CAT 1997

Ans .

(c)Rain : Reign

1. Explanation :

   (c) is a pair of homophones. (a), (b) and (d) do not have pairs of homophones.

Ans .

(d) Pulp fiction : Novelist

1. Explanation :

   Doggerel is a badly written verse, which is written by a poet. Pulp fiction is a badly written piece of fiction, written by a novelist. (a), (b) and (c) do not show this derogatory relationship.

Ans .

(b) Hypothesis : Theory

1. Explanation :

   A premise is evidence which leads to a conclusion. An assumption does not lead to an inference. An assumption, if wrong, will weaken an inference. But a hypothesis does lead to a theory. A hypothesis is a suggested explanation for a group of facts or phenomena that is accepted as likely to be true.

Ans .

(a) Shovel : Implement

1. Explanation :

   A barge is a kind of a vessel, and a shovel is a kind of an implement. (b), (d) and (e) do not show this item to categorise relationship.

Ans .

(d) Sorrow : Misery

1. Explanation :

   The second word in the pair is a higher degree of the first. (a), (b) and (c) do not display such a relationship.

Ans .

(d) Dinosaur : Tyrannosaurus

1. Explanation :

   The second word belongs to the family in the first word. (a), (b) and (c) do not display such a relationship.

Ans .

(b) ABE

1. Explanation :

   

Ans .

(c) FEB

1. Explanation :

   

Ans .

(a) DAC

1. Explanation :

   

Ans .

(a) ACB

1. Explanation :

   

Ans .

(a) AFE

1. Explanation :

   

Ans .

(b) DA

1. Explanation :

   Sam is not drunk, so he must be ill. One of the either ... or condition is true.

Ans .

(c) DB

1. Explanation :

   As Ram did not lose sleep, it shows that he did not hear of the tragedy. When A, then B. Not B, hence not A.

Ans .

(d) BC

1. Explanation :

   The train is not late, so it must have derailed. One of the either ... or condition is true.

Ans .

(a) CB

1. Explanation :

   I did not have a nightmare, so I must not have read a horror story. When A, then B. Not B, hence not A.

Ans .

(b) BC

1. Explanation :

   I did not get rashes which shows that I did not eat berries. When A, then B. Not B, hence not A.

Ans .

(d) whether the subsequent one will do so

1. Explanation :

   The sentence is incomplete as 'will do' does not have an object. It should therefore be followed by 'so'. (a) is not correct as ‘government’ is repeated. ‘policy’ is undefined in (b) and (c).

Ans .

(a) let go of the reins

1. Explanation :

   We let go ‘of’ something, but we turn ‘off’ the lights. The proposals in (b) and (d) might go beyond the scope of the sentence.

Ans .

(c) started mushrooming in every corner of the country

1. Explanation :

   The correct idiomatic usage to refer to a proliferation of something is 'have mushroomed'. ‘blooming’ and ‘blossoming’ are not words that we use to indicate that a lot of schools have come up overnight. ‘Mushrooming’ is most apt, literally and figuratively, in this regard. ‘all over’ is a more generic term than ‘in every corner’; the latter term is more specific.

Ans .

(a) It is important that

1. Explanation :

   The phrase used is grammatically correct. There is a huge difference between ‘important’ and ‘fact’. (d) similarly overlooks the serious tone of the sentence. (c) sounds verbose.

Ans .

(b) It must be noted

1. Explanation :

   We take ‘note’ of an important clause. There is nothing to ‘notice’ in the sentence, so (a) and (d) are ruled out. (c) sounds awkward when read along with the rest of the sentence.

Ans .

(c) reopens the first chapter

1. Explanation :

   An act of vengeance relates to the 'beginning' of the misdeeds, and thus reopens the first chapter. Look for a suitable complement in sentences split with a semicolon. When there is a semicolon in the sentence, one has to look for a logical complement — ‘closes : reopens’.

Ans .

(a) as far as

1. Explanation :

   The correct idiomatic usage is 'as far as' something can go. (b) and (d) sound extremely confusing as they add parameters. (c) sounds needlessly verbose.

Ans .

(a) set out to

1. Explanation :

   One sets out to achieve something. ‘thought of’ is not right as it should be followed by ‘achieving’. ‘thought to’ does not sound as active as the author might wish it to be. ‘went to’ sounds similarly vague.

Ans .

(b) tough talking

1. Explanation :

   One does 'tough talking'. ‘talk tough’ is a general idiomatic expression. ‘has done some’ should be followed by an -ing form of the verb, such as ‘investigating’ or ‘probing’.

Ans .

(b) year by year

1. Explanation :

   'Year by year' is the correct idiomatic usage here. ‘annually’ and ‘progressively’ are not the right words to use as we are just making a general observation, not dealing with statistics. The singular stress on ‘each’ is unwarranted in this sentence.

Ans .

(b) many more

1. Explanation :

   'Amendments' is a countable noun and so 'many' should be used as a quantifier for it. (c) and (d) tamper with the pronouncement in the sentence by using weak quantifiers.

Ans .

(a) more crucial than ever

1. Explanation :

   'More crucial than ever' shows that though they were important earlier too, now they are even more important. (a) matches the verbal tense in the sentence ‘more crucial than (they have) ever (been)’.

Ans .

(a) break down

1. Explanation :

   'Break down' is the correct idiomatic use here. ‘barriers’ are not ‘crumbled’ or ‘dismantled’. We can ‘break’ a record. For an erect barrier, the appropriate verb would be ‘break down’.

Ans .

(b) CBAD

1. Explanation :

   C gives some examples to support 1. B introduces the era of computers as another example, A talks about the increasing technical terms, D introduces the idea of slangs, which is continued in 6.

Ans .

(c) BADC

1. Explanation :

   6 speaks of a study of IIT undergraduates’ mindset. C speaks of culture developed by IIT students. Therefore, C6 is mandatory. D speaks of success stories of IIT graduates and therefore follows A.

Ans .

(d) ABDC

1. Explanation :

   A talks about the taste of the Maharaja of Kapurthala, B introduces another Maharaja with an exquisite taste, D introduces something in contrast to this, C continues with the idea which is exemplified in 6.

Ans .

(d) ABDC

1. Explanation :

   A shows how 'his' gifts were unveiled, B states the effect it had on McLaughlin, D states his reaction to the same and C states the ultimate outcome.

Ans .

(a) CADB

1. Explanation :

   C states why India is on the brink of a major public health disaster, A states what happens if TB is untreated for 5 years, D presents some statistics to highlight the point, B states how the disease spreads and 6 continues with the fact.

Ans .

(b) BDAC

1. Explanation :

   B introduces atypical pneumonia as the subject of the passage, D states that it appears like an ordinary flu, A states its symptoms and C states how these symptoms progress to give rise to complications.

Ans .

(a) BCAD

1. Explanation :

   B introduces the problem of snakes, C states why there is not enough anti-snake serum, A elaborates on non-availability of the same, and D concludes the passage by stating what the final outcome could be.

Ans .

(a) BACD

1. Explanation :

   B talks about the previous records of mid-term elections, and its implications on the present situation, A presents a contradictory fact, and C states the implications of this fact. D concludes the passage.

Ans .

(b) ABDC

1. Explanation :

   A introduces critical elections as the subject of the passage, B explains it, D states that none of the Indian elections so far has been a critical election, instead as C states, there have been many semi-critical ones

Ans .

(a) ABDC

1. Explanation :

   A introduces the subject, B elaborates on it, D states who is the current champion of the game and C states who other contenders are.

Ans .

(b) ACBD

1. Explanation :

   A introduces the benefit of good advertising, C states why this benefit is important, B gives an example and D concludes by saying that in spite of this a minimum quality has to be maintained.

Ans .

(c) ACBD

1. Explanation :

   B uses the word ‘it’ that refers to the ‘philosophy’ in C and so CB is a mandatory pair. Moreover, A ‘century ago’, C ‘for 90 years’, and B ‘today’, makes a chain and D concludes the passage.

Ans .

(c) BACD

1. Explanation :

   B states that RBI has wrested many powers from the government, A states that in spite of this the government has the final say, C elaborates on this fact and D questions this state of affairs.

Ans .

(c) BDCA

1. Explanation :

   B introduces the fact that the author was depressed, D gives a reason for the same, C shows the extent of his depression and A concludes the passage.

Ans .

(a) BCDA

1. Explanation :

   B introduces the idea of the possibility of stopping the decline in writing skills, C states how this is being done, D talks about a number of programmes being developed for the same and A gives the example of one such programme.

Ans .

(b) Kin

1. Explanation :

   All others except ‘kin’ are synonyms.

Ans .

(b) Adapt

1. Explanation :

   All others except ‘adapt’ are synonyms.

Ans .

(c) Bell

1. Explanation :

   All others except ‘bell’ refer to circular shapes. Bell is an object.

Ans .

(a) Computer

1. Explanation :

   All others except ‘computer’ refer to some kind of a network.

Ans .

(d) Withstand

1. Explanation :

   Withstand is almost the opposite of the other three words.

Ans .

(d) Bridge

1. Explanation :

   All others except ‘bridge’ refer to some kind of a gap or opening.

Ans .

(c) India is yet to understand itself.

1. Explanation :

   In the first five paragraphs, the author makes it clear that Indians do not understand themselves yet. (a) is far from the truth. (b) is unlikely and (d) is not true.

Ans .

(b) insightful.

1. Explanation :

   The author tries to show what exactly was India's history like and what are the prospects for the future. The writer is making observations and analysing these, hence there is no reason why the attitude should be critical, cynical or cold.

Ans .

(c) it is time that India came to terms with the past.

1. Explanation :

   Through the example he has tried to show us what centuries of slaughter and plunder actually meant for the country. (a) and (b) are not true, the writer is not glorifying the Vijayanagar empire.

Ans .

(a) the child's view of history.

1. Explanation :

   The author is critical of people having a child's view of history and equates it with the slave's idea of the ruler's mercy. (b) is not true as the writer does take a critical stand on history. (c) is besides the fact.

Ans .

(c) during and after the British period.

1. Explanation :

   The writer says that during British rule, and for 50 years after that, there was a revival of energy and intellect. (d) is not true in light of facts presented in the passage. (a) and (b) are not true in an isolated context.

Ans .

(d) Both (b) and (c)

1. Explanation :

   With self-awareness, people ask for more of everything. (b) and (c) are both found in the ninth paragraph. (a) is simply not true.

Ans .

(c) primitive and messy

1. Explanation :

   He says that India's present situation is 'primitive and messy'. The writer has not expressed any pessimistic opinion ‘bleak’ or an extreme opinion ‘horrific’.

Ans .

(a) self-criticism does not stop.

1. Explanation :

   Self-criticism is important for a country to be alive and progressive. Refer to the last paragraph. (b) and (c) are thus not true.

Ans .

(b) it will be chaotic.

1. Explanation :

   The writer says that the future will be fairly chaotic. (a), (c) and (d) find no mention in the passage.

Ans .

(c) the decimation of the country's talented people.

1. Explanation :

   Every invasion was accompanied by slaughter of the country's most talented people. (a) and (b) did take place, but it is (c) which is the main feature of the tyranny of foreign rulers.

Ans .

(a) critical.

1. Explanation :

   The author is critical of the government policies. Refer to the beginning of each paragraph. The writer is not rude enough to be derisive. There is no reason for the writer to be sarcastic or ironical.

Ans .

(c) the government looked upon its industrialists as crooks.

1. Explanation :

   He is surprised as in all other cases government looked at the industrialists as crooks. (a) is a different point of view. (b) is a fact presented in the passage that does not contribute to the writer’s surprise. (d) is not true as the reason is cited below the writer’s feelings.

Ans .

(c) foreign exchange bankruptcy and paucity of funds with the government.

1. Explanation :

   Foreign exchange bankruptcy and paucity of funds compelled government to open up its economy. (a) and (b) in no way influenced the government’s move.

Ans .

(b) pessimism

1. Explanation :

   The author says that in another 50 years the world would have moved even further ahead. Hence, there is no room for any kind of optimism or pragmatism.

Ans .

(b) it had better infrastructure.

1. Explanation :

   Its infrastructure should have helped India to perform better than other Asian countries. (c) is not cited in the passage. Given (b), (a) cannot be a better answer as India’s infrastructure is compared with the infrastructure of the other countries.

Ans .

(d) Both (a) and (b)

1. Explanation :

   (a) and (b) are reasons for India being in a better condition than other nations. Refer to the third paragraph. (c) is not stated in the passage.

Ans .

(a) economic isolationism

1. Explanation :

   Economic isolationism has led to India's poor performance. Refer to the beginning of the fourth paragraph. Hence, (b) and (c) are rendered void.

Ans .

(d) discouragement of imports.

1. Explanation :

   Government tried to protect its own industries through discouraging imports. Refer to the beginning of the fourth paragraph. Hence, (a), (c) and (b) are not the best answers.

Ans .

(b) India's poor performance in the international market.

1. Explanation :

   While Korean Cielos are sold in India, no Indian cars are sold abroad. (a), (c) and (d) are opinionated answers, hence, not necessarily true.

Ans .

(a) India's politicians are myopic in their vision of the country's requirements.

1. Explanation :

   Indian politicians are unable to see beyond their noses. Whether (b) and (c) are true or not is unclear from the passage.

Ans .

(d) None of these

1. Explanation :

   The passage actually talks about the advantages of democracy. Hence, the opinions expressed in (a), (b) and (c) find no place in the passage.

Ans .

(b) not all dictators will be enlightened.

1. Explanation :

   The passage says that there is no guarantee that all dictatorships will be enlightened. Refer to the beginning of the third paragraph. Hence, there is no reason to mark (a), (c) or (d), though they may have a shade of truth.

Ans .

(c) a low but stable rate of growth is preferred to a high rate of growth.

1. Explanation :

   The author sees a low but unfaltering rate of growth as a sign of stability amidst growth. (b) and (d) are not true. (a) is also doubtful, after all, how low can the growth be?

Ans .

(c) making huge mistakes and risking everything.

1. Explanation :

   Dictatorships are more prone to making huge mistakes and risking everything on a single decision. (c) is a more complete answer as compared to (a) and (b).

Ans .

(b) under no circumstances should statism be a welcome move.

1. Explanation :

   The writer does not support statism under any circumstances. Refer to the penulitmate paragraph. (a) is a confusing response. (c) and (d) do not address the question.

Ans .

(d) All of these

1. Explanation :

   All the choices (a), (b) and (c) have been implied in the sixth paragraph.

Ans .

(c) Internet will play a crucial role in the global market in the years to come.

1. Explanation :

   The passage states that Internet will play an important role in the decades to come. Refer to the eighth paragraph. We cannot infer (b) for sure. (a) is almost stated in the passage.

Ans .

(d) None of these

1. Explanation :

   Though (a) and (b) are desirable outcomes, they are not specifically stated in the passage.

Ans .

(b) India is not at the mercy of dictators.

1. Explanation :

   The main reason is (b), the dictatorship factor that figures so often in the passage. (a), (c) and (d) may be desirable factors, but not conclusive.

Ans .

(d) None of these

1. Explanation :

   (a), (b) or (c) have not been distinctly mentioned in the passage.

Ans .

(a) by awarding stock options.

1. Explanation :

   Infosys has awarded stock options among its employees. (b) has not been mentioned in the passage. Refer to the second paragraph.

Ans .

(b) control is not exerted through a system of hierarchy

1. Explanation :

   Infosys does have a hierarchy, it does not have a hierarchy ‘just’ for control. Refer to the third paragraph. (d) may be true, but it is a rather vague response. (a) and (c) are not true.

Ans .

(b) betterment of man through ethical creation of wealth.

1. Explanation :

   He believes that betterment of man can happen through creation of wealth, ethically and legally. Refer to the sixth paragraph. Given (b), (a) and (c) are weaker choices.

Ans .

(d) All of these

1. Explanation :

   The example highlights all the given facts. The qualities stated in (a), (b) and (c) are evident in the case.

Ans .

(c) a process that helps him to learn from failure.

1. Explanation :

   Murthy believes that learning is a process that helps him learn through failure. (a) is not the focus of the question. Learning transcends (b) as per information given in paragraph 9.

Ans .

(d) working backwards is a hallmark of Infosys' functioning today.

1. Explanation :

   Today the company works backwards to achieve its goals. Refer to the penultimate paragraph. Given (d), the other choices (a), (b) and (c) are weak.

Ans .

(d) Both (a) and (b)

1. Explanation :

   Openness at Infosys includes payment of taxes as well as giving complete information. (c) sounds rather ambiguous.

Ans .

(a) Infosys will have to devise new strategies to meet the challenges of the 21st century.

1. Explanation :

   (a) is stated in the last paragraph. (b) and (c) sound rather extreme.

Ans .

(d) satisfaction of personal needs.

1. Explanation :

   Infosys’ HR treats its employees as customers. (d) is directly stated in the passage in paragraph 4, line 3. (a), (b) and (c) are generic and not very strong contenders for the answer.

Ans .

(a) Infosys is a reflection of its CEO.

1. Explanation :

   The CEO's actions set the template for all Infoscians. (b), (c) and (d) do not reflect the truth as per the passage.

Ans .

(b) diverse cultural and socio-economic factors.

1. Explanation :

   The diverse cultural and socio-economic factors are a major problem affecting the Indian education system. (a) and (c) are not stated in the passage.

Ans .

(d) None of these

1. Explanation :

   'Grizzled mandarins' refers to bureaucrats. It would be unfair to label the mandarins as (a), (b) or (c).

Ans .

(c) administrators in charge of education are out of touch with ground realities.

1. Explanation :

   Those in charge of education are totally out of touch with the ground reality. This point is given in the fourth paragraph. Hence, it will not be necessary to mark (a), (b) or (d) as the answer.

Ans .

(a) decentralising education planning and implementation.

1. Explanation :

   The author advocates decentralizing education planning and implementation to improve the education system. This point is given in the fourth paragraph. Hence, it will not be necessary to mark (b), (c) or (d) as the answer.

Ans .

(c) Rajasthan, Bihar and Madhya Pradesh.

1. Explanation :

   Rajasthan, Bihar and Madhya Pradesh show very low education levels. The answer is given in the second paragraph. We are not sure about (a), (b) or (d).

Ans .

(c) launched in 1994 has been successful in 122 districts.

1. Explanation :

   The programme, launched in 1994, has been successful in 122 districts. The answer is given in the fifth paragraph. Choices (a), (b) and (d) are thus rendered void.

Ans .

(d) Both (b) and (c)

1. Explanation :

   The village panchayats are responsible for scholarships, construction and maintenance of primary schools and for organizing non-formal education. We do not know if (a) forms part of the portfolio.

Ans .

(c) politicians.

1. Explanation :

   Politicians are specially responsible for obstructing the implementation of education policies as decentralization of educational administration will take away certain powers from them. We are not sure about the intentions of (a), (b) or (d).

Ans .

(d) None of these

1. Explanation :

   None of the given statements can be related to primary education, on the basis of the passage.

Ans .

(a) greater community involvement.

1. Explanation :

   The author advocates greater community involvement for successful implementation of education policy. This point is given in the fourth paragraph. We are not sure about either (b) or (c).

Ans .

(c) This is not possible

1. Explanation :

   If he travels at minimum speed over stretch A (i.e. 40 km/hr), the total time taken to cover this stretch = \( \frac{2}{40} \) = \( \frac{1}{20} \) hr = 3min.
   If he then travels at the fastest speed over stretch B (i.e. 50 km/hr), the total time taken to cover this stretch = \( \frac{2}{50} \) = \( \frac{1}{25} \) hr = 3min
   Thus, total time taken over the first two stretches = 3 + 2.4 = 5.4 min.
   In order to break the previous record he will have to cover the third stretch in (10 – 5.4) = 4.6 min.
   To do this he will have to cover the third stretch at \( \frac{2}{4.6} \) = 0.434 km per minute or 26.08 km/hr. But the maximum speed over the stretch C is 20 km/hr. Hence, it is not possible for C to break the previous record.

Ans .

(b) 13.3 km/hr

1. Explanation :

   The minimum speed in stretch A is 40 km/hr. If Mr Hare travels the first stretch at this speed, then the time taken by him to cover this stretch = \( \frac{2}{40} \) = 3 min. Also he takes 3 min to cover stretch B. And he covers the entire race in (1.5 × 10) = 15 min. This means that he should have taken (15 – 3 – 3) = 9 min to cover stretch C.
   Hence, his speed over this stretch should be \( \frac{2}{9} \) = 0.22 km per minute or 13.3 km/hr.

Ans .

(c) 10 km/hr

1. Explanation :

   Let his average speed over the last stretch be x. Hence, his average speed for first two stretches = 4x. So the total time taken to cover the three stretches = \( \frac{4}{4x} \) + \( \frac{2}{x} \)
   His average speed over the race is 20 km/hr.
   Hence, the time taken to complete the race =\( \frac{6}{20} \)
   Hence, we have the equation \( \frac{4}{4x} \) + \( \frac{2}{x} \) = \( \frac{6}{20} \)
   Solving this equation, we get x = 10 km/hr.

Ans .

(d) Cannot be determined

1. Explanation :

   Although the number of students in group D is more than in any other group, we still cannot say anything about the average weight of this group as nothing is mentioned about the average weights of any of the groups or of the individual students.

Ans .

(c) The average weight of the class remains the same

1. Explanation :

   Although one student is shifted from group A to group B, the number of students in the class and the total weight of the students remain the same. Therefore, the average weight of the class remains the same.

1. Explanation :

   The total weight of any group will vary according to the number of students in that group. Hence, the total weight of group A and C which has (15 + 25) = 40 will be twice that of students in group B which has 20 students. However, it is clear that if all the students are of same weight, then the average weight of all groups remains same irrespective of how many students are present in each group. Hence, clearly the statement given in option (c) is false.

Ans .

(c) 4

1. Explanation :

   Let his marks be 100, 90, 80, 70 and 60 in the five subjects. Hence, totally he has scored 400 marks. This constitutes only 60% of the total marks. Hence, total marks = \( \frac{400}{0.6} \) = 667, Since the total marks in each subject is the same, hence maximum marks in each subject will be ( \( \frac{667}{5} \) ) ~ 133. Out of this 50% is the passing marks. In other words, to pass in a subject he needs to score 66.5 marks. We can see that only in one subject he scored less than this, viz. 60. Hence, he passed in 4 subjects.

Ans .

(b) 2 × 8!

1. Explanation :

   
   If we consider the Chairman and the vice chairman as one set, we can see that this set can fit 8 slots in between the 8 directors. Hence, this can be done in 8! ways. Between themselves, the chairman and the vice chairman can be arranged in 2 ways. Hence, the required answer = 2 x 8!.

Ans .

(c) 4

1. Explanation :

   \(log_{2}[log_{7}(x^{2} - x + 37)] = 1\)
   ⇒ \(log_{7}(x^{2} - x + 37) = 2^{1}\)
   ⇒ \((x^{2} - x + 37) = 7^{2} = 49\)
   ⇒ \(x^{2} – x – 12\) = 0
   ⇒ x = 4 or x = –3.
   The value that satisfies the given answer choices is x = 4.

Ans .

(a) 28.56%

1. Explanation :

   Hint: Students please note that the percentages that are given are the basic percentages derived from basic fractions. E.g. 11.11% = \( \frac{1}{9} \) and 14.28 = \( \frac{1}{7} \)
   Hence, you should make use of the most of this kind of knowledge. So let the CP be Re 1. Since he makes a profit of \( \frac{1}{7} \) , his SP = (1 + \( \frac{1}{7} \)) = Rs.\( \frac{8}{7} \).
   His marked price should be \( \frac{1}{9} \) above this. So if we subtract \( \frac{1}{9} \) of MP from the MP, we will get the SP.
   So (MP – ( \frac{1}{9} \) MP) = SP = \( \frac{8}{7} \)
   Hence, MP = \( \frac{9}{7} \)
   Therefore, percentage of mark-up on CP
   = (MP – CP)/CP
   = (\( \frac{9}{7} \) – 1)/1 = \( \frac{2}{7} \)= 2(\( \frac{1}{7} \)) = 2 × 14.28 = 28.56%
   Alternative method:
   We can use the formula z = x – y – \( \frac{xy}{100} \), where
   z = Gain percentage
   x = Percentage above CP
   y = Discount percentage
   ∴ 14.28% = x – 11.11% – \( \frac{11.1x}{100} \)
   or 14.28 =
   \( \frac{100x-1111-11.1x}{100} \)
   or 1428 – 1111 = 88.89x
   or x = 28.56% (Approximately)

Ans .

(d) None of these

1. Explanation :

   The given expression can be written as
   \(\frac{16n^{2}}{n} + \frac{7n}{n} + \frac{6}{n} = 16n + 7 + \[frac{6}{n} \)
   Since n is an integer, the expression (16n + 7) will always be an integer. Hence, for the entire expression to be an integer, the part \(\frac{6}{n} \) should also be an integer. This can be possible only if n is a factor of 6, viz. n = 1, 2, 3, 6, –1, –2, –3 and –6. Hence, n can have eight values.

Ans .

(d) None of these

1. Explanation :

   Let he mix 3 kg, 4 kg and 5 kg of dry fruits at Rs. 100, Rs. 80 and at Rs. 60 per kilogram respectively. Hence, his effective cost of the dry fruits per kilogram should be the weighted average
   = \(\frac{3*100+4*80+5*60}{3+4+5} = \frac{920}{12} \)
   In order to make a 50% profit, he will have to sell it at\(\frac{920}{12} * 1.5 = \frac{920}{12} * \frac{3}{2} = \frac{920}{12} = \) Rs. 115 per kilogram. Since none of the answer-choices confirms this, the answer is (d).

Ans .

(b) 2.5 kg

1. Explanation :

   20 kg fresh grapes will contain (0.9 × 20) = 18 kg water and 2 kg mass. If the dry grape has to contain 2 kg mass, it should constitute 80% of that. Hence, if 80% of dry grapes corresponds to 2 kg, its total weight will be\( \frac{2}{0.8} = 2.5 kg. \)

Ans .

(c) 27 s

1. Explanation :

   Effective speed of two trains = 80 – 40 = 40 km/hr. (Since they are moving in the same direction as inferred from the word ‘overtakes’). At this speed in 54 s, they would travel an effective distance of \( \frac{40 * 54 }{3600} = 0.6 km or 600 m. \)This effective distance should be equal to the sum of the lengths of the two trains. So, if length of the express train is L, length of the goods train will be 2L. Hence, our equation will be L + 2L = 600 or L = 200 m.
   So, the time taken by this train to cross a platform 400 m long will be = \( \frac{(200 + 400) }{80 * \frac{5}{18}= 27s.}\)(Note that we have converted the denominator in metres per second. Hence, the factor of \( \frac{5}{18} \)).
   

Ans .

(a) 1584

1. Explanation :

   This equation is very straightforward. If the number is 'x', then \( \frac{7x}{8} - \frac{7x}{18} = 770\). On solving this equation, we get x = 1584.
   Hint: Students please note that if the difference in \( \frac{7}{8} \) and \( \frac{7}{18} \) of a number is 770, then the difference in \( \frac{1}{8} \) and \( \frac{1}{18} \) of the number should be 110. If we express this as an equation, we get
   \( \frac{x}{8} \) and \( \frac{x}{18}=110 \)
   or 10x = 110 × 18 × 8
   or x = 11 × 18 × 8
   You can further proceed from here in two ways: (i) the last digit of the required answer should be
   (1 × 8 × 8) = 4,
   (ii) number should be divisible by 11.
   In both cases, the answer that is obtained from the given choices is 1584.

Ans .

(d) 35

1. Explanation :

   If we were to express 64 as product of two positive integers, we can get the following combinations: (64 × 1), (32 × 2), (16 × 4), (8 × 8). Thus, we find that P + Q cannot be 35.

Ans .

(b) 60

1. Explanation :

   Total marks scored by the student in 10 papers = (80 × 10) = 800. If we exclude the papers in which he scored the highest and the lowest marks, then the total marks scored by him in remaining 8 papers = (81 × 8) = 648. Hence, his total in these two papers in which he scored the highest and the lowest marks = (800 – 648) = 152. Since his highest score is 92, his lowest score is (152 – 92) = 60.

Ans .

(a) c = –15

1. Explanation :

   We know that the sum of the roots = –\( \frac{b}{a} \)
   \(x_{1}+x_{2} = 2\) Now we have two equations, viz. \(x_{1}+x_{2} = 2\) ...(1)
   and \(7x_{2}-x_{1} = 47\) ...(2)
   Solving these two equations, we get \(x_{1}=-3 and x_{2} = 5\). Since it does not satisfy options (b) and (c), we will verify it for option (a). The product of the roots = (–3) × 5 = –15,\( \frac{c}{a} \) in our case is c. Hence, c = –15.
   Alternative method:
   Put values of x1, x2 in equation (ii). Do not match. So put c = –15 in equation (i) to get the roots of equation. After finding the roots of equation (i), check whether they satisfy equation (ii) or not. The roots (5, –3) satisfy the equation (ii) so answer is (a).

Ans .

(a) 4

1. Explanation :

   If the radii of two circles are \(r_{1} \) and \(r_{2} \) then the two equations can be written \(πr_{1}^{2}+πr_{2}^{2}=153π \) or \((r_{1}^{2}+r_{2}^{2})\)=153 and \(r_{1}+ r_{2}\)=15
   Now \(r_{1}^{2}+r_{2}^{2} =(r_{1}+ r_{2})^{2}-2r_{1}r_{2}\)
   Therefore, \( 153 = (15)^{2}-2r_{1}r_{2} or r_{1}r_{2}=36\)
   If 36 is to be expressed as the product of two integers, it could be (36 × 1), (18 × 2), (12 × 3), (9 × 4), (6 × 6). The only two factors that add up to 15 are 12 and 3.
   Hence, \(r_{1} \)=12, \(r_{1} \)= 3. Therefore, the ratio of larger radius to the smaller one is 12 : 3 = 4.

Ans .

(c) m + n is divisible by 10

1. Explanation :

   The best way to solve this is the method of simulation, e.g. let m = 10 and n = 5. Therefore, m – n = 5, which is divisible by 5.
   \(m^{2} -n^{2}\) = 100 – 25 = 75, divisible by 25.
   m + n = 10 + 5 = 15 is not divisible by 10.
   Hence, the answer is (c).
   Note that for the sum of two multiples of 5 to be divisible by 10, either both of them should be odd (i.e. ending in 5) or both of them should be even (i.e. ending in 0).

Ans .

(b)\( 7^{3^{2}} > (7^{3})^{2} \)

1. Explanation :

   \( 7^{3^{2}} = 7^{9} \) and \( (7^{3})^{2} = 7^{6} \) .Since \( 7^{9}> 7^{6} \) ⇒ \( 7^{3^{2} } \)>\( (7^{3})^{2} \) .

Ans .

(c) 15%

1. Explanation :

   To maximize g, in equation (v), we put d = e = f = 0
   ∴Maximum value of g = \( \frac{34}{2} \) =17
   ∴Required percentage = \( \frac{17}{200} \)*100 =8.5%

Ans .

(a) 2%

1. Explanation :

   5% of people watch DD and CNN implies
   f + g = 10 ...(vi)
   10% of people watch DD and BBC implies
   d + g = 20 ...(vii)
   (v) – (vi) – (vii) gives
   e = 4
   ∴Required percentage \frac{4}{200} \)*100= 2%

Ans .

(d) Cannot be determined

1. Explanation :

   From equation (v), we have (d + 4 + f) + 2g = 34 ⇒ (d + f) + 2g = 30
   Since we cannot find the values of d and f, the value of g cannot be ascertained.

Ans .

(b) 15%

1. Explanation :

   The two equations can be written as:
   2000(\frac{x}{100}+2000(frac{y}{100})=700 \))
   2000(\frac{x}{100}+300(frac{y}{100})=900 \))
   The equations can be simplified to x + y = 35 and 2x + 3y = 90.
   Solving these two equations simultaneously, we get x = 15%.

Ans .

(d) None of these

1. Explanation :

   
   Since AB is the diameter of the circle, ∠ACB would be right angle. In this triangle, we know AB = 15 and AC = 12. So we can find BC. Hence, BC = 9. Since BC = BD, AD = AC (similar triangles).
   Hence, area of ∆ACB = Area of ∆ ABD
   =\( \frac{1}{2} \)AC × CB = \( \frac{1}{2} \)=54\( cm^{2} \)
   So the area of quadrilateral ACBD = 2 × 54 = 108 sq. cm.

Ans .

(c) 9

1. Explanation :

   As P, Q and R are consecutive odd numbers, Q = P + 2 and R = P + 4. Now 3P = 2(P + 4) – 3. On solving this equation, we get P = 5. Therefore, R = 5 + 4 = 9

Ans .

(b) ma (x, y, z)< la (x, y, z)

1. Explanation :

   This question can be done by assuming some values for x, y and z. E.g. let x = 4, y = 3 and z = 1. Thus, la(4, 3, 1) = min(7, 4) = 4; le(x, y, z) = max(1, 2)
   = 2; ma(x, y, z) =\( \frac{1}{2} \)(4 + 2) = 3.
   Hence, we can see that the only answer-choice that satisfies the relationship is ma(x, y, z) < la(x, y, x).

Ans .

(b) 6.5

1. Explanation :

   ma (10, 4, le (la (10, 5, 3) , 5, 3))
   =ma (10, 4, le (min (15,3) , 5, 3))
   =ma (10, 4, le (8 , 5, 3))
   =ma (10, 4, max (3,2))
   ma (10, 4, 3)
   = \( \frac{1}{2} \) [le(10, 4, 3) + la(10, 4, 3)]
   =\( \frac{1}{2} \)[max(6,1) + min(14, 7)]
   =\( \frac{1}{2} \)(6 + 7) = 6.5

Ans .

(c) 9

1. Explanation :

   le(15,min(10,6), le(9,8,ma(15,10,9)))
   Now ma(15,10,9) = \( \frac{1}{2} \)[le(15, 10, 9) + la(15, 10, 9)]
   = \( \frac{1}{2} \)[max(5, 1) + min(25,19)]
   =\( \frac{1}{2} \)(5 + 19) = 12
   Hence, our original expression would now be
   le(15,min(10,6), le(9,8,12))
   =le(15,6, max(1,-4))
   = le(1,6,15) = max(9, 5) = 9

Ans .

(c) 4

1. Explanation :

   The value of ABC, three-digit number should sat
   The maximum value of three digit number is 999 and minimum is 100.
   We observe that 7! = 5040 > 999
   So the 3-digits of the number must be
   6 as 6! = 720
   and/or 5 as 5! = 120
   and/or 4 as 4! = 24
   and/or 3 as 3! = 6
   and/or 2 as 2! = 4
   and/or 1 as 1! = 1
   If we consider 6 at the hundred’s place digit we see that condition (i) is not satisfied as 600 < 720 (6!)
   So we conclude that 6 cannot occupy any position in the number.
   If we place ‘5’ at the hundred’s place then the number should lie between the range of 500 and 600. Considering the RHS of equation (i) by putting A + B = C = 5 we get the sum as 360 which is less than 500. Similarly, putting 4, 3, 2 at the hundred’s place does not satisfies the given condition (i).
   Only 1 can be placed at hundred place and 5 should be one of the digit at other two position in order to make it a three digit number.
   Thus, only combination we satisfies the given condition (i) is (1, 4, 5) i.e. 145 = 1! + 4! + 5! = 145.

Ans .

(b) 30 sq. unit

1. Explanation :

   
   The diagonal of the innermost square is 2 units. The diagonal of every successive square would increase by 2 units (since corners are one unit apart). So the diagonal of the 7th square = 14 units and that of the 8th square = 16 units. Area of the 7th square = \( \frac{1}{2}(14)^{2} \) and that of 8th square = \( \frac{1}{2}(16)^{2} \), i.e. 98 and 128 respectively. Hence, the difference in their areas = 128 – 98 = 30 sq.units.

Ans .

(d) B is the smallest

1. Explanation :

   A = \( \frac{(2.000004)}{[(2.000004)^{2}+2(2.000004)]}\)
   = \( \frac{(2.000004)}{2.000004[2.000004+2]}\)
   = \( \frac{(1)}{[2.000004+2]}\)
   = \( \frac{(1)}{4.000004}\)
   = \( \frac{(1)}{4}\) = 0.25(Approximately)
   B = \( \frac{(3.000003)}{[(3.000003)^{2}+3(3.000003)]}\)
   = \( \frac{(3.000003)}{3.000003[3.000003+3]}\)
   = \( \frac{(1)}{[3.000003+3]}\)= \( \frac{(1)}{6.000003}\)
   C = \( \frac{(4.000002}{[(4.000002)^{2}+2(4.000002)]}\)
   = \( \frac{(4.000002)}{4.000002[4.000002+2]}\)
   = \( \frac{(1)}{[4.000002+2]}\)= \( \frac{(1)}{6.000002}\)
   Looking at the answer choices, we can see that the only (d) satisfies the relationship, viz. B is the smallest.

Ans .

(b) 9 : 4

1. Explanation :

   Let D1, T1 and D2, T2 denote the diameters and the thickness of the two coins respectively. If V1 and V2 are the values of the two coins.
   \( \frac{V1}{V2} = (\frac{D1^{2}T1}{D2^{2}T2}) =(\frac{D1}{D2})^{2}(\frac{T1}{T2}) \)
   Therefore, \( \frac{4}{1} = (\frac{4}{1})^{2}(\frac{T1}{T2})⇒(\frac{T1}{T2})=\frac{9}{4} \)

Ans .

(c) 5 sq. unit

1. Explanation :

   In a triangle, the line joining the mid-points of any two sides is half the length of its third side. Hence, every side of ∆PQR would be half the sides of ∆ABC. Hence, area of ∆PQR would be \( \frac{1}{4} \) the area of ∆ABC = \( \frac{1}{4} \) × 20 = 5 sq. unit.

Ans .

(d) 3 : 4

1. Explanation :

   Let L and B denote the length and the breadth of the rectangle. So the diagonal will be \( \sqrt{(L^{2}+b^{2})} \) . Hence, from the condition given, (L + B) – \( \sqrt{(L^{2}+b^{2})} = \frac{1}{2} L ⇒ \sqrt{(L^{2}+b^{2})} = \frac{L}{2} +B \)
   Squaring both sides, we get
   \( (L^{2}+b^{2}) = (\frac{L}{2})^{2} \)⇒ \(L^{2} = \frac{L^{2}}{4} +LB ⇒ \frac{3L^{2}}{4}=LB ⇒ \frac{B}{L}= \frac{3}{4} \)
   Shortcut:
   First write the relation (L + B) –\( \sqrt{(L^{2}+b^{2})} = \frac{1}{2}L \) or \( \frac{L}{2}+B = \sqrt{(L^{2}+b^{2})} \)
   Putt the values of options. Option (d) satisfies. So the answer is (d).

Ans .

(c) Either (a) or (b)

1. Explanation :

   As there is no day in the week whose first letter is R, it can be concluded that Raja does not have any holidays. Since 1996 is a leap year, we can figure out that Raja has totally worked for 7 days. Let his rate of doing the job be one unit per day. So he would complete 7 units of work in a week. J's situation is similar to Raja and does not have any holiday during the week. T will have two holidays in a week (Tuesday and Thursday). Since the rate of working for all the three of them is the same, the working pattern of J and T would be as follows.
   We can see that depending on which day is February 25, 1996, to complete 7 units, they would either take 4 days or 5 days. Hence, the answer is (c).
   

Ans .

(c) March 22, 1996

1. Explanation :

   Now Raja has worked for (5 days in February + 31 days in March + 2 days in April) = 38 days. Let us assume his rate to be the same as in the previous question, viz. one unit a day. Hence, he completes 38 units totally. In a week, T takes holiday on Tuesday and Thursday, while S takes holiday on Saturday and Sunday. We can see that their working pattern would be as follows.
   
   So in a week they work together 10 units work. Thus, in three weeks, they would complete 30 units work. It can be found out that February 25 is Sunday. So the remaining 8 units of work can be completed only on Friday, i.e. March 22.

Ans .

(b) 4,500 miles

1. Explanation :

   Overall, X has travelled for 25 hr (including stoppages) at an average speed of 180 miles per hour. Hence, the distance between Frankfurt and India is (25 × 180) = 4500 miles.

Ans .

(a) 24 hr

1. Explanation :

   On the return journey, X halts at Boston for one hour less than his previous halt there. Therefore, X takes 24 hr for his return journey.

Ans .

(a) 176 mph

1. Explanation :

   Since distance between Frankfurt and India is 4,500 miles, overall distance travelled by him (to and fro)
   = 9000 miles. And he has taken (25 + 24 +1\( \frac{11}{12} \)) = 50\( \frac{11}{12} \) hr in all to cover this distance.
   *Note: 1\( \frac{11}{12} \) hr has been accounted for the halt that he had in India (from 1 a.m. to 2.55 a.m.). Hence, his average speed for the entire journey = \( \frac{9000}{50 \frac{11}{12} } \)i.e. 176.75 mph.

Ans .

(a) 1 : 4

1. Explanation :

   
   In ∆BEC and ∆AED ∠CBE = ∠CDE ( Angles in the same segment of a circle are equal)
   Similarly, ∠BCE = ∠EAD ( Angles in the same segment of a circle are equal)
   ∠BEC = vAED (Vertical angles are equal)
   ∴By AAA similarity
   ∆CEB ~ ∆AED
   We know that the ratio of the areas of two similar triangles is equal to the ratio of the squares of the corresponding sides
   ∴\( \frac{Area(∆ BEC)}{Area(∆ AED)}=(\frac{BC}{DA} )^{2}=(\frac{12}{24} )^{2}= (\frac{1}{2} )^{2}=\frac{1}{4} \)

Ans .

(b) 5

1. Explanation :

   
   We know that length of the line joining the mid-points of two sides of a triangle is half the length of third side. Hence, the required length is half the length of side AC. Since EADF is rectangle, EF = AD = 8. CD = (22 – 16) = 6.
   So in the right-angled ∆ADC, AD = 8 and CD = 6. Therefore, AC = 10. Hence, length of the line joining the mid-points of AB and BC =\( \frac{1}{2} \)(10)=5

Ans .

(c) 3.15 p.m.

1. Explanation :

   Since the policeman started 15 min late, in this time the thief would have already covered \( \frac{60}{4} \) = 15 km. To catch the thief, the policeman will have to make up for this distance of 15 km. Every hour the policeman is travelling (65 – 60) = 5 km more than the thief. Hence, to make up the distance of 15 km, he would take 3 hr. Since policeman started at 12.15 p.m., he would catch the thief at 3.15 p.m.

Ans .

(b) 15 km

1. Explanation :

   Every hour the second policeman covers (65 – 60) = 5 km less than the first one. Since the first policeman catches the thief in 3 hr, in this time the second policeman will be (3 × 5) = 15 km behind.

Ans .

(d) if the question cannot be answered even with the help of both statements together.

1. Explanation :

   \( a^{3}+b^{3} = (a+b)(a^{2}+b^{2}-ab) \) Combining statements I and II, we get the value of (a + b) = √28 or –√28. Since we do not have the unique value of (a + b), we cannot get the unique answer \( a^{3}+b^{3} \)

Ans .

(b) if the question can be answered with the help of any one statement independently.

1. Explanation :

   11 and 9 are coprimes of 99, and hence the number divisible by 99 must be divisible by 9 and 11. Certainly statement I alone is sufficient to answer the question. Statement II says when the digits of the number are reversed, the new number formed is divisible by 9 and 11. The best way to handle this particular case is by simulation. Let us select any number which is divisible by 9 and 11. Let us select 1386 which is divisible by 9 and 11. Hence, the original number will be 6831 which, in turn, is also divisible by 99. Hence, statement II also is independently sufficient to answer the question. Since both the statements are independently sufficient to answer the question, the answer is (b).

Ans .

(b) if the question can be answered with the help of any one statement independently.

1. Explanation :

   
   The diagram will be as shown. M is Mali and P is Pali. Consider statement I. When the person covers\( \frac{1}{3} \) distance, he is 3 km east and 1 km north of Mali. Based on this statement alone, we can easily find out where he will be on line MP by using Pythagoras’ theorem. Once we find this distance, we can easily get distance MP by multiplying it by 3. Similarly, based on statement II alone also, we can find distance MP. Hence, both the statements are independently sufficient to answer the question. Hence, the answer is (b).

Ans .

(d) if the question cannot be answered even with the help of both statements together.

1. Explanation :

   Students! be careful. Generally, as we see two unknowns (i.e. x and y in this case) and two equations, we tempt to mark the answer as (c), i.e. combining two statements, we can easily find the values of x and y.But have a look at the equations 3x + 2y = 45 and 10.5x + 7y = 157.5. Multiplying 1st equation by 3.5, we get 2nd equation. Hence, these are not really two different equations. Hence, data is insufficient to answer the question. In general, remember the following rule. If we have two equations \(A_{x} + B_{y} = k_{1} and C_{x} + D_{y} = k_{2} \), and A × D = B × C, then the equations cannot be solved.