). A clear look at the lines above the missing one will reveal that what we need in the missing line is something that shows what the Government can do (using its buying power) to improve the security of the products. Thus, options (1), (3), (4) and (5) all get negated. Option (1) speaks of fake products (an unnecessary inclusion). (4) specifies that the cybersecurity issue will be dealt with in the fullest, while the statement in the last line mentions "improved security" not "complete security". (3) and (5) talk nothing about the "buying power" of the Government.
38.
Ans.(3). A careful analysis will reveal that the author is trying to hold the American leadership and the citizens responsible for the sorry state that America portrays on the global front today. Thus, options (1), (4) and (5) can be negated because they are trying to say that the world has been unworthy of America's efforts. Among options (2) and (3), option (3) is a brilliant filler because it quickly ditributes the onus of the responsibility for the American predicament between the people and the leaders. Option (2) could have been a better choice if only option (3) was not there.
39.
Ans.(4). This one should be easy. When one compares the options and looks up what are the differences, she/he can easily make out two: indicate(s); and lie/lay. Considering the subjectverb agreement, "information" will entail an "indicate". Thus, options (1), (2) and (3) are ruled out. Option (5) is wrong because it uses the incorrect verb "lay" rather than "lie". Lay usually implies "put into a certain place or abstract location". While lie is "to have a place in relation to something else".
40.
Ans.(1). Here we need to be clear about the usage of few, fewer, less and lesser. 'Fewer' answers the question, "How many?" (bats, balls, dogs, chairs) and 'less' answers the question, "How much?" (cola, dirt, salt, capacity). Fewer and lesser are always used when comparing things. This eliminates answer choices (2), (4), and (5). Answer choice (3) is unnecessarily wordy and implies that the auditoriums had already been built before the buttonholing began.
41.
Ans.(3). Statement A can be classified as an inference because even though we do not have the data from where this conclusion has been drawn, yet we are sure that it is a conclusion atleast. B is a judgement because of the use of the word "narrowly". This is an unquantifiable adjective, i.e. it can change according to the perspective of the person and the tendency of the situation. C and D are facts and can be easily verified.
42.
Ans.(5). Statements A and C are facts that can be easily verified. B is acknowledged as a fact because it is something that someone has spoken publicly. This can be verified for its truth value. D is an inference because a conclusion has been drawn in the later part of the sentence based on the former half.
43.
Ans.(2). Statement A is an inference drawn from data that is not provided in the question. B and C are inferences based on information given in A and B respectively. D is a fact because the function of the State Water Resource Regulatory Authority can be confirmed.
44.
Ans.(1). Statement A is a fact and can be verified whether differnet cases of incest have come up in the country or not after the expose of the Mira Road case. C is a fact and can be identified first among all. B is a conclusion drawn based on the information provided in A. D is a judgement becasue of the unquantifiable phrase "frowned upon". One cannot say for certain what this may mean to the speaker. Hence, option (1) is the correct choice.
45.
Ans.(4). Statement A is a judgement of the situation presented by the speaker. Statements B and C are conclusions drawn. In B, we can see "How that will pan out remains uncertain" is the conclusion drawn on the basis of information provided ahead in the line. In C, the second part of the sentence after the comma is the inference drawn as the speaker clears that the "No Means Yes" brigade may have to move on. D is a clear judgement that the speaker is passing on the prevalent situation.
46.
Ans.(3). The quote means that mercy blesses both the giver and the taker and its blessings are not exhausted by the increase in the number. That is why, everyone should show mercy to others.
47.
Ans.(4). An optimist's quest for looking at the brighter side everywhere can lead to trying situations. Any person who gets through these traumas can be pardoned if he doubts things and becomes a pessimist. Option (4) is the best answer. Option (3) is near but it labels all optimism as bad which is not what is meant here.
48.
Ans.(4). The quote implies that real intelligence is comprehending the length and the breadth of one's knowledge. Only option (4) is correct.
49.
Ans.(4). The quote can be understood as "a custom that is honoured by not observing it and rather breaching or avoiding it." Hence, option (4) is correct.
50.
Ans.(3). The opposite of a true statement can be a false statement. But as the quote says the opposite of a profound truth can be another profound truth. This implies that truly nature doesn't distinguish between right or wrong and treats both of them equally. Thus, option (3) is the only correct option.
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For Questions 5154 The number of people in each of these categories can be calculated by adding all the values of the columns: 3(Lords + Vyaparies + Brahmans + Kshatriyas + Vaishya + Shudra + Bhikshuk) = 3375 Hence, total number of people from all the categories =1125 Now, the number of people from the Shudra category = 1125 –(Brahmans +Kshatriyas + Vaishya) – (Bhikshuk + Lords + Vyaparies) = 1125 – (425) – (600) = 100 Similarly, all the values can be determined:
51.
Lords
250
Vyaparies
200
Brahmans
75
Kshatriyas
50
Vaishya
300
Shudra
100
Bhikshuk
150
For getting the minimum number of categories that have more than 50 people unhappy, 70% of 50 = 35 55% of 75 = 41.25 33% of 100 = 33 30% of 150 = 45 24% of 200 = 48 20% of 250 = 50 65% of 300 = 195 Hence, only 1 category is possible. Ans.(1)
52.
The number of categories with more than 200 people can be counted from the above table (Lords and Vaishyas). Ans.(5)
53.
The number of unhappy people in the categories, Vaishya, Lords, Vyaparies, Bhikshuk, Shudra and Brahmans can be at the most more than 40 if the percentage distribution is: 20, 24, 30, 33, 55, 65 and 70 respectively. Ans.(4)
54.
If the number of people in the Shudra category is reduced by 25%, then the number of people = 100 × 75% = 75. 70% of 75 = 52.5. Thus, the maximum number of unhappy people = 52. Ans.(5)
55.
It is clear that if we know who made the sixth move, we also know who can make the seventh move and can eventually win. If Gautam (zeroes) has made the sixth move, there are three possible situations after five moves: Possibility 1: O O X
X X
Possibility 2: O O X X X
Possibility 3: O X X X
O
Based on the rules of the game, only possibility 1 could have resulted in the present situation after six moves. In that case, there are three possibilities for ‘possibility 1’ to result in the present situation Thus, after four moves: Possibility 1: O O
X X
Possibility 2: O O X
X
Possibility 3: O O X
X
Based on the rules of the game, Maithli (crosses) would have made the winning move, which however did not happen. From this we can conclude that Maithli did not make the fifth move and hence, Gautam did not make the sixth move. So, it must have been Maithli who made the sixth move and Gautam then makes the seventh, winning move. To check that Maithli made the sixth move, we look at the the following three possibilities after five moves: O O X
Possibility 1: O X
O O X
Possibility 2: O X
O O
Possibility 3: O X X
Based on the rules of the game, only possibility 3 can result in the situation after six moves. So, Maithli indeed made the sixth move. Ans.(2)
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For Questions 5657 We will indicate the numbers in the long division in the manner shown below: _ _ _ / _ _ _ _ _ _ _ _ \ _ _ 8 _ _
A / B \ C
_ _ _
D
_ _ _ _
E
_ _ _
F
_ _ _ _
G
_ _ _ _
H
0
0
For E and G, two blank spaces have been brought down; therefore both the second and the fourth space of C are 0. Because F consists of three spaces and equals the outcome of 8 times A, A must be smaller than 1000/8 or 125. Number H consists of four spaces and is the product of number A and the last space of C. Therefore, H is at least 1000, and because A is smaller than 125, the last space of C must be 9. Moreover, A must be at least 1000/9 and hence, larger than 111. Because the number D is subtracted from a number represented by four spaces and the outcome of the subtraction consists of two spaces, the first space of D must be 9. This is possible only if the first space of C is 8. Now we know that the number C equals 80809 and number B is at least 10000000. From this, it follows that A is at least 124. Because we also know that A lies between 111 and 125, A equals 124. The complete long division can now be filled in: 1 2 4 / 1 0 0 2 0 3 1 6 \ 8 0 8 0 9 9 9 2 1 0 0 3 9 9 2 1 1 1 6 1 1 1 6 0 56.
The problem has a unique solution. Ans.(1)
57.
From 0 to 9, only 5 and 7 are not required to complete the long division. Ans.(2)
For Q.58 to Q.61 58. To find the maximum number of employees who were recruited in January and not fired at the end of August, the fired employees must include all the employees of that particular month except January and if there are more number of fired employees in a month than the recruited ones, only then we will assume the January employees to be fired. TABLE1 Month January February March April May June July August
New recruitments(at the beginning of the corresponding month) 80 70 45 56 80 62 56 20
Fired Emoloyees(after the corresponding month) 55 74 48 66 70 73 50 6
Employees who were not fired since the month of January 25 254=21 213=18 1810=8 8 8(1110) 7 7
Hence, 7 employees were recruited in January and were not fired till the end of August. Ans.(3)
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59.
To find the maximum number of employees who were recruited in March and were not fired till the end of June, we need to follow the table:
Month
New recruitments(at the beginning of the corresponding month)
Fired Employees (after the corresponding month)
Employees recruited in March and not fired at the end of the month
January February March April May June July August
80 70 45 56 80 62 56 20
55 74 48 66 70 73 50 6
18 8 8 7
Ans.(3) 60.
The employees who were recruited in a particular month and fired exactly after 3 months would be the employees who were recruited in the months of January, March and May. So, from table 1, the number of employees who were recruited in January and were fired at the end of March were 21. The so the number of employees who were recruited in the month of March and were not fired in the same month were 18 as shown in the table. In the month of April 10 employees from the previous month were fired. Thus, the number of new recruitments in March who were not fired in the next month were 8. In the month of May 80 employees were recruited at the begining and 70 were fired at the end of the month. So, 8 employees who were recruited in March were fired at the end of May while 18 employees who were recruited in May were not fired at the end of same month. In the month of June, total 73 emplyees were fired out of which 62 must be new June recruitments. Thus, 11 employees who were recruited in the month of May were fired at the end of June. So, 7 emplyees who were recruited in May were left and were fired at the end of July. So, maximum total number of employees who wre recruited in a month and were fired after exactly after three months were 21 + 8 + 7 = 36. Hence, the total amount the company would have paid to these employees = 36 × 15000 = 540000 Rs. Ans.(3)
61.
The maximum number of employees who were recruited at the beginning of a month and fired at the end of the same month were 55 + 70 + 45 + 56 + 70 + 62 + 50 + 6 = 414. Ans.(3)
For Q.62 to Q.64 Given that 40% of the total employees who joined AMA as Marketing Executives = 21720 So, total employees from the other company who joined AMA = (21720 × 100)/40 = 54300 This is equal to 80% of the total employee base of the other company. So, the total number of employees of the other company = (54300 × 100)/80 = 67875
Total number of employees of other company (OC) 67875
80% of 16% of 80% of OC 44% of 80% of OC 40% of 80% of OC OC who joined HR who joined Finance who joined Marketing 54300
8688
23892
21720
16% of the total employees who joined as HR executive AMA = 20% of the total employees who failed the promotion test = 8688 So, total employees who failed the promotion test = (8688 × 100)/20 = 43440 This is equal to 30% of the total employees of AMA. So, total number of employees of AMA before the merger = (43440 × 100) / 30 = 144800 Total number of employees who passed the promotion test = (70 × 144800) / 100 = 101360 30% of TEP Total employees who 25% of TEP promoted as 40% of TEP promoted as promoted as Finance passed the test (TEP) HR executive Marketing executive executive 101360
25340
30408
45612
62.
So the total number of employees after the merger = 144800 + 54300 = 199100. Ans.(1)
63.
We can calculate only the number of male employees before the merger. But we cannot calculate the number of male or female employees after the merger, because we do not know about the number of males or females who joined AMA from the other company. Ans.(5)
64.
Following table is prepared from the given information: Company
Total number of employees
HR
Marketing
Finance
Other employees
AMA
144800
25340
45612
30408
43440
OC
67875
8688
21720
23892
212675
34028
67332
54300
43440
Old Finance executives = 30408 25% got pink slip, so, remaining 75% = (75 × 30408) / 100 = 22806 15% of the HR executives changed their department and joined as Finance executives, i.e. (15 × 34028)/100 = 4563 So, total Finance executives = 4563 + 22806 + 23892 = 51261. Ans.(3)
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For Questions 6568 From the given information, following tables can be prepared: Table I Price in INR Dress
(1 Euro = 65 INR)
(1 GBP = 75 INR)
(1 USD = 50 INR)
(1 SGD = 35 INR)
(1 AUD = 30 INR)
Ladies Evening Dress
65000
135000
60000
60000
45500
Knit Cover up
91000
58500
84000
49500
68250
Voile Cover up
58500
84750
65000
56100
57750
Cotton Ladies Tunic
103350
69000
72500
63000
68250
Embroidered Tunic
78000
125250
88000
54000
50750
Stylish Ladies Tunic
88400
115500
71500
35400
65100
Party wear saree
77350
71250
43000
52500
44100
Wedding Wear
149500
197250
114500
101400
97300
Table II Custom Duty on goods Dress
bought from Milan is bought from London 1% is 2%
bought from San francisco is 0%
bought from singapore is 20%
bought from Rosemount is 5%
12000
2275
Ladies Evening Dress
650
2700
0
Knit Cover up
910
1170
0
9900
3412.5
Voile Cover up
585
1695
0
11220
2887.5
Cotton Ladies Tunic
1033.5
1380
0
12600
3412.5
Embroidered Tunic
780
2505
0
10800
2537.5
Stylish Ladies Tunic
884
2310
0
7080
3255
Party wear saree
773.5
1425
0
10500
2205
Wedding Wear
1495
3945
0
20280
4865
Table III Total cost price (Basic price + Custom duty) Dress
Milan (Italy)
London (UK)
San francisco (USA)
Singapore (Singapore)
Rosemount (Australia)
Ladies Evening Dress
65650
137700
60000
72000
47775
Knit Cover up
91910
59670
84000
59400
71662.5
Voile Cover up
59085
86445
65000
67320
60637.5
Cotton Ladies Tunic
104383.5
70380
72500
75600
71662.5
Embroidered Tunic
78780
127755
88000
64800
53287.5
Stylish Ladies Tunic
89284
117810
71500
42480
68355
Party wear saree
78123.5
72675
43000
63000
46305
Wedding Wear
150995
201195
114500
121680
102165
65.
From table III, the minimum amount that Mrs. Aadhunikwala must carry = 2 × 70380 = 140760 (from London Fashion Week, UK) Ans.(5)
66.
From table III, the price of Ladies Evening Dress at London Fashion Week (UK) = 137700 and the price of Ladies Evening Dress at Rosemount (Australia) = 47775. So, the maximum difference = 137700 47775 = 89925 Ans.(2)
67.
We can calculate the price of all these five dresses from table III Party Wear Saree, Rosemount Fashion Week = 95% of 46305 Voile Cover Up, Milan Fashion Week = 95% of 59085 Ladies Evening Dress, Rosemount Fashion Week = 95% of 47775 Party Wear Saree, San Francisco Fashion Week = 95% of 43000 Stylish Ladies Tunic, Singapore Fashion Week = 95% of 42480 So, we can observe that Stylish Ladies Tunic at Singapore Fashion Week is the cheapest. Ans.(5)
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68.
Ladies Evening Dress, Rosemount Fashion Week = 47775 Party Wear Saree, San Francisco Fashion Week = 43000 Stylish Ladies Tunic, Singapore Fashion Week = 42480 So, the maximum number of dresses that she can buy with an amount of Rs.180000 (INR) is 3. Ans.(1)
For Questions 6971 Number of programs offered by University Year of Inception
Nanda University
2001 2002 2003 2004 2005 2006 2007 2008 Total Average
9 12 6 17 6 19 18 13 100 12.5
Taxla University Appa University 6 18 17 9 13 15 16 11 105 13.125
Sherpa University
Rana University
11 7 16 10 11 13 5 19 92 11.5
20 17 11 18 6 12 19 7 110 13.75
12 8 13 17 14 9 10 18 101 12.625
69.
There are 4 universities which on an average offer more than 12 programs. Ans.(4)
70.
There are three universities which offer more than 100 programs. Number of programs offered by University
Year of Inception
Taxla University
Appa University
Rana University
2001 2002 2003 2004 2005 2006 2007 2008 Total
6 18 17 9 13 15 16 11 105
12 8 13 17 14 9 10 18 101
20 17 11 18 6 12 19 7 110
P1 = 105 + 101 + 110 = 316 P2 = 100 + 105 + 101 + 92 + 110 = 508 Hence, required percentage = (316 × 100)/508 = 62.20 % Ans.(2) 71.
The maximum percentage drop in new programs offered was by Rana University in the year 2005 over 2004. Ans.(5)
For Questions 7275 72. From the question we get the following table R a ting T REAT ME Me dic in a l In fra struc tu re N T US ED re se rve & e qu ipme n t
Ho sp ita l n a me
WH A / WO HA
CHILDREN'S HOSPITAL
WOHA
ART, AT
7.5
7.5
CIVIC CENTER HOSPITAL FOUNDATION
WOHA
UT, AT
9
6
ESKATON DOCTORS HOSPITAL
WOHA
HT, MT
9
9
HAYWARD HOSPITAL
WOHA
UT, AT
13.5
10.5
NAVAL HOSPITAL
WOHA
ART, AT
10.5
10.5
OGORMAN INFANT
WOHA
AT, HT
9
6
PERALTA HOSPITAL
WOHA
HT, MT, UT
7.5
4.5
Hence, there are 7 hospitals where Mr. Chopar can get treated. Ans.(3)
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73.
From the question we get the following table: Ra tin g R a tio of ra ting S um o f T REAT M Me d ic in ra tin g o f o f fe e d b a c k to ENT a l Do c to rs F e e db a c k me dic in a l su m o f ra ting US ED of me dic in a l re se rve re se rve a nd d oc tor re se rve a n d do c tor HT, ART, 10.5 9 10.5 19.5 0.538461538 RT
H ospita l na me
WH A / WO HA
BOOTH MEMORIAL HOSPITAL
WHA
CHILDREN'S HOSPITAL
WOHA
ART, AT
7.5
10.5
13.5
18
0.75
WHA
MT, ART, UT
7.5
7.5
10.5
15
0.7
WHA
HT, UT
7.5
7.5
7.5
15
0.5
WHA
RT, MT, ART
10.5
13.5
12
24
0.5
WHA
AT, ART, UT
10.5
9
10.5
19.5
0.538461538
OGORMAN INFANT
WOHA
AT, HT,
9
9
9
18
0.5
PERALTA HOSPITAL
WOHA
HT, MT, UT
7.5
7.5
7.5
15
0.5
WHA
RT, ART, UT
9
9
12
18
0.666666667
WHA
RT, UT
13.5
9
10.5
22.5
0.466666667
SAN LEANDRO HOSPITAL EDEN MEDICAL CENTER SUMMIT MEDICAL CENTER OAKLAND HOSPITAL CORPORATI
SUMMIT MEDICAL FOUNDATION HERRICK MEMORIAL HOSPITAL
Hence, there are 9 hospitals. Ans.(5)
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74.
Number of hospitals which do not have In House facility of Ambulance having ART or HT and their rating of doctors is more than 7.5 are given below. CHILDREN'S HOSPITAL
WHA / WOHA
TREATMENT USED
Doc tors
CHILDREN'S HOSPITAL
WOHA
ART, AT
10.5
NAVAL HOSPITAL
WOHA
ART, AT
9
OGORMAN INFANT
WOHA
AT, HT
9
Also, number of hospitals which have In House facility of Ambulance having RT or UT and their rating of Infrastructure & equipments equal or greater than 7.5 are given below. Ho sp ita l na me
WH A / WO HA
T REAT ME N T US ED
In fra stru c ture & e q uip me n t
BOOTH MEMORIAL HOSPITAL
WHA
HT, ART, RT
9
SAN LEANDRO HOSPITAL
WHA
MT, ART, UT
7.5
HERRICK MEMORIAL HOSPITAL
WHA
RT, UT
9
KAISER HOSPITAL
WHA
UT, RT, HT
12
KAISER HOSPITAL
WHA
AT, UT
15
SUMMIT MEDICAL CENTER
WHA
RT, MT, ART
10.5
OAKLAND HOSPITAL CORPORATION
WHA
AT, ART, UT
10.5
SUMMIT MEDICAL FOUNDATION
WHA
RT, ART, UT
7.5
Hence, the required ratio = 3/8. Ans.(1) 75.
From the inforamtion in the question, only following three hospitals have both RT and ART treatment facilities OVREALL RATING
Rating
Hospital name
{(Rating of WHA / TREATME RATING OF feedback) × WOH Medic i RATING NT USED feedb MEDICINAL 5 + 3 A nal OF FEED ac k RESERVE × ×(Rating of reserve BACK × 5 3 medic inal reserve ) }
BOOTH MEMORIAL WHA HOSPITAL SUMMIT MEDICAL WHA CENTER SUMMIT MEDICAL WHA FOUNDATIO N
HT, ART, RT
10.5
10.5
52.5
31.5
84
RT, MT, ART
10.5
12
60
31.5
91.5
RT, ART, UT
9
12
60
27
87
Ans.(2) 76.
Factorizing the numbers, 120 = 2 3 x 3 1 x 5 1 1320 = 2 3 x 3 1 x 5 1 x 11 A is definitely a multiple of 11, but it cannot be a perfect square as A cannot have 11 2 as a factor. 1680 = 120 x 2 x 7 = 2 4 x 3 1 x 5 1 x 7 1 B is definitely a multiple of 2 4 x 7 1 but it cannot be a perfect square as B cannot have 7 2 as a factor. 1800 = 120 x 3 x 5 = 2 3 x 3 2 x 5 2 Since, the LCM of 120 and C is 1800, therefore, C can be a perfect square. One of the possible values of C is 3 2 x 5 2 . But it is not necessary that C be a perfect square. Ans.(5)
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77.
Since, in the new number system, decimal number 5 is represented by a single sign, so the base of that number system is atleast 6. Similarly, the decimal number 95 is represented by three signs, so the base of this number system is not more than 9. Now, checking for base 6, decimal number 20 can be written as (32)6 and decimal number 95 can be written as (235)6. But each sign represents different decimal number. So, base 6 is not possible. Now, checking for base 7, decimal number 5 is represented by (5)7, decimal number 20 can be represented by (26)7 and decimal number 95 can be represented by (164)7. So, according to the signs provided in the question, 1 = 'µ', 2 = '+', 4 = '#', 5 = '$' and 6 = '%'. Therefore, decimal number 778 can be written as (2161)7 in the number system of base 7 Or, (+µ%µ). Ans.(4)
78.
(x + 1)yz = 12
………………(1)
(y + 1)zx = 4
………………(2)
(z + 1)xy = 4
………………(3)
Dividing equation (1) by (2), (x + 1)y = 3 (y + 1)x x =
y (2y + 3)
Dividing equation (2) by (3), z = y Now, on subtracting equation (2) from equation (1), we get y 2 – xy = 8
(Since, y = z)
by putting the value
y x = (2y + 3)
, the equation becomes
y 2 y = 8 (2y + 3) 2
On solving for y, we get y = –2, 3 Now, for y = –2, xyz = 2 × –2 × –2 = 8, an integer. 1
for y = 3, xyz = 3 × 3 × 3 = 3, an integer. Ans. (5) 79.
Given: A 5 = B 4 , also A, B, C and D are positive integers. Hence, only possible values of A and B are A = 1 and B = 1. Now, (C – A) = 3, so C = 4. Also, C 6 = D 2 Hence, 4 6 = D 2 So, D 2 = 4096, so D = 64. Therefore, D – A = 64 – 1 = 63. Ans. (4)
80.
Let the speed of the bus and the scooter be x and y respectively, Distance from A to Mumbai = 2x Distance from Mumbai to B = x/2 Distance from A to B = 2x x/2 = 3x/2 To cover a distance 3x/2 (from A to B), the scooter takes 7/2 hours (from 2pm to 5:30 pm) Now, to cover the remaining distance from B to Mumbai i.e. x/2, the scooter will take 7/6 more hours or 1 hour 10 minutes from 5:30 pm. So, the scooter will reach Mumbai at 6:40 pm. Ans.(2)
81.
Let A be the event that there are exactly 4 Chinese among the first 6 speakers. Let B be the event that the seventh speaker is a Chinese.
F G B I J H A K
P
Then, Required Probability = P(A) ´ Now, 5
C 4 ´ 7 C 2 C 6
F G B I J 1 H A K =Prob. that the seventh speaker is a Chinese given that there were 4 Chinese speakers among the first 6 speakers= 6
P
12
P(A) =
and
5
C 4 ´ 7 C 2 12
Hence, required probability =
12 of 17
C 6
´
1 6
5
= 264 Ans.(3)
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82.
On generalizing the above equation, F(x)=2x 2 + a(b–c) 2 x + abc We know that for an equation ax 2 +bx+c=0, the minimum or the maximum value of f(x) lies at x = –b/2a. Therefore, –a[(b–c) 2 ]/4 = –128 or a(b–c)=512 Now, the sum a + (bc) + (bc) + (bc) will be minimum when a = b–c = 8 Hence, the minimum value of a + 3(bc) = 8 + 8 + 8 + 8 = 32 Ans.(3)
83.
1st process Divide the larger square in 4 equal squares of side A/2. Then the area of total scrap = 4[(A/2) 2 – p(A/4) 2 ] = A 2 (4 p)/4 2nd process Area of total scrap generated in this process = A 2 – p(A/2) 2 = A 2 (4 – p)/4 So, required ratio = 1:1. Ans.(3)
84.
For a given volume, cuboidal shape of minimum surface area is a cube. So, he will arrange all the cubes in the form of a large cube and the side of this cube will be 9 cm. Therefore, the length of the diagonal = 9 3 cm. Ans.(4)
85.
Let the number be n = a p × b q × c r ……………… where a,b,c are prime numbers & p,q,r natural numbers. We know numbers of facters of n = (p+1)(q+1)(r+1)…………= 4 So, either 1×4 or 2×2 = 4 Or, p+1 = 4 & q = 0 or p+1 = q+1 = 2 p = 3 & q = 0 OR p = q = 1 either n = a 3 or n = a×b So, a + a 2 = 72, i.e., a = 8 and n = 512 Or, a + b = 72 assuming a<b (a,b) = (5,67), (11,61), (13,59), (19,53), (29,43), (31,41) Hence, required sum = 512 + 5×67 + 11×61 + 13×59 + 19×53 + 29×43 + 31×41 = 512 + 335 + 671 + 767 + 1007 + 1247 + 1271 = 5810. Ans.(4) P
O A
86.
Q
B S
R
The sides of triangle PQR = 1unit PO = OS = 3 / 4 units and angle AOP is 120° (Central angle theorem) 1 3 3 1 3 3 3 3 3 ´ ´ ´ Sin 120 ° = ´ ´ ´ = 4 2 4 4 2 64 Area of triangle POA = Area of triangle POB = 2 4
F 3 I = p G H 4 JK 16 2
120 ° ´ p 360 °
Area of the minor sector OASB =
Area of the part of triangle that lies outside = Area of triangle PQR [Area of triangle POA + Area of triangle POB + Area of minor arc OASB] = 87.
3 / 4 - [ 3 3 / 32 + p / 16 ] = ( 5 3 - 2 p ) / 32
. Ans.(3)
If (a,b) is a solution then obviously a = 0 and (a,b) is a solution too. For a = 0, we get two solutions (0, 2) and (0, 2). Now, let (a,b) be a solution with a>0; The equation can be rewritten as, 2 a (1+2 a+1 ) = (b+1)(b–1) Shows that the factors b–1 and b+1 are even, exactly one of them divisible by 4. Hence a ³ 3 and one of these factors is divisible by 2 a1 but not by 2 a . So, b = 2 a–1 m + c1, m odd
………………….(1)
Putting this into the original equation we obtain 2 a (1 + 2 a+1 ) = (2 a1 m + c–1) 2 –1=2 2a–2 m 2 +2 a mc or, equivalently
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1+2 a+1 = 2 a–2 m 2 + mc. Therefore, 1– cm = 2 a–2 (m 2 – 8).
………………….(2)
For c = 1 this yields m 2 – 8 £ 0, i.e., m = 1, which fails to satisfy (2). For c = –1 equation (2) gives us 1 + m = 2 a–2 (m 2 – 8) ³ 2(m 2 – 8), Or, 2m 2 – m – 17 £ 0. Hence, m = 3; on the other hand m cannot be 1 according to (2). Because m is odd, we obtain m = 3, leading to a = 4. From (1) we get b = 23. These values satisfy the given equation. Thus, (a,b): (0, 2), (0,2), (4, 23), (4,23). Ans.(3) 88.
Let a, b be the roots of the equation. The equation will have both the roots greater than 3 if it satisfies the conditions given below Condtion 1: D 0 Condtion 2: a + b > 6 Condtion 3: Value of equation at x = 3 is greater than 0 From condition 1, 36a 2 – 8 + 8a – 36a 2 0 Or, a 1 From condition 2, 6a > 6 Or, a > 1 From condition 3, 9 – 18a + 2 – 2a + 9a 2 > 0 Or, 9a 2 – 20a + 11 > 0 So, a < 1 or a > 11/9 Combining results from the above conditions, a > 11/9 satisfies all constraints. Ans. (3)
89.
We have
37 x 17 < < 197 y 77
77 y 197 < < or 17 x 37 4.53 <
or,
y £ 5.32 x
x has minimum value 1 (it is a positive integer). To satisfy the given inequalities y can have a minimum value of 5 since it is also an integer. Ans.(3) 90.
3 2 > 2 3 or
2 log 2 3 > 3 log 2 2
log 2 3 > 3 / 2
..........................(1)
5 2 < 3 3 2 log 3 5 < 3 log 3 3 log 3 5 < 3 / 2
..........................(2)
9 > 8 or 9/4 >2 3 / 2 > 2
..........................(3)
and, 27>24 (3/2) 3 > 3 ( 3 / 2 ) > 3 3
..........................(4)
By comparing all the above four equations we can conclude that 91.
log 2 3
is the largest number the given four numbers. Ans.(4)
The new hexagon formed, will have its side equal to Ö3/2 times the earlier hexagon. Thus, the perimeter will also be Ö3/2 times that of earlier Hexagon. Hence the perimeter of all the Hexagons thus formed will be sum of an infinite GP. = 540 / (1–Ö3/2). Or, 1080 / (2–Ö3). Ans.(4)
92.
SE : ER = 5 : 4 RF : FS = 8 : 1
Q
P
SE = 5x and ER = 4x RF = 8y and FS = y so, SR = 9x = 9y or, x = y Let x = 1
S
F
E
R
Area of Trapezium PQFS = 1/2 (FS + PQ) × PS = 49
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On putting the values of FS and PQ, we get PS = 49/5 Area of Trapezium PQRE = 1/2 (ER + PQ) × PS On putting the values of ER, PQ and PS, we get [1/2 × (4 + 9)] × 49/5 = 63.7 Even if the value of x changes, the answer remains unchanged because the value of PS varies with x. Ans. (3) 93.
The number of ways of choosing the three digits other than 0 and 1 = 8 C3 = 56 These can be arranged in 6!/(2! × 2! × 2!) = 90 ways And the digit 1 can be placed in any of the seven possible locations with respect to the six digits. Total number of ways = 7 × 90 × 56 = 35280. Ans.(1)
94.
log 10567 = log 10(81×7) = log10(3 4 ×7) = x 4log 103 + log 107 = x log 101029 = log10(3×7 3 ) = log103 + 3log107 = y 4log 103 + log 107 = x
……………(1)
log 103 + 3log 107 = y
……………(2)
By solving (1) and (2) log 107 = (4y–x)/11 And log 103 = (3x–y)/11 Now, log1021 = log10(3×7) = log103 + log 107 =(4y–x)/11+(3x–y)/11 =(3y+2x)/11 Ans.(1) 95.
For getting a sum of 109 The minimum number of cards required are (13 × 4 + 12 × 4 + 9 × 1) = 109, i.e., 9 Similarly, (11 × 4 + 10 × 1 + 8 × 2) = 70, i.e., 7 and, (10 × 3 + 9 × 2 + 8 × 2) = 64, i.e., 7. Ans.(1)
96.
X = 20!(1/20! + 1/19! + 1/18!2! + 1/17!3! + … + 1/2!18! + 1/19! + 1/20!) Or, X = (20!/20! + 20!/19! + 20!/18!2! + 20!/17!3! + … + 20!/2!18! + 20!/19! + 20!/20!) These terms are binomial coefficients in the expansion of (1 + x) 20 where x is assumed to be 1 which will lead to the conclusion that 20 C
0 +
20 C
1 +
20 C
20 20 2 + … + C20 = 2
So, X – 1 = 2 20 – 1 X – 1/1023 = 2 20 – 1/1023 = [(2 10 )2 – 1]/ (2 10 – 1) = 2 10 + 1. Ans.(4) 97.
The top of the prism is an isosceles triangle,
F 1 + a + a I a G H 2 2 J K Slant surface area of all the four prisms = 4 F 2 + 1 + 1 I = 4 a F 2 + 2 I = 4 a 2 + 1 = 4 a G H 2 J K G H 2 JK e j 2
2
2
Total surface area of the cube = 6a 2
e 2 + 1 j : 6 a = 2 e 2 + 1 j : 3 . Ans.(5)
= 4 a 2
Therefore, required ratio = 98.
2
180=2 2 ×3 2 ×5 The highest power of 5 in 1!×2!×3!.............49! is 5×[0+1+2+3+4+6+7+8+9+10] = 5×[50] = 250 The highest power of 3 in 1!×2!×3!.............49! is 3×[(22×23)/2 (3+7+11+12+16+20)]22 = 530 Highest powers of 5 and 9 are 250 and 265 respectively. We need not consider power of 4 as it will definetely be greater than 265 Since b is not a multiple of 5, a is the highest power of 5, 250. Ans.(4)
99.
a*a=a + a – a 2 = 2a – a 2 = a(2 – b) Similarly, b*b = b(2 – b) 2a – a 2 < 2b – b 2 2(a – b) < a 2 – b 2 2(a – b) < (a – b)(a + b) (a – b){2 –(a + b)} < 0 Then, 1 st case: (a – b) < 0 and 2 – (a + b) > 0 a < b and 2 > (a + b)
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1 > b > a 2 nd case: (a – b) > 0 and 2 – (a + b) < 0 a > b and 2 < (a + b) a > b > 1 which is not true for 0.5 < (a, b) <1, hence it is rejected so only 1 st case satisfies. Ans.(1) 100. We have100 £ 15k £ 10 5 Or, 6.66 £ k £ 6666.66 or 7 £ k £ 6666 The integer 15k is divisible by 35 if and only if k is divisible by 7. So, k = 7q we have 7£ 7q £6666 1 £ q £952.28 or1 £ q £ 952 Hence, the required number of positive integers = 952. Ans.(3)
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Objective key
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1.(3)
2.(1)
3.(1)
4.(1)
5.(3)
6.(5)
7.(5)
8.(4)
9.(4)
10.(2)
11.(4)
12.(3)
13.(2)
14.(4)
15.(2)
16.(1)
17.(4)
18.(3)
19.(3)
20.(4)
21.(2)
22.(2)
23.(3)
24.(4)
25.(2)
26.(2)
27.(5)
28.(1)
29.(5)
30.(1)
31.(2)
32.(1)
33.(4)
34.(3)
35.(2)
36.(3)
37.(2)
38.(3)
39.(4)
40.(1)
41.(3)
42.(5)
43.(2)
44.(1)
45.(4)
46.(3)
47.(4)
48.(4)
49.(4)
50.(3)
51.(1)
52.(5)
53.(4)
54.(5)
55.(2)
56.(1)
57.(2)
58.(3)
59.(3)
60.(3)
61.(3)
62.(1)
63.(5)
64.(3)
65.(5)
66.(2)
67.(5)
68.(1)
69.(4)
70.(2)
71.(5)
72.(3)
73.(5)
74.(1)
75.(2)
76.(5)
77.(4)
78.(5)
79.(4)
80.(2)
81.(3)
82.(3)
83.(3)
84.(4)
85.(4)
86.(3)
87.(3)
88.(3)
89.(3)
90.(4)
91.(4)
92.(3)
93.(1)
94.(1)
95.(1)
96.(4)
97.(5)
98.(4)
99.(1) 100.(3)
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1 of (17)
1.
Ans.(3). If we look up paragraph 3, we can understand that the author has a grudge against tacking the story up with the gameplay. Why does he think so? Because as he explains further, the storyline moved previously with one motivator, which was "fun". Even in the newer version of the game, this inducement could have done its part. There was no actual need for the added narrative. Now, the answer to question would require us to understand what is "blatant". It means something that is completely obvious or vehemently loud. The reason why the storyline justifies this adjective is that according to the author it is the most visible feature because of its uselessness. Thus, option (3) is correct because it encompasses all the major points. Option (1) misses out the unsuccessfulness of the storyline. Option (2) is an innocuous one and could have been chosen given there was a lack of better choice. Option (4) is not supported by the author. He may have mentioned that the narrative was redundant but he never says that it shifts the focus away. These are two different things. Option (5) is not even close as it is talking of improving the gameplay, when the question asks about the fallacies of the move.
2.
Ans. (1). Harrowing means "causing pain, or trouble". Option (2) is incorrect because intertwining means overlapping which isn't the intended meaning. Option (5) is wrong because levels is not what the author meant by courses. Among options (1), (3) and (4) option (1) is a better choice because when one is talking about the difficulty of the game what one means is that it is troublesome, and not traumatic or agonizing. These are higher degrees which should be avoided.
3.
Ans.(1). Read the first line of the passage and it becomes clear that the author loves the newer version (Marble Saga) over the older one (Marble Mania). Also, throughout the passage, he maintains this tone. Options (3) and (4) are wrong as they ask for the removal of the narrative for the making of the choice. This, as is evident from the passage is not a necessary condition. Of course, the improvement of the controls is an enhancement in the later version, but this is mentioned as a sideline benefit.
4.
Ans.(1). The passage uses disarming as "Marble Saga Kororinpa is disarming in its simplicity". Here, the clear meaning is that Marble Saga has won over the critic's heart with its simplicity. Even the meaning of the word "disarming" is "to win over".
5.
Ans.(3). Option (3) best rounds up what the author has in mind. Options (1) and (2) are incorrect because they compare the newer version with the older one; this is not required. Option (5) misses out the negative feedback. Option (4) is a close one but it forgets to mention the game's "already great formula".
6.
Ans.(5). The third reason given in the passage about the acceptance of relativism talks of accepting different reasons or logics in view of different cultures. So, option (1) is ruled out. Options (2) and (3) can be deduced from the first paragraph. Option (4) implies the same as the other three and says that there is no singular benchmark for absolute truth. Hence, the answer is option (5).
7.
Ans.(5). A doctrine is selfrefuting if its truth implies its falsehood .Option(1) plays on the definition of relativism, since the truth value of a particular statement is relative, it can at the same time be true or false with respect to different statements hence it clearly implies that relativism itself is false, at least relative to some standpoints. Option (2) is a clear example of self refutation given in the passage. Option (3) is stated in the opening paragraphs of the passage.
8.
Ans.(4). Options (1), (2) and (3) can be inferred from the second ,third and fourth reasons for acceptance of cognitive relativism. Media here refers to the broader term that reflects all medium of expression, viz. Drama, Literature, etc. Option (5) is stated in the seventh and eighth paragraph. Option (4) is the only one that is not supported by the passage.
9.
Ans (4). Option(1) is not correct as this is the view of critics and not that of realists themselves. Option (2) is also wrong as it describes the perspective of certain 'sophisticated' relativists and not that of all relativists on the whole. Option (3) is wrong as the passage says "cognitive relativism is a thought to undermine………..",i.e. , not the view of realists themselves. Option (4) is right as it has been explicitly stated in the passage.
10.
Ans.(2). Option (1) fails because it brands all unintelligent people to be the degrader of relativism. Option (3) speaks about who do not represent relativism, while the paragraph was talking about who represent relativism incorrectly. Option (4) is close but covers only one part of the paragraph and leaves out what this activity leads to. Option (5) is incorrect as it intends to state information contrary to the paragraph.
11.
Ans.(4). If we look at the given statement in the passage, we clearly see that author agrees to it as being an issue, but an overrated one and not as serious as is made out to be. Option (1) is given nowhere in the passage. Option (2) though has been given in the passage but is not the right answer because it does not relate to the question. It is just a justification of how other issues have been overshadowed by global warming. Option (3) shows how activists exaggerate things and does not convey the meaning of given, it is simply an example to prove it. Option (5) clearly does not fit in.
12.
Ans.(3). Immediately before the last statement, the author has said that popular media has given 300 problems arising out of global warming. Last line is a mockery of this and means that just the way people believed pope when he said witches caused deaths due to cold, similarly people today believe global warming as being the "witch" that is causing all the problems. Although author believes that activists sometimes misguide people he does not relate it to people's belief about witches. Nowhere has the author talked about superstition as being one of the major problems. Hence, option (4) is rejected.
13.
14.
Ans.(2) At first glance option(5) seems to be right as all others have been mentioned in the passage but on reading again we find that though the author has talked of countereffects of global warming, nowhere does he say that the two will balance out each other's effects. Option (1) finds mention in the last line of paragraph 3. Option (3) has been justified in the last paragraph. Option (4) can be inferred from paragraph 4. Ans.(4) This is the correct answer as in the last two paragraphs, the author talks of investing funds wisely and equally in all the major problems than just focusing on global warming. This is on the same lines as options (3) and (5) but is more appropriate as it justifies them both. Thus, (4) is an all inclusive answer. Options (1) and (2) are the assertions made by author as reasons causing the exaggeration of issue. He does not talk of eradicating them.
15.
Ans.(2). Arrant actually means "without qualification; used informally as (often pejorative) an intensifier". Clearly, option (2) is the correct one. We can solve this question by looking up the context in which this word has been used in the passage.
16.
Ans.(1). It is clear that all options are mentioned in the passage except option (1). This is contrary to what the passage says that 'Chickens and eggs raised on small, sustainable farms seem relatively expensive' in paragraph 2.
17.
Ans.(4). The line has to mean that after eating your first egg sandwich, the taste that lingers in the mouth is one that you remember and hence in every next purchase, you try to have something like it or better than it. So, the eggs that you purchase, you try to have the ones that can provide the best possible taste. This is mentioned in option (4). All other options can be true if we visualise the line alone. But if taken in the context of the passage, only option (4) fits in.
18.
Ans.(3). The author is thrilled in the first paragraph to witness eggs being sold at $6. This reveals that this is a high price and yet there are people who are buying the eggs. This goes to show that there is a change in the buying pattern of the consumers. This change becomes evident as we read the next few paragraphs. Thus, option (3)is the best answer.
19.
Ans.(3). Paragraph 1 states that the author viewed $6 eggs as a rarity. He felt thrilled to see this. The answer to why he felt thrilled can be given by answering why he considered the eggs as a rarity. He did that because he had never seen so expensive eggs being sold. This eliminates options (2), (4) and (5). Option (1) is cancelled out because the inability to sell eggs at $4 or $5 was not a discovery for the author as the option makes us believe.
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20.
Ans.(4). Only option (4) is incorrect as the passage says "humane standards for the animals" which means treating animals considerately and kindly, not humanly.
21.
Ans.(2). The passage undoubtedly talks about winemaking, but in clear reference to the state of Burgundy. Even from the first paragraph one can deduce the author's motive that he wishes to examine the role played by Burgundy in the making of wine. Only option (2) speaks about this.
22.
Ans.(2). If all the grapes from differnet vineyards could provide similar (best) quality of the grapes they could be used to create a similar (best) quality of wine. Thus, option (2) seems the most plausible answer. Options (1) and (3) are redundant as they state something that the passage states. Option (4) has the flaw that the advantage enlisted has nothing to do with the development of winemaking.
23.
Ans.(3). This question can be answered only by understanding the text that follows this line in the passage. On reading it we can ascertain that the author is speaking about the experience a person has after drinking Burgundy wine. The person savours the taste for the first time but then cannot experience it again because of the wine being present there everytime. Thus, there is a clear indication to overabundance of wines, and hence option (3) is correct.
24.
Ans.(4). Ethereral as used in the passage can correspond to an experience which is outofordinary, or simply something higher than earthly things. All options except option (4) refer to something that is out of ordinary. Option (4) erroneously links commonsense to ethereal.
25.
Ans.(2). Option (1) finds a mention in paragraph 4. Option (3) is there in paragraph 2 and option (4) is there in the next to last paragraph. Option (2) is incorrect as the passage states that Gamay grape was considered to be unfit for human consumption and hence was not grown. Pinot Noir was grown for making wine. Gamay grape was not the reason for growing Pinot Noir.
26.
Ans.(2). The argument in option (2) is essentially that the proposed creation of a Censor Board makes no sense because sitcoms show the same content. The argument relies explicitly on an analogy between movies and sitcoms. Thus, the two must be similar in all respects relevant to the argument. Otherwise, the argument is unconvincing. Option (2) affirms that sitcoms are in fact detrimental, thereby solidifying the analogy between the two. (1), (3) and (4) each in its own way supports the bare assertion that the proposed Censor Board might not be effective. However, none of these answer choices confirms the argument's essential reasoning. (5) actually weakens the argument, by providing a reason why sitcoms and movies are not relevantly similar.
27.
Ans.(5). A typical weekend IPL match generates more revenue than a typical Art Exhibition. Hence, increasing the number of weekend IPL matches is the surest way, among the five choices, for Detro to maximize revenues, especially if the number of days per year that the stadiums are used for Art Exhibitions would at least remain the same, as (5) implies. Options (1) and (2) are incorrect for essentially the same reason. By increasing the admission fee, Detro might either enhance or reduce its total revenues, depending on the decrease in attendance (if any) due to the fee increase. Besides, neither plan would add to the number of days during which one or the other type of event takes place. Hence, neither is as likely to succeed as the one that option (5) suggests. (3) is the worst of the five choices, and the easiest one to eliminate; replacing an event with one that generates significantly less revenue can only serve to reduce revenues. Option (4) suggests a course of action that is unlikely to be as effective as the one that option (5) suggests. Increasing the number of weekend exhibitions might boost revenues. However, since a weekend art exhibition generates less revenue than a weekend IPL match, the boost would be less than if the number of weekend IPL matches were increased instead.
28.
Ans.(1). The argument relies on the unstated assumption that no other event since the fest could have caused the outbreak instead. Statement (1) provides some evidence that the students who have reported Psoriasis symptoms in fact contracted it at least one week ago. Accordingly, (1) helps support the claim that it was the swim in the contaminated water during the trip two weeks ago that caused the outbreak. (4) has no effect on the argument. It is the time after contact that symptoms begin to occur, not the duration of those symptoms, that is key to identifying the source of spread. (2) actually weakens the claim, by providing another possible explanation for the outbreak. Specifically, (2) provides for the possibility that the outbreak can be attributed to the water in the swimming pool of the school rather than the dip at the picnic. (3) provides some support for the argument, insofar as it helps to explain why only one of those reporting symptoms has tested positive so far. Additional statistical information would be required to assess whether (5) supports the argument. For example, assume for the moment that several studentsincluding the 63 later reporting Psoriasis symptoms attended the trip. In this event (5) would strengthen the teacher's claim, by providing an explanation for how the picnic bath could have been contaminated if only a small percentage of attendees have reported Psoriasis symptoms. Or assume on the other hand that the only students attending the trip were the 63 later reporting Psoriasis symptoms. In that case all who took a bath showed symptoms for Psoriasis and hence, teacher’s assertion will be repealed.
29.
Ans.(5). The argument relies on the unstated assumption that Tamil Nadu's Karanatakan population either remained stable or increased during 2007. However, (5) provides that this population actually declined in 2007, despite the influx of Karanatakans. Given that the number of Karanatakans residing in Tamil Nadu decreased while the crime rate increased, (5) reduces the likelihood that it was Karanatakans who were responsible for the increase in violent crime in 2007. (1) would appear to weaken the argument, by providing ostensible evidence that Tamil Nadu citizens are more likely than Karanatakans to commit violent crimes. However, (1) does not account for the possibility that in Karanataka far more violent criminals go unapprehended than in Tamil Nadu. In fact, the argument's explicit reference to "reported" violent crimes underscores this possibility, which prohibits us from drawing any firm conclusion as to which group is more likely responsible for violent crimes. (2) provides no information useful in evaluating the argument. Whether (2) strengthens the argument depends on additional considerations as well, such as: the total population of Karanataka compared to Tamil Nadu; whether the Karanatakan population increased or decreased in each state during the year; and whether the crime rate in Karanataka increased or decreased during 2007. (3) actually strengthens the argument. By providing evidence that number of Karanatakans residing in Tamil Nadu increased in 2007, (3) makes it more likely that Karanatakans were responsible for the increase in violent crime that year. (4) actually strengthens the argument, by affirming the essential premise that the number of violent crimes in Karanataka increased dramatically during 2007.
30.
Ans.(1). According to the passage, the total aluminium demand for packaging has been decreasing, while the amount of aluminium packaging recycled for the same purpose has been increasing. These two facts, considered together, lend strong support to the conclusion that manufacturers have substituted recycled aluminiumpackaging for "fresh" aluminium to meet their demand for aluminium packaging. (2) is not strongly inferrable from the passage, because without any numbers, it is impossible to compare the total amount of recycled packaging to the total amount of "fresh" packaging. (3) is incorrect because the passage provides no information for the inference that all recycled aluminium packaging has been used to meet the aluminium packaging demands of manufacturers. (4) is not a strong option. The only information in the passage about the demand for packaging material involves aluminium packaging. It is impossible to draw any strong conclusions about the demand for nonaluminium packaging material. In (5), just because the amount of recycled aluminium packaging has increased, it is unfair to conclude that the amount of aluminium from products has also increased.
31.
Ans.(2). It is clear that in protectionist policies one country would protect its own jobs whatever the type of job may be. Thus, global is incorrect. Since, the paragraph is not worried about the type of job, we can even cancel out options (3), (4) and (5). Ans.(1). Since we are talking of a grave situation, option (1) clearly is the best choice. Option (2) is in opposite context. Option (3) though might seem true with respect to protectionism but does not fit in because nowhere has the authenticity of situation been questioned. Option (4) is not right because such a situation already occurred in 1930. Option (5) is close but ponderous (heavy; or having a great mass and weight and unwieldiness) is not of the required level that is expected from an occurence that causes end of globalization.
32.
IC : PTpnrps03
3 of (17)
33.
Ans.(4). Selfish in this option cannot fit because it would be redundant to speak "selfish protectionist" when protectionism has the meaning of selfish built in. Tender will be inept because the speaker is condemning protectionism. Fearsome implies something that is dreadful or frightening. Fearful might have been an apt choice. Mediocre doesn't explain anything. Only shortsighted seems correct as the speaker warns that decisions like these may hamper growth in the future.
34.
Ans.(3). Since we are talking of a threat against globalization, options (2) and (4) are ruled out. Options (1) and (5) talk of temporary hindrance, but option (3) says choke off; i.e. ,complete devastation and thus option (3) most aptly defines the threat.
35.
Ans.(2). Since we are talking of resisting protectionism, (1) and (5) are rejected as instead of tackiling it, they would further promote it. Options (3) and (4) are general words and do not fully bring out the graveness of the need to work together. Hence option (2) is the right answer.
36.
Ans.(3). Options (1) and (4) that mention "special mark" presupposing that it has been introduced are incorrect as it is nowhere in the first part of the paragraph. Option (5) is close but is incorrect because had it been in the paragraph, the construction would have looked like, "Its not just this attitude that is mysterious. Its also their special mark". There is an also missing there. Option (2) is wrong because long eyelashes and sombre face does not prepare the donkeys for long journeys. Only option (3) gives a link between the two parts.
37.
Ans.(2). A clear look at the lines above the missing one will reveal that what we need in the missing line is something that shows what the Government can do (using its buying power) to improve the security of the products. Thus, options (1), (3), (4) and (5) all get negated. Option (1) speaks of fake products (an unnecessary inclusion). (4) specifies that the cybersecurity issue will be dealt with in the fullest, while the statement in the last line mentions "improved security" not "complete security". (3) and (5) talk nothing about the "buying power" of the Government.
38.
Ans.(3). A careful analysis will reveal that the author is trying to hold the American leadership and the citizens responsible for the sorry state that America portrays on the global front today. Thus, options (1), (4) and (5) can be negated because they are trying to say that the world has been unworthy of America's efforts. Among options (2) and (3), option (3) is a brilliant filler because it quickly ditributes the onus of the responsibility for the American predicament between the people and the leaders. Option (2) could have been a better choice if only option (3) was not there.
39.
Ans.(4). This one should be easy. When one compares the options and looks up what are the differences, she/he can easily make out two: indicate(s); and lie/lay. Considering the subjectverb agreement, "information" will entail an "indicate". Thus, options (1), (2) and (3) are ruled out. Option (5) is wrong because it uses the incorrect verb "lay" rather than "lie". Lay usually implies "put into a certain place or abstract location". While lie is "to have a place in relation to something else".
40.
Ans.(1). Here we need to be clear about the usage of few, fewer, less and lesser. 'Fewer' answers the question, "How many?" (bats, balls, dogs, chairs) and 'less' answers the question, "How much?" (cola, dirt, salt, capacity). Fewer and lesser are always used when comparing things. This eliminates answer choices (2), (4), and (5). Answer choice (3) is unnecessarily wordy and implies that the auditoriums had already been built before the buttonholing began.
41.
Ans.(3). Statement A can be classified as an inference because even though we do not have the data from where this conclusion has been drawn, yet we are sure that it is a conclusion atleast. B is a judgement because of the use of the word "narrowly". This is an unquantifiable adjective, i.e. it can change according to the perspective of the person and the tendency of the situation. C and D are facts and can be easily verified.
42.
Ans.(5). Statements A and C are facts that can be easily verified. B is acknowledged as a fact because it is something that someone has spoken publicly. This can be verified for its truth value. D is an inference because a conclusion has been drawn in the later part of the sentence based on the former half.
43.
Ans.(2). Statement A is an inference drawn from data that is not provided in the question. B and C are inferences based on information given in A and B respectively. D is a fact because the function of the State Water Resource Regulatory Authority can be confirmed.
44.
Ans.(1). Statement A is a fact and can be verified whether differnet cases of incest have come up in the country or not after the expose of the Mira Road case. C is a fact and can be identified first among all. B is a conclusion drawn based on the information provided in A. D is a judgement becasue of the unquantifiable phrase "frowned upon". One cannot say for certain what this may mean to the speaker. Hence, option (1) is the correct choice.
45.
Ans.(4). Statement A is a judgement of the situation presented by the speaker. Statements B and C are conclusions drawn. In B, we can see "How that will pan out remains uncertain" is the conclusion drawn on the basis of information provided ahead in the line. In C, the second part of the sentence after the comma is the inference drawn as the speaker clears that the "No Means Yes" brigade may have to move on. D is a clear judgement that the speaker is passing on the prevalent situation.
46.
Ans.(3). The quote means that mercy blesses both the giver and the taker and its blessings are not exhausted by the increase in the number. That is why, everyone should show mercy to others.
47.
Ans.(4). An optimist's quest for looking at the brighter side everywhere can lead to trying situations. Any person who gets through these traumas can be pardoned if he doubts things and becomes a pessimist. Option (4) is the best answer. Option (3) is near but it labels all optimism as bad which is not what is meant here.
48.
Ans.(4). The quote implies that real intelligence is comprehending the length and the breadth of one's knowledge. Only option (4) is correct.
49.
Ans.(4). The quote can be understood as "a custom that is honoured by not observing it and rather breaching or avoiding it." Hence, option (4) is correct.
50.
Ans.(3). The opposite of a true statement can be a false statement. But as the quote says the opposite of a profound truth can be another profound truth. This implies that truly nature doesn't distinguish between right or wrong and treats both of them equally. Thus, option (3) is the only correct option.
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For Questions 5154 The number of people in each of these categories can be calculated by adding all the values of the columns: 3(Lords + Vyaparies + Brahmans + Kshatriyas + Vaishya + Shudra + Bhikshuk) = 3375 Hence, total number of people from all the categories =1125 Now, the number of people from the Shudra category = 1125 –(Brahmans +Kshatriyas + Vaishya) – (Bhikshuk + Lords + Vyaparies) = 1125 – (425) – (600) = 100 Similarly, all the values can be determined:
51.
Lords
250
Vyaparies
200
Brahmans
75
Kshatriyas
50
Vaishya
300
Shudra
100
Bhikshuk
150
For getting the minimum number of categories that have more than 50 people unhappy, 70% of 50 = 35 55% of 75 = 41.25 33% of 100 = 33 30% of 150 = 45 24% of 200 = 48 20% of 250 = 50 65% of 300 = 195 Hence, only 1 category is possible. Ans.(1)
52.
The number of categories with more than 200 people can be counted from the above table (Lords and Vaishyas). Ans.(5)
53.
The number of unhappy people in the categories, Vaishya, Lords, Vyaparies, Bhikshuk, Shudra and Brahmans can be at the most more than 40 if the percentage distribution is: 20, 24, 30, 33, 55, 65 and 70 respectively. Ans.(4)
54.
If the number of people in the Shudra category is reduced by 25%, then the number of people = 100 × 75% = 75. 70% of 75 = 52.5. Thus, the maximum number of unhappy people = 52. Ans.(5)
55.
It is clear that if we know who made the sixth move, we also know who can make the seventh move and can eventually win. If Gautam (zeroes) has made the sixth move, there are three possible situations after five moves: Possibility 1: O O X
X X
Possibility 2: O O X X X
Possibility 3: O X X X
O
Based on the rules of the game, only possibility 1 could have resulted in the present situation after six moves. In that case, there are three possibilities for ‘possibility 1’ to result in the present situation Thus, after four moves: Possibility 1: O O
X X
Possibility 2: O O X
X
Possibility 3: O O X
X
Based on the rules of the game, Maithli (crosses) would have made the winning move, which however did not happen. From this we can conclude that Maithli did not make the fifth move and hence, Gautam did not make the sixth move. So, it must have been Maithli who made the sixth move and Gautam then makes the seventh, winning move. To check that Maithli made the sixth move, we look at the the following three possibilities after five moves: O O X
Possibility 1: O X
O O X
Possibility 2: O X
O O
Possibility 3: O X X
Based on the rules of the game, only possibility 3 can result in the situation after six moves. So, Maithli indeed made the sixth move. Ans.(2)
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For Questions 5657 We will indicate the numbers in the long division in the manner shown below: _ _ _ / _ _ _ _ _ _ _ _ \ _ _ 8 _ _
A / B \ C
_ _ _
D
_ _ _ _
E
_ _ _
F
_ _ _ _
G
_ _ _ _
H
0
0
For E and G, two blank spaces have been brought down; therefore both the second and the fourth space of C are 0. Because F consists of three spaces and equals the outcome of 8 times A, A must be smaller than 1000/8 or 125. Number H consists of four spaces and is the product of number A and the last space of C. Therefore, H is at least 1000, and because A is smaller than 125, the last space of C must be 9. Moreover, A must be at least 1000/9 and hence, larger than 111. Because the number D is subtracted from a number represented by four spaces and the outcome of the subtraction consists of two spaces, the first space of D must be 9. This is possible only if the first space of C is 8. Now we know that the number C equals 80809 and number B is at least 10000000. From this, it follows that A is at least 124. Because we also know that A lies between 111 and 125, A equals 124. The complete long division can now be filled in: 1 2 4 / 1 0 0 2 0 3 1 6 \ 8 0 8 0 9 9 9 2 1 0 0 3 9 9 2 1 1 1 6 1 1 1 6 0 56.
The problem has a unique solution. Ans.(1)
57.
From 0 to 9, only 5 and 7 are not required to complete the long division. Ans.(2)
For Q.58 to Q.61 58. To find the maximum number of employees who were recruited in January and not fired at the end of August, the fired employees must include all the employees of that particular month except January and if there are more number of fired employees in a month than the recruited ones, only then we will assume the January employees to be fired. TABLE1 Month January February March April May June July August
New recruitments(at the beginning of the corresponding month) 80 70 45 56 80 62 56 20
Fired Emoloyees(after the corresponding month) 55 74 48 66 70 73 50 6
Employees who were not fired since the month of January 25 254=21 213=18 1810=8 8 8(1110) 7 7
Hence, 7 employees were recruited in January and were not fired till the end of August. Ans.(3)
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59.
To find the maximum number of employees who were recruited in March and were not fired till the end of June, we need to follow the table:
Month
New recruitments(at the beginning of the corresponding month)
Fired Employees (after the corresponding month)
Employees recruited in March and not fired at the end of the month
January February March April May June July August
80 70 45 56 80 62 56 20
55 74 48 66 70 73 50 6
18 8 8 7
Ans.(3) 60.
The employees who were recruited in a particular month and fired exactly after 3 months would be the employees who were recruited in the months of January, March and May. So, from table 1, the number of employees who were recruited in January and were fired at the end of March were 21. The so the number of employees who were recruited in the month of March and were not fired in the same month were 18 as shown in the table. In the month of April 10 employees from the previous month were fired. Thus, the number of new recruitments in March who were not fired in the next month were 8. In the month of May 80 employees were recruited at the begining and 70 were fired at the end of the month. So, 8 employees who were recruited in March were fired at the end of May while 18 employees who were recruited in May were not fired at the end of same month. In the month of June, total 73 emplyees were fired out of which 62 must be new June recruitments. Thus, 11 employees who were recruited in the month of May were fired at the end of June. So, 7 emplyees who were recruited in May were left and were fired at the end of July. So, maximum total number of employees who wre recruited in a month and were fired after exactly after three months were 21 + 8 + 7 = 36. Hence, the total amount the company would have paid to these employees = 36 × 15000 = 540000 Rs. Ans.(3)
61.
The maximum number of employees who were recruited at the beginning of a month and fired at the end of the same month were 55 + 70 + 45 + 56 + 70 + 62 + 50 + 6 = 414. Ans.(3)
For Q.62 to Q.64 Given that 40% of the total employees who joined AMA as Marketing Executives = 21720 So, total employees from the other company who joined AMA = (21720 × 100)/40 = 54300 This is equal to 80% of the total employee base of the other company. So, the total number of employees of the other company = (54300 × 100)/80 = 67875
Total number of employees of other company (OC) 67875
80% of 16% of 80% of OC 44% of 80% of OC 40% of 80% of OC OC who joined HR who joined Finance who joined Marketing 54300
8688
23892
21720
16% of the total employees who joined as HR executive AMA = 20% of the total employees who failed the promotion test = 8688 So, total employees who failed the promotion test = (8688 × 100)/20 = 43440 This is equal to 30% of the total employees of AMA. So, total number of employees of AMA before the merger = (43440 × 100) / 30 = 144800 Total number of employees who passed the promotion test = (70 × 144800) / 100 = 101360 30% of TEP Total employees who 25% of TEP promoted as 40% of TEP promoted as promoted as Finance passed the test (TEP) HR executive Marketing executive executive 101360
25340
30408
45612
62.
So the total number of employees after the merger = 144800 + 54300 = 199100. Ans.(1)
63.
We can calculate only the number of male employees before the merger. But we cannot calculate the number of male or female employees after the merger, because we do not know about the number of males or females who joined AMA from the other company. Ans.(5)
64.
Following table is prepared from the given information: Company
Total number of employees
HR
Marketing
Finance
Other employees
AMA
144800
25340
45612
30408
43440
OC
67875
8688
21720
23892
212675
34028
67332
54300
43440
Old Finance executives = 30408 25% got pink slip, so, remaining 75% = (75 × 30408) / 100 = 22806 15% of the HR executives changed their department and joined as Finance executives, i.e. (15 × 34028)/100 = 4563 So, total Finance executives = 4563 + 22806 + 23892 = 51261. Ans.(3)
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For Questions 6568 From the given information, following tables can be prepared: Table I Price in INR Dress
(1 Euro = 65 INR)
(1 GBP = 75 INR)
(1 USD = 50 INR)
(1 SGD = 35 INR)
(1 AUD = 30 INR)
Ladies Evening Dress
65000
135000
60000
60000
45500
Knit Cover up
91000
58500
84000
49500
68250
Voile Cover up
58500
84750
65000
56100
57750
Cotton Ladies Tunic
103350
69000
72500
63000
68250
Embroidered Tunic
78000
125250
88000
54000
50750
Stylish Ladies Tunic
88400
115500
71500
35400
65100
Party wear saree
77350
71250
43000
52500
44100
Wedding Wear
149500
197250
114500
101400
97300
Table II Custom Duty on goods Dress
bought from Milan is bought from London 1% is 2%
bought from San francisco is 0%
bought from singapore is 20%
bought from Rosemount is 5%
12000
2275
Ladies Evening Dress
650
2700
0
Knit Cover up
910
1170
0
9900
3412.5
Voile Cover up
585
1695
0
11220
2887.5
Cotton Ladies Tunic
1033.5
1380
0
12600
3412.5
Embroidered Tunic
780
2505
0
10800
2537.5
Stylish Ladies Tunic
884
2310
0
7080
3255
Party wear saree
773.5
1425
0
10500
2205
Wedding Wear
1495
3945
0
20280
4865
Table III Total cost price (Basic price + Custom duty) Dress
Milan (Italy)
London (UK)
San francisco (USA)
Singapore (Singapore)
Rosemount (Australia)
Ladies Evening Dress
65650
137700
60000
72000
47775
Knit Cover up
91910
59670
84000
59400
71662.5
Voile Cover up
59085
86445
65000
67320
60637.5
Cotton Ladies Tunic
104383.5
70380
72500
75600
71662.5
Embroidered Tunic
78780
127755
88000
64800
53287.5
Stylish Ladies Tunic
89284
117810
71500
42480
68355
Party wear saree
78123.5
72675
43000
63000
46305
Wedding Wear
150995
201195
114500
121680
102165
65.
From table III, the minimum amount that Mrs. Aadhunikwala must carry = 2 × 70380 = 140760 (from London Fashion Week, UK) Ans.(5)
66.
From table III, the price of Ladies Evening Dress at London Fashion Week (UK) = 137700 and the price of Ladies Evening Dress at Rosemount (Australia) = 47775. So, the maximum difference = 137700 47775 = 89925 Ans.(2)
67.
We can calculate the price of all these five dresses from table III Party Wear Saree, Rosemount Fashion Week = 95% of 46305 Voile Cover Up, Milan Fashion Week = 95% of 59085 Ladies Evening Dress, Rosemount Fashion Week = 95% of 47775 Party Wear Saree, San Francisco Fashion Week = 95% of 43000 Stylish Ladies Tunic, Singapore Fashion Week = 95% of 42480 So, we can observe that Stylish Ladies Tunic at Singapore Fashion Week is the cheapest. Ans.(5)
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68.
Ladies Evening Dress, Rosemount Fashion Week = 47775 Party Wear Saree, San Francisco Fashion Week = 43000 Stylish Ladies Tunic, Singapore Fashion Week = 42480 So, the maximum number of dresses that she can buy with an amount of Rs.180000 (INR) is 3. Ans.(1)
For Questions 6971 Number of programs offered by University Year of Inception
Nanda University
2001 2002 2003 2004 2005 2006 2007 2008 Total Average
9 12 6 17 6 19 18 13 100 12.5
Taxla University Appa University 6 18 17 9 13 15 16 11 105 13.125
Sherpa University
Rana University
11 7 16 10 11 13 5 19 92 11.5
20 17 11 18 6 12 19 7 110 13.75
12 8 13 17 14 9 10 18 101 12.625
69.
There are 4 universities which on an average offer more than 12 programs. Ans.(4)
70.
There are three universities which offer more than 100 programs. Number of programs offered by University
Year of Inception
Taxla University
Appa University
Rana University
2001 2002 2003 2004 2005 2006 2007 2008 Total
6 18 17 9 13 15 16 11 105
12 8 13 17 14 9 10 18 101
20 17 11 18 6 12 19 7 110
P1 = 105 + 101 + 110 = 316 P2 = 100 + 105 + 101 + 92 + 110 = 508 Hence, required percentage = (316 × 100)/508 = 62.20 % Ans.(2) 71.
The maximum percentage drop in new programs offered was by Rana University in the year 2005 over 2004. Ans.(5)
For Questions 7275 72. From the question we get the following table R a ting T REAT ME Me dic in a l In fra struc tu re N T US ED re se rve & e qu ipme n t
Ho sp ita l n a me
WH A / WO HA
CHILDREN'S HOSPITAL
WOHA
ART, AT
7.5
7.5
CIVIC CENTER HOSPITAL FOUNDATION
WOHA
UT, AT
9
6
ESKATON DOCTORS HOSPITAL
WOHA
HT, MT
9
9
HAYWARD HOSPITAL
WOHA
UT, AT
13.5
10.5
NAVAL HOSPITAL
WOHA
ART, AT
10.5
10.5
OGORMAN INFANT
WOHA
AT, HT
9
6
PERALTA HOSPITAL
WOHA
HT, MT, UT
7.5
4.5
Hence, there are 7 hospitals where Mr. Chopar can get treated. Ans.(3)
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73.
From the question we get the following table: Ra tin g R a tio of ra ting S um o f T REAT M Me d ic in ra tin g o f o f fe e d b a c k to ENT a l Do c to rs F e e db a c k me dic in a l su m o f ra ting US ED of me dic in a l re se rve re se rve a nd d oc tor re se rve a n d do c tor HT, ART, 10.5 9 10.5 19.5 0.538461538 RT
H ospita l na me
WH A / WO HA
BOOTH MEMORIAL HOSPITAL
WHA
CHILDREN'S HOSPITAL
WOHA
ART, AT
7.5
10.5
13.5
18
0.75
WHA
MT, ART, UT
7.5
7.5
10.5
15
0.7
WHA
HT, UT
7.5
7.5
7.5
15
0.5
WHA
RT, MT, ART
10.5
13.5
12
24
0.5
WHA
AT, ART, UT
10.5
9
10.5
19.5
0.538461538
OGORMAN INFANT
WOHA
AT, HT,
9
9
9
18
0.5
PERALTA HOSPITAL
WOHA
HT, MT, UT
7.5
7.5
7.5
15
0.5
WHA
RT, ART, UT
9
9
12
18
0.666666667
WHA
RT, UT
13.5
9
10.5
22.5
0.466666667
SAN LEANDRO HOSPITAL EDEN MEDICAL CENTER SUMMIT MEDICAL CENTER OAKLAND HOSPITAL CORPORATI
SUMMIT MEDICAL FOUNDATION HERRICK MEMORIAL HOSPITAL
Hence, there are 9 hospitals. Ans.(5)
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74.
Number of hospitals which do not have In House facility of Ambulance having ART or HT and their rating of doctors is more than 7.5 are given below. CHILDREN'S HOSPITAL
WHA / WOHA
TREATMENT USED
Doc tors
CHILDREN'S HOSPITAL
WOHA
ART, AT
10.5
NAVAL HOSPITAL
WOHA
ART, AT
9
OGORMAN INFANT
WOHA
AT, HT
9
Also, number of hospitals which have In House facility of Ambulance having RT or UT and their rating of Infrastructure & equipments equal or greater than 7.5 are given below. Ho sp ita l na me
WH A / WO HA
T REAT ME N T US ED
In fra stru c ture & e q uip me n t
BOOTH MEMORIAL HOSPITAL
WHA
HT, ART, RT
9
SAN LEANDRO HOSPITAL
WHA
MT, ART, UT
7.5
HERRICK MEMORIAL HOSPITAL
WHA
RT, UT
9
KAISER HOSPITAL
WHA
UT, RT, HT
12
KAISER HOSPITAL
WHA
AT, UT
15
SUMMIT MEDICAL CENTER
WHA
RT, MT, ART
10.5
OAKLAND HOSPITAL CORPORATION
WHA
AT, ART, UT
10.5
SUMMIT MEDICAL FOUNDATION
WHA
RT, ART, UT
7.5
Hence, the required ratio = 3/8. Ans.(1) 75.
From the inforamtion in the question, only following three hospitals have both RT and ART treatment facilities OVREALL RATING
Rating
Hospital name
{(Rating of WHA / TREATME RATING OF feedback) × WOH Medic i RATING NT USED feedb MEDICINAL 5 + 3 A nal OF FEED ac k RESERVE × ×(Rating of reserve BACK × 5 3 medic inal reserve ) }
BOOTH MEMORIAL WHA HOSPITAL SUMMIT MEDICAL WHA CENTER SUMMIT MEDICAL WHA FOUNDATIO N
HT, ART, RT
10.5
10.5
52.5
31.5
84
RT, MT, ART
10.5
12
60
31.5
91.5
RT, ART, UT
9
12
60
27
87
Ans.(2) 76.
Factorizing the numbers, 120 = 2 3 x 3 1 x 5 1 1320 = 2 3 x 3 1 x 5 1 x 11 A is definitely a multiple of 11, but it cannot be a perfect square as A cannot have 11 2 as a factor. 1680 = 120 x 2 x 7 = 2 4 x 3 1 x 5 1 x 7 1 B is definitely a multiple of 2 4 x 7 1 but it cannot be a perfect square as B cannot have 7 2 as a factor. 1800 = 120 x 3 x 5 = 2 3 x 3 2 x 5 2 Since, the LCM of 120 and C is 1800, therefore, C can be a perfect square. One of the possible values of C is 3 2 x 5 2 . But it is not necessary that C be a perfect square. Ans.(5)
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77.
Since, in the new number system, decimal number 5 is represented by a single sign, so the base of that number system is atleast 6. Similarly, the decimal number 95 is represented by three signs, so the base of this number system is not more than 9. Now, checking for base 6, decimal number 20 can be written as (32)6 and decimal number 95 can be written as (235)6. But each sign represents different decimal number. So, base 6 is not possible. Now, checking for base 7, decimal number 5 is represented by (5)7, decimal number 20 can be represented by (26)7 and decimal number 95 can be represented by (164)7. So, according to the signs provided in the question, 1 = 'µ', 2 = '+', 4 = '#', 5 = '$' and 6 = '%'. Therefore, decimal number 778 can be written as (2161)7 in the number system of base 7 Or, (+µ%µ). Ans.(4)
78.
(x + 1)yz = 12
………………(1)
(y + 1)zx = 4
………………(2)
(z + 1)xy = 4
………………(3)
Dividing equation (1) by (2), (x + 1)y = 3 (y + 1)x x =
y (2y + 3)
Dividing equation (2) by (3), z = y Now, on subtracting equation (2) from equation (1), we get y 2 – xy = 8
(Since, y = z)
by putting the value
y x = (2y + 3)
, the equation becomes
y 2 y = 8 (2y + 3) 2
On solving for y, we get y = –2, 3 Now, for y = –2, xyz = 2 × –2 × –2 = 8, an integer. 1
for y = 3, xyz = 3 × 3 × 3 = 3, an integer. Ans. (5) 79.
Given: A 5 = B 4 , also A, B, C and D are positive integers. Hence, only possible values of A and B are A = 1 and B = 1. Now, (C – A) = 3, so C = 4. Also, C 6 = D 2 Hence, 4 6 = D 2 So, D 2 = 4096, so D = 64. Therefore, D – A = 64 – 1 = 63. Ans. (4)
80.
Let the speed of the bus and the scooter be x and y respectively, Distance from A to Mumbai = 2x Distance from Mumbai to B = x/2 Distance from A to B = 2x x/2 = 3x/2 To cover a distance 3x/2 (from A to B), the scooter takes 7/2 hours (from 2pm to 5:30 pm) Now, to cover the remaining distance from B to Mumbai i.e. x/2, the scooter will take 7/6 more hours or 1 hour 10 minutes from 5:30 pm. So, the scooter will reach Mumbai at 6:40 pm. Ans.(2)
81.
Let A be the event that there are exactly 4 Chinese among the first 6 speakers. Let B be the event that the seventh speaker is a Chinese.
F G B I J H A K
P
Then, Required Probability = P(A) ´ Now, 5
C 4 ´ 7 C 2 C 6
F G B I J 1 H A K =Prob. that the seventh speaker is a Chinese given that there were 4 Chinese speakers among the first 6 speakers= 6
P
12
P(A) =
and
5
C 4 ´ 7 C 2 12
Hence, required probability =
12 of 17
C 6
´
1 6
5
= 264 Ans.(3)
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82.
On generalizing the above equation, F(x)=2x 2 + a(b–c) 2 x + abc We know that for an equation ax 2 +bx+c=0, the minimum or the maximum value of f(x) lies at x = –b/2a. Therefore, –a[(b–c) 2 ]/4 = –128 or a(b–c)=512 Now, the sum a + (bc) + (bc) + (bc) will be minimum when a = b–c = 8 Hence, the minimum value of a + 3(bc) = 8 + 8 + 8 + 8 = 32 Ans.(3)
83.
1st process Divide the larger square in 4 equal squares of side A/2. Then the area of total scrap = 4[(A/2) 2 – p(A/4) 2 ] = A 2 (4 p)/4 2nd process Area of total scrap generated in this process = A 2 – p(A/2) 2 = A 2 (4 – p)/4 So, required ratio = 1:1. Ans.(3)
84.
For a given volume, cuboidal shape of minimum surface area is a cube. So, he will arrange all the cubes in the form of a large cube and the side of this cube will be 9 cm. Therefore, the length of the diagonal = 9 3 cm. Ans.(4)
85.
Let the number be n = a p × b q × c r ……………… where a,b,c are prime numbers & p,q,r natural numbers. We know numbers of facters of n = (p+1)(q+1)(r+1)…………= 4 So, either 1×4 or 2×2 = 4 Or, p+1 = 4 & q = 0 or p+1 = q+1 = 2 p = 3 & q = 0 OR p = q = 1 either n = a 3 or n = a×b So, a + a 2 = 72, i.e., a = 8 and n = 512 Or, a + b = 72 assuming a<b (a,b) = (5,67), (11,61), (13,59), (19,53), (29,43), (31,41) Hence, required sum = 512 + 5×67 + 11×61 + 13×59 + 19×53 + 29×43 + 31×41 = 512 + 335 + 671 + 767 + 1007 + 1247 + 1271 = 5810. Ans.(4) P
O A
86.
Q
B S
R
The sides of triangle PQR = 1unit PO = OS = 3 / 4 units and angle AOP is 120° (Central angle theorem) 1 3 3 1 3 3 3 3 3 ´ ´ ´ Sin 120 ° = ´ ´ ´ = 4 2 4 4 2 64 Area of triangle POA = Area of triangle POB = 2 4
F 3 I = p G H 4 JK 16 2
120 ° ´ p 360 °
Area of the minor sector OASB =
Area of the part of triangle that lies outside = Area of triangle PQR [Area of triangle POA + Area of triangle POB + Area of minor arc OASB] = 87.
3 / 4 - [ 3 3 / 32 + p / 16 ] = ( 5 3 - 2 p ) / 32
. Ans.(3)
If (a,b) is a solution then obviously a = 0 and (a,b) is a solution too. For a = 0, we get two solutions (0, 2) and (0, 2). Now, let (a,b) be a solution with a>0; The equation can be rewritten as, 2 a (1+2 a+1 ) = (b+1)(b–1) Shows that the factors b–1 and b+1 are even, exactly one of them divisible by 4. Hence a ³ 3 and one of these factors is divisible by 2 a1 but not by 2 a . So, b = 2 a–1 m + c1, m odd
………………….(1)
Putting this into the original equation we obtain 2 a (1 + 2 a+1 ) = (2 a1 m + c–1) 2 –1=2 2a–2 m 2 +2 a mc or, equivalently
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1+2 a+1 = 2 a–2 m 2 + mc. Therefore, 1– cm = 2 a–2 (m 2 – 8).
………………….(2)
For c = 1 this yields m 2 – 8 £ 0, i.e., m = 1, which fails to satisfy (2). For c = –1 equation (2) gives us 1 + m = 2 a–2 (m 2 – 8) ³ 2(m 2 – 8), Or, 2m 2 – m – 17 £ 0. Hence, m = 3; on the other hand m cannot be 1 according to (2). Because m is odd, we obtain m = 3, leading to a = 4. From (1) we get b = 23. These values satisfy the given equation. Thus, (a,b): (0, 2), (0,2), (4, 23), (4,23). Ans.(3) 88.
Let a, b be the roots of the equation. The equation will have both the roots greater than 3 if it satisfies the conditions given below Condtion 1: D 0 Condtion 2: a + b > 6 Condtion 3: Value of equation at x = 3 is greater than 0 From condition 1, 36a 2 – 8 + 8a – 36a 2 0 Or, a 1 From condition 2, 6a > 6 Or, a > 1 From condition 3, 9 – 18a + 2 – 2a + 9a 2 > 0 Or, 9a 2 – 20a + 11 > 0 So, a < 1 or a > 11/9 Combining results from the above conditions, a > 11/9 satisfies all constraints. Ans. (3)
89.
We have
37 x 17 < < 197 y 77
77 y 197 < < or 17 x 37 4.53 <
or,
y £ 5.32 x
x has minimum value 1 (it is a positive integer). To satisfy the given inequalities y can have a minimum value of 5 since it is also an integer. Ans.(3) 90.
3 2 > 2 3 or
2 log 2 3 > 3 log 2 2
log 2 3 > 3 / 2
..........................(1)
5 2 < 3 3 2 log 3 5 < 3 log 3 3 log 3 5 < 3 / 2
..........................(2)
9 > 8 or 9/4 >2 3 / 2 > 2
..........................(3)
and, 27>24 (3/2) 3 > 3 ( 3 / 2 ) > 3 3
..........................(4)
By comparing all the above four equations we can conclude that 91.
log 2 3
is the largest number the given four numbers. Ans.(4)
The new hexagon formed, will have its side equal to Ö3/2 times the earlier hexagon. Thus, the perimeter will also be Ö3/2 times that of earlier Hexagon. Hence the perimeter of all the Hexagons thus formed will be sum of an infinite GP. = 540 / (1–Ö3/2). Or, 1080 / (2–Ö3). Ans.(4)
92.
SE : ER = 5 : 4 RF : FS = 8 : 1
Q
P
SE = 5x and ER = 4x RF = 8y and FS = y so, SR = 9x = 9y or, x = y Let x = 1
S
F
E
R
Area of Trapezium PQFS = 1/2 (FS + PQ) × PS = 49
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On putting the values of FS and PQ, we get PS = 49/5 Area of Trapezium PQRE = 1/2 (ER + PQ) × PS On putting the values of ER, PQ and PS, we get [1/2 × (4 + 9)] × 49/5 = 63.7 Even if the value of x changes, the answer remains unchanged because the value of PS varies with x. Ans. (3) 93.
The number of ways of choosing the three digits other than 0 and 1 = 8 C3 = 56 These can be arranged in 6!/(2! × 2! × 2!) = 90 ways And the digit 1 can be placed in any of the seven possible locations with respect to the six digits. Total number of ways = 7 × 90 × 56 = 35280. Ans.(1)
94.
log 10567 = log 10(81×7) = log10(3 4 ×7) = x 4log 103 + log 107 = x log 101029 = log10(3×7 3 ) = log103 + 3log107 = y 4log 103 + log 107 = x
……………(1)
log 103 + 3log 107 = y
……………(2)
By solving (1) and (2) log 107 = (4y–x)/11 And log 103 = (3x–y)/11 Now, log1021 = log10(3×7) = log103 + log 107 =(4y–x)/11+(3x–y)/11 =(3y+2x)/11 Ans.(1) 95.
For getting a sum of 109 The minimum number of cards required are (13 × 4 + 12 × 4 + 9 × 1) = 109, i.e., 9 Similarly, (11 × 4 + 10 × 1 + 8 × 2) = 70, i.e., 7 and, (10 × 3 + 9 × 2 + 8 × 2) = 64, i.e., 7. Ans.(1)
96.
X = 20!(1/20! + 1/19! + 1/18!2! + 1/17!3! + … + 1/2!18! + 1/19! + 1/20!) Or, X = (20!/20! + 20!/19! + 20!/18!2! + 20!/17!3! + … + 20!/2!18! + 20!/19! + 20!/20!) These terms are binomial coefficients in the expansion of (1 + x) 20 where x is assumed to be 1 which will lead to the conclusion that 20 C
0 +
20 C
1 +
20 C
20 20 2 + … + C20 = 2
So, X – 1 = 2 20 – 1 X – 1/1023 = 2 20 – 1/1023 = [(2 10 )2 – 1]/ (2 10 – 1) = 2 10 + 1. Ans.(4) 97.
The top of the prism is an isosceles triangle,
F 1 + a + a I a G H 2 2 J K Slant surface area of all the four prisms = 4 F 2 + 1 + 1 I = 4 a F 2 + 2 I = 4 a 2 + 1 = 4 a G H 2 J K G H 2 JK e j 2
2
2
Total surface area of the cube = 6a 2
e 2 + 1 j : 6 a = 2 e 2 + 1 j : 3 . Ans.(5)
= 4 a 2
Therefore, required ratio = 98.
2
180=2 2 ×3 2 ×5 The highest power of 5 in 1!×2!×3!.............49! is 5×[0+1+2+3+4+6+7+8+9+10] = 5×[50] = 250 The highest power of 3 in 1!×2!×3!.............49! is 3×[(22×23)/2 (3+7+11+12+16+20)]22 = 530 Highest powers of 5 and 9 are 250 and 265 respectively. We need not consider power of 4 as it will definetely be greater than 265 Since b is not a multiple of 5, a is the highest power of 5, 250. Ans.(4)
99.
a*a=a + a – a 2 = 2a – a 2 = a(2 – b) Similarly, b*b = b(2 – b) 2a – a 2 < 2b – b 2 2(a – b) < a 2 – b 2 2(a – b) < (a – b)(a + b) (a – b){2 –(a + b)} < 0 Then, 1 st case: (a – b) < 0 and 2 – (a + b) > 0 a < b and 2 > (a + b)
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1 > b > a 2 nd case: (a – b) > 0 and 2 – (a + b) < 0 a > b and 2 < (a + b) a > b > 1 which is not true for 0.5 < (a, b) <1, hence it is rejected so only 1 st case satisfies. Ans.(1) 100. We have100 £ 15k £ 10 5 Or, 6.66 £ k £ 6666.66 or 7 £ k £ 6666 The integer 15k is divisible by 35 if and only if k is divisible by 7. So, k = 7q we have 7£ 7q £6666 1 £ q £952.28 or1 £ q £ 952 Hence, the required number of positive integers = 952. Ans.(3)
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Objective key
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1.(3)
2.(1)
3.(1)
4.(1)
5.(3)
6.(5)
7.(5)
8.(4)
9.(4)
10.(2)
11.(4)
12.(3)
13.(2)
14.(4)
15.(2)
16.(1)
17.(4)
18.(3)
19.(3)
20.(4)
21.(2)
22.(2)
23.(3)
24.(4)
25.(2)
26.(2)
27.(5)
28.(1)
29.(5)
30.(1)
31.(2)
32.(1)
33.(4)
34.(3)
35.(2)
36.(3)
37.(2)
38.(3)
39.(4)
40.(1)
41.(3)
42.(5)
43.(2)
44.(1)
45.(4)
46.(3)
47.(4)
48.(4)
49.(4)
50.(3)
51.(1)
52.(5)
53.(4)
54.(5)
55.(2)
56.(1)
57.(2)
58.(3)
59.(3)
60.(3)
61.(3)
62.(1)
63.(5)
64.(3)
65.(5)
66.(2)
67.(5)
68.(1)
69.(4)
70.(2)
71.(5)
72.(3)
73.(5)
74.(1)
75.(2)
76.(5)
77.(4)
78.(5)
79.(4)
80.(2)
81.(3)
82.(3)
83.(3)
84.(4)
85.(4)
86.(3)
87.(3)
88.(3)
89.(3)
90.(4)
91.(4)
92.(3)
93.(1)
94.(1)
95.(1)
96.(4)
97.(5)
98.(4)
99.(1) 100.(3)
17 of (17)
