**UPSC PRELIMS 2022 PAPER II -- ANSWER KEYS**

**BIRD'S EYEVIEW**

- In the GS paper 2 (CSAT), candidates have to only secure minimum qualifying marks that are 1/3rd of the total (66.67 marks).
- Overall the
**GS II paper (CSAT) 2022 was moderately tough,**and proper choice of questions was important to score well. The RC passages were neither too easy nor too tough. Some questions were direct. Some questions in Maths were not easy at all. The trick was to know what to avoid. **The CSAT has been a qualifying test from 2015, was manageable in 2016, and quite tough in 2017. But 2018 saw a not-too-tough version! And then 2019 was again tough. 2020 was also quite tough. And 2021 also left many frustrated. 2022 was not too tough.****Pattern changes over the years:**Year 2017 saw only RC, Reasoning and Maths being asked. They balanced it out in 2018, by asking many questions from Data Interpretation (DI) and Visual Reasoning also! Then they again “imbalanced it” in 2019! In 2020, Data Sufficiency made a comeback with 5 questions. In 2021, Assertion and reasoning questions were the toughest and left many confused. DS was absent. 2022 saw DS make a big comeback!**Lesson:**Patterns change, be ready!**Major points in structure of 2022 Test:**Questions asked only from 3 major topics. The distribution of questions was – 31 questions on**Mathematics and Basic Numeracy,**28 questions on**Reading Comprehension**(15 passages) and 9 questions**on Logical and Analytical Reasoning.**(Check comparison table given)**Reading Comprehension:**The RC questions (mirror copy in English and Hindi) were tough and excellent!**Overall 28 questions spread over 15 passages.**That made sure that only the readers with reasonable speed could perform.**Some RC questions were tough,**and options were tricky. Questions were from all hot topics (agriculture, employment, economic liberalization, environment, ecology, global warming, vaccines, science and technology, biology etc.) that we read daily as part of our preparations!**Maths not easy:**Once again, Maths was not easy, and even the arithmetic type questions required some work. For the complete maths-haters & / or non-Maths students, it could be a problem. Sitters were not more than 5.- Overall, some practice is indeed required for the CSAT. You cannot just assume you’ll breeze through it without any preparation. Those who took it very lightly may pay the ultimate price : cracking Paper I and getting stuck here. We hope it doesn’t happen with anyone. Best of luck!
**Data Interpretation which came in a big way in 2018 was**completely missing in 2019, and only one question in 2020. In 2021, only 2 questions, and in 2022, zero.**Data Sufficiency was 0 in 2021, and 12 questions in 2022.****Aptitude:**Aptitude is a key part of an administrative officer’s life, and it is wrong to say that it should be only qualifying by nature.

**TOPICWISE DISTRIBUTION**

**DETAILED QUESTIONWISE SOLUTIONS (Set A)**

**Directions for the following 4 (four) items: **

Read the following two passages and answer the items that follow the passages. Your answers to these items should be based on the passages only.

**Passage — 1**

Natural selection cannot anticipate future environments on the earth. Therefore, the set of existing organisms can never be fully prepared for environmental catastrophes that await life. An outcome of this is the extinction of those species which cannot overcome environmental adversity. This failure to survive, in modem terms, can be attributed to the genomes which are unable to withstand geological vagaries or biological mishaps (infections, diseases and so on). In biological evolution on the earth, extinction of species has been a major feature. The earth may presently have up to ten million species, yet more than 90% of species that have ever lived on the earth are now extinct. Once again, the creationist doctrines fail to satisfactorily address why a divine creator will firstly bother to create millions of species and then allow them to perish. The Darwinian explanation for extinct life is once again simple, elegant and at once convincing—organisms go extinct as a function of environmental or biological assaults for which their inheritance deems them ill-equipped. Therefore, the so-called Darwinian theory of evolution is not a theory at all. Evolution happens—this is a fact. The mechanism of evolution (Darwin proposed natural selection) is amply supported by scientific data. Indeed, to date no single zoological, botanical, geological, paleontological, genetic or physical evidence has refuted either of the central two main Darwinian ideas. If religion is not taken into consideration, Darwinian laws are acceptable just like the laws proposed by Copernicus, Galileo, Newton and Einstein—sets of natural laws that explain natural phenomena in the universe.

**1.**According to the passage, natural selection cannot anticipate future environments on the earth as

- species not fully prepared to face the environmental changes that await them will face extinction
- all the existing species would get extinct as their genomes will not withstand biological mishaps
- inability of the genome to withstand environmental changes would result in extinction
- extinction of species is a common feature

Select the correct answer using the code given below.

- 1, 2 and 3
- 2. 3 and 4
- 1, 3 and 4
- 1, 2 and 4

**2.**The passage suggests that Darwinian theory of evolution is not a theory at all because

- it does not satisfy the creationist doctrine
- extinction is a function of environment and biological assaults
- there are no evidences to refute it
- existence of organisms is attributed to a creator

**3.**With reference to the passage, the following assumptions have been made:

- Only species that have fee ability to overcome environmental catastrophes will survive and perpetuate.
- More than 90% of the species on the earth are in the danger of getting extinct due to drastic changes in the environment.
- Darwin's theory explains all the natural phenomena.

Which of the above assumptions is/are valid?

- 1 only
- 1 and 2 only
- 3 only
- 1, 2 and 3

**Sol 1. Ans.(c).** The passage is based on an analysis of Charles Darwin’s Theory of Evolution by natural selection. Statement 2 is clearly wrong ("all species"). {Also, the question seems to be framed wrongly. It should be "hence" not "as" at the end!}

**Sol 2. Ans.(c).** A theory is an idea or set of ideas that tries to explain something. But according to the passage the Darwinian theory of evolution is not a theory because ‘evolution’ is a fact and no single zoological, botanical, geological, paleontological, genetics or physical evidence has refuted either of two central Darwinian ideas. Option (c) is the correct answer. Option (b) comes close but no!

**Sol 3. Ans.(a).** Statement 2 is incorrect. The passage says that “90% of species that have ever lived on earth are now extinct”. So, only possible options are (a) and (c). Darwin’s theory does not explain all the natural phenomena, neither does the passage says so. Hence statement says so. Hence statement 3 can’t be true. [Summary - Statement 2 is clearly wrong factually. Statement 3 is foolishly worded.]

**Passage — 2**

With steady economic growth, higher literacy and increasing skill levels, the number of Indian middle-class families has gone up exponentially. Direct results of the affluence have been changes in dietary patterns and energy consumption levels. People have moved to a higher protein-based diet like milk products, fish and meat, all of which need significantly more water to produce than cereal- based diets. Increasing use of electronic and electric machines/gadgets and motor vehicles needs more and more energy and generation of energy needs water.

**4.**Which one of the following statements best reflects the crux of the passage?

- People should be persuaded to continue with the mainly Indian traditional cereal-based diets.
- India needs to focus on developing agricultural productivity and capacity for more energy generation in the coming years.
- Modem technological developments result in the change of cultural and social behaviour of the people.
- Water management practices in India need to change dramatically in the coining years.

**Sol. Ans.(d).** **The passage is concerned with water usage.** No clues of option (a), (b) and (c). In option (a), there is no mention of persuasion to continue with cereal-based diets. In option (b), no mention of focusing on developing agricultural productivity. In option (c), no mention of change in cultural behaviour. So, option (d) is the correct answer.

**5.**How many seconds in total are there in x weeks, x days, x hours, x minutes and x seconds?

- 11580x
- 11581x
- 694860x
- 694861x

**Sol. Ans.(d).** Just convert everything to seconds eventually. **It is not a tough question, so don’t worry!**

x minutes = 60 x seconds;

x hours = 60 x minutes = 3600 x seconds;

x days = 24 x hours = 24×60 x minutes = 24 × 3600 x seconds = 86400 x seconds;

x weeks = 7 x days = 7 × 24 x hours = 7 × 24 × 60 x minutes = 7 × 24 × 3600 x seconds = 6,04,800 x seconds.

Hence in x weeks, x days, x hours, x minutes and x seconds there will be 6,04,800 x + 86400 x + 3600 x + 60 x + x = **694861 x seconds.**

**6.**P, Q, R, S, T and U are six members of a family. R is the spouse of Q. U is the mother of T and S is the daughter of U. P's daughter is T and R's son is P. There are two couples in the family.

Which one of the following is correct?

- Q is the grandfather of T
- Q is the grandmother of T
- R is the mother of P
- T is the granddaughter of Q

**Sol. Ans.(d).** In such questions, making a diagram is always useful. From the diagram given, it can be said that the gender of Q and R is not defined. So, options (a), (b) and (c) are not definitely correct. Clearly T is the granddaughter of Q.

**7.**Consider the Question and two Statements given below in respect of three cities P, Q and R in a State:

Question: How far is city P from city Q?

Statement-1: City 0 is 18 km from city R.

Statement-2: City P is 43 km from city R.

Which one of the following is correct in respect of the Question and the Statements?

- Statement-1 alone is sufficient to answer the Question
- Statement-2 alone is sufficient to answer the Question
- Both Statement-1 and Statement-2 arc sufficient to answer the Question
- Both Statement-1 and Statement-2 are not sufficient to answer the Question

**Sol. Ans.(d).** **This is a “Data Sufficiency” type question. **

Question: How far is City P from City Q?

Statement 1: City Q is 18 km from City R, no mention of distance between City P and City Q. So, 1 alone is not sufficient to answer.

Statement 2: City P is 43 km from City R, no mention of distance between City P and City Q. So, 2 alone is not sufficient to answer.

Statement 1 + 2: Even if you use both the statements, we do not get the unique answer as there are multiple possibilities, out of which some are shown below. Cities P and Q may be mutually located in many ways.

**8.**Two Statements followed by four Conclusions are given below. You have to take the Statements to be true even if they seem to be at variance from the commonly known facts. Read all the Conclusions and then decide which of the given Conclusions logically follows/ follow from the Statements, disregarding the commonly known facts:

Which one of the following is correct?

- Only Conclusion-I
- Only Conclusion-II
- Both Conclusion-III and Conclusion-IV
- None of the Conclusions follows

**Sol. Ans.(d).** By the diagram, it is clear that none of the conclusions is true. Multiple possibilities exist for Chairs.

**9.**Three Statements followed by three Conclusions are given below. You have to take the Statements to be true even if they seem to be at variance from the commonly known facts. Read all the Conclusions and then decide which of the given Conclusions locally follows/ follow from the Statements, disregarding the commonly known facts:

Statement-1 : Some doctors are teachers.

Statement-2 : All teachers are engineers

Statement-3 : All engineers are scientists.

Conclusion-I : Some scientists are doctors.

Conclusion-II : All engineers are doctors.

Conclusion-III : Some engineers are doctors.

Which one of the following is correct?

- Only Conclusion-I
- Only Conclusion-II
- Both Conclusion-I and Conclusion-III
- Both Conclusion-I and Conclusion-II

**Sol. Ans.(c).**

Refer to the adjacent diagram. It is clear that I and III are true.

**10.**Eight students A, B, C, D, E, F, G and H sit around a circular table, equidistant from each other, facing the centre of the table, not necessarily in the same order. B and D sit neither adjacent to C nor opposite to C. A sits in between E and D and F sits in between B and H. Which one of the following is definitely correct?

- B sits in between A and G
- C sits opposite to G
- E sits opposite to F
- None of the above

**Sol 10. Ans.(d).** Two cases are possible. They are shown below. Clearly none of the options is definitely correct.

**Directions for the following 3 (three) items:**

Read the following passage and answer the items that follow the passage. Your answers to these items should be based on the passage only.

**Passage**

In some places in the world, the productivity of staples such as rice and wheat has reached a plateau. Neither new strains nor fancy agrochemicals are raising the yields. Nor is there much unfarmed land left that is suitable to be brought under the plough. If global temperature continues to rise, some places will become unsuitable for farming. Application of technology can help overcome these problems. Agricultural technology is changing fast. Much of this change is brought about by affluent farmers in the West/Americas. Techniques developed in the West are being adapted in some places to make tropical crops more productive. Technology is of little use if it is not adapted. In the developing world, that applies as much to existing farming techniques as it does to the latest advances in genetic modification. Extending to the smallholders and subsistence farmers of Africa and Asia the best of today's agricultural practices, in such simple matters as how much fertilizers to apply and when, would lead to a greatly increased availability of food for humanity. So would things like better roads and storage facilities, to allow for the carriage of surpluses to markets and reduce wastage.

**11.**Based on the above passage, the following assumptions have been made:

- Development of agricultural technology is confined to developed countries.
- Agricultural technology is not adapted in developing countries.

Which of the above assumptions is/are valid?

- 1 only
- 2 only
- Both 1 and 2
- Neither 1 nor 2

**12.**Based on the above passage, the following assumptions have been made:

- Poor countries need to bring about change in their existing fanning techniques.
- Developed countries have better infrastructure and they waste less food.

Which of the above assumptions is/are valid?

- 1 only
- 2 only
- Both 1 and 2
- Neither 1 nor 2

**13.**Based on the above passage, the following assumptions have been made:

- Growing enough food for future generations will be a challenge.
- Corporate farming is a viable option for food security in poor countries.

Which of the above assumptions is/are valid?

- 1 only
- 2 only
- Both 1 and 2
- Neither 1 nor 2

**Sol 11. Ans.(b).** The passage mentions that, “techniques developed in the West are being adapted in some places to make tropical crops more productive”, it means that it is not assumed that development of agriculture technology is confined to developed countries.

"Much of this change" means not all technology change is happening in the West. Some is happening in developing world too. So 1 is wrong, hence (a) and (c) are eliminated.

The passage mentions that there is a need of extending modern agriculture practices to smallholder and subsistence farmers of Africa and Asia, so it must have assumed that agriculture technology is not adapted in developing countries.

**Sol 12. Ans.(a).** Statement 1 is an assumption. In the passage we find ‘Technology is of little use if it is not adapted. In the developing world, that applies to as much…’. Statement 2 is not an assumption.

**Sol 13. Ans.(a).** Statement 1 is clearly an assumption. Several clues are there like, ‘In some places in the world, the productivity of staples such as ‘If global temperature continue to rise, some places will become unsuitable for farming…’. No mention of corporate farming in the passage so statement 2 is not an assumption.

**14.**The letters A, B, C, D and E are arranged in such a way that there are exactly two letters between A and E. How many such arrangements are possible?

- 12
- 18
- 24
- 36

**Sol. Ans.(c).** Letters can be in following forms –

I. _ A _ _ E – 6 ways

II. A _ _ E _ – 6 ways

III. _ E _ _ A – 6 ways

IV. E _ _ A _ – 6 ways

So, total 24 ways are possible.

**15.**Consider the Question and two Statements given below:

Question: Is Z brother of X?

Statement-1 : X is a brother of Y and y is a brother of Z.

Statement-2 -: X, Y and Z are siblings.

Which one of the following is correct in respect of the Question and the Statements?

- Statemcnt-1 alone is sufficient to answer the Question
- Statement-2 alone is sufficient to answer the Question
- Both Statement-1 and Statement-2 are sufficient to answer the Question
- Both Statement-1 and Statement-2 are not sufficient to answer the Question

**Sol. Ans.(d).** Question: Is Z brother of X? (Z’s gender should be known)

Statement 1: X is brother of Y and Y is brother of Z. But gender of Z is not known, so Z can be brother or sister of X. So this statement alone is not sufficient to answer the question.

Statement 2: X, Y and Z are siblings. Gender of X, Y and Z is not known. Multiple possibilities are there, they all can be brothers or they all can be sisters or one brother two sisters etc. So this statement alone is not sufficient to answer the question.

Even combining both the statements will not give any useful information to get a unique answer. So answer is (d).

**16.**On one side of a 1-01 km long road, 1.01 plants are planted at equal distance from each other. What is the total distance between 5 consecutive plants?

- 40 m
- 40.4 m
- 50 m
- 50.5 m

**Sol. Ans.(b).** Be cautious as the number of gaps will be one less than the number of elements.

Total Distance = 1.01 km = 1.01 × 1000 = 1010 m.

Now, 101 plants will divide 1010 m in 100 equal parts each of length 1010/100 = 10.10 m.

So five consecutive plants will have 4 such distances.

So correct answer 4 × 10.1 = 40.4 m.

**17.**A, B and C are three places such that there are three different roads from A to B, four different roads from B to C and three different roads from A to C. In how many different ways can one travel from A to C using these roads?

- 10
- 13
- 15
- 36

**Sol. Ans.(c).** There are two ways to move from A to C –

1. Directly from A to C – 3 ways

2. Via B. From A to B and then B to C = 3 × 4 = 12. So, total number of ways = 15 ways.

**18.**A has some coins. He gives half of the coins and 2 more to B. B gives half of the coins and 2 more to C. C gives half of the coins and 2 more to D. The number of coins D has now, is the smallest two- digit number. How many coins does A have in the beginning?

- 76
- 68
- 60
- 52

**Sol. Ans.(d).** Working backwards is a good way to solve this question. Another way is –

Let us assume the number of coins D has = smallest two digit number = 10.

If D = 10 then C = 2 (10 – 2) = 16. (so half of 16 is 8, plus 2 is 10)

If C = 16, then B = 2(16 – 2) = 28.

If B = 28, then A = 2(28 – 2) = 52.

**19.**In the series AABABCABCDABCDE.., which letter appears at the 100th place?

- G
- H
- I
- J

**Sol. Ans.(c).** The trick in all such questions is to find the pattern first.

Given Series = A (1 Letter) AB (2 Letters) ABC (3 Letters) ABCD (4 Letters) ABCDE (5 Letters) …… so on up to 100th letter.

Sum of first 13 natural numbers = 1 + 2 + 3 + 4 + 5 ….. 13 = n(n+1)/2 = 13×14/2 = 91.

So, if we have to count upto 100th letter, in the last string (100 – 91) = 9 letters would be there.

Which would be – ABCDEFGHI.

So I is the correct answer.

**20.**Three persons A, B and C are standing in a queue not necessarily in the same order. There are 4 persons between A and B, and 7 persons between B and C If there are 11 persons ahead of C and 13 behind A, what could be the minimum number of persons in the queue?

- 22
- 28
- 32
- 38

**Sol. Ans.(a).**

As shown in the diagram, two cases are possible. Minimum number would be in second case i.e., 22.

**Directions for the following 4 (four) items:**

Read the following two passages and answer the items that follow the passages. Your answers to these items should be based on the passages only.

**Passage — 1**

"In simple matters like shoe-making, we think only a specially trained person will serve our purpose, but in politics, we presume that everyone who knows how to get votes knows how to administer a State. When we are ill, we call for a trained physician, whose degree is a guarantee of specific preparation and technical competence—we do not ask for the handsomest physician, or the most eloquent one : well then, when the whole State is ill should we not look for the service and guidance of the wisest and the best?"

**21.** Which one of the following statements best reflects the message of the author of the passage?

- We assume that in a democracy, any politician is qualified to administer a State
- Politicians should be selected from those trained in administration.
- We need to devise a method of barring incompetence from public office.
- As voters select their administrators, the eligibility of politicians to administer a State cannot be questioned.

**Sol. Ans.(b).** The passage is about the problem of matching qualifications with jobs. Words used in passage like “we presume that everyone who knows how to get votes knows how to administer a state” clearly indicates the same. Option (d) is clearly wrong. Options (b) and (c) both can be right.

**Passage — 2**

The poverty line is quite unsatisfactory when it comes to grasping the extent of poverty in India. It is not only because of its extremely narrow definition of who is poor and the debatable methodology used to count the poor, but also because of a more fundamental assumption underlying it. It exclusively relies on the notion of poverty as insufficient income or insufficient purchasing power. One can better categorize it by calling it income poverty. If poverty is ultimately about deprivations affecting human well-being, then income poverty is only one aspect of it. Poverty of a life, in our view. lies not merely in the impoverished state in which the person actually lives, but also in the lack of real opportunity given by social constraints as well as personal circumstances—to choose other types of living. Even the relevance of low incomes, meagre possessions, and other aspects of what are standardly seen as economic poverty relate ultimately to their role in curtailing capabilities, i.e., their role in severely restricting the choices people have to lead variable and valued lives.

**22.**Why is the methodology adopted in India to count the "poor* debatable?

- There is some confusion regarding what should constitute the 'poverty line'.
- There are wide diversities in the condition of the rural and urban poor.
- There is no uniform global standard for measuring income poverty.
- It is based on the proposition of poverty as meagre income or buying capacity.

**Sol. Ans.(d).** The passage is questioning the methods used to calculate poverty in India. As given, ‘income poverty is only one aspect of poverty’, so (d) is the correct option. This topic is important, and was covered directly in our Power of 10 editorial analysis series ( part of the UPSC Powerpack programme. Enrol here - https://bit.ly/upscias )

**23.**Why is income poverty only one measure of counting the ‘poor'?

- It talks of only one kind of deprivation ignoring all others.
- Other deprivations in a human life have nothing to do with lack of purchasing power.
- Income poverty is not a permanent condition, it changes from time to time.
- Income poverty restricts human choices only at a point of time.

**Sol. Ans.(a).** It is clearly mentioned in the passage that in this measure, there is only one form of deprivation getting counted while ignoring others (like the lack of real opportunity due to social constraints and as well as personal circumstances).

**24.**What does the author mean by "poverty of a life?

- All deprivations in a human life which stem not only from lack of income but lack of real opportunities
- Impoverished state of poor people in rural and urban areas
- Missed opportunities in diverse personal circumstances
- Material as well as non-material deprivations in a human life which restrict human choices permanently

**Sol. Ans.(a).** Clearly, correct option is (a). Option (d) sounds good but those words are missing in the passage.

**25.**X and Y run a 3 km race along a circular course of length 300 m. Their speeds are in the ratio 3:2. If they start together in the same direction, how many times would the first one pass the other (the start-off is not counted as passing)?

- 2
- 3
- 4
- 5

**Sol. Ans.(b).** This is a question from time-speed-distance.

The ratio of speeds of X and Y is given as 3 : 2.

Let speed of X = 3 mps and the speed of Y = 2 mps.

Time required by X to complete one round of 300 m = 300/3 = 100 seconds.

Time required by Y to complete one round of 300 m = 300/2 = 150 seconds.

Time in which they will meet = LCM of (100, 150) = 300 seconds. It means every third round of the faster person.

Total number of rounds to complete = 3000/300 = 10. So, they will meet in 3rd, 6th and 9th round.

So total three times.

**26.**If the order of the letters in the English alphabet is reversed and each letter represents the letter whose position it occupies, then which one of the following represents ‘LUCKNOW?

- OGXPMLD
- OGXQMLE
- OFXPMLE
- OFXPMLD

**Sol. Ans.(d).** An easy coding-decoding type question.

The coding will be as follows –

Letter - A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Code - Z Y X W V U T S R Q P O N M L K J I H G F E D C B A

Correct code for LUCKNOW is OFXPMLD.

**27.**In a tournament of Chess having 150 entrants, a player is eliminated whenever he loses a match. It is given that no match results in a tie/draw. How many matches are played in the entire tournament?

- 151
- 150
- 149
- 148

**Sol. Ans.(c).**

First 150 persons will have 150/2 = 75 matches

Then 75 persons will have (75 – 1)/2 = 37 matches

Then 37 + 1 (left in the last step) = 38 person will have 38/2 = 19 matches

Then 19 persons will have (19 – 1)/2 = 9 matches

Then 9 + 1 (left in the last step) = 10 persons will have 10/2 = 5 matches

Then 5 persons will have (5 – 1)/2 = 2 matches

Then 2 + 1 (left in the last step) = 3 persons will have (3 - 1)/2 = 1 match

Then this 1 person will have a match with a person left in the last step = 1 match

Total matches = 75 + 37 + 19 + 9 + 5 + 2 + 1 + 1 = 149.

**28.**How many 3-digit natural numbers (without repetition of digits) are there such that each digit is odd and the number is divisible by 5?

- 8
- 12
- 16
- 24

**Sol. Ans.(b).** This is a good question from number system theory.

Each digit is odd and number is divisible by 5 means the unit digit would be 5 (and not zero).

So, the number will be in the form _ _ 5. For the first two digits we use remaining odd digits (1, 3, 7, 9) which can happen in 4 × 3 = 12 ways (as repetition of digits is now allowed).

**29.**Consider the Question and two Statements given below:

Question: Is x an integer?

Statement-1: x/3 is not an integer.

Statement-2: 3x is an integer.

Which one of the following is correct in respect of the Question and the Statements?

- Statement-1 alone is sufficient to answer the Question
- Statement-2 alone is sufficient to answer the Question
- Both Statement-1 and Statement-2 are sufficient to answer the Question
- Both Statement-1 and Statement-2 are not sufficient to answer the Question

**Sol. Ans.(d).** This is another question from Data Suffiency.

Question – Is x an integer? So, answer would be in the form of ‘yes’ or ‘no’.

Statement 1 – x/3 is not an integer. If we take x = 4 (integer), then x/3 = 4/3 is not an integer. But if we take x = 2/3 (not integer) then also x/3 = 2/9 is not an integer. So, by using information provided in this statement we cannot say whether x is integer or not. So, 1 alone is not sufficient.

Statement 2 – 3x is an integer. If we take x = 4 (integer) then 3x = 12 is an integer. But if we take x = 1/3, then also 3x is an integer. So, by using information provided in this statement we cannot say whether x is integer or not. So, 2 alone is not sufficient.

Combining Statement 1 and 2 – If we take x = 4 (integer) then x/3 is not integer and 3x = 12 is an integer. But if we take x = 1/3, then also x/3 is not an integer and 3x is an integer. So, even combining both of the statements we can not say that whether x is an integer or not. Hence, correct answer is (d).

This was a tough question, and you could have left it.

**30.**The increase in the price of a certain item was 25%. Then the price was decreased by 20% and then again increased by 10%. What is the resultant increase in the price?

- 5%
- 10%
- 12-5%
- 15%

**Sol. Ans.(b).** A simple question on percentages.

Let initial price = 100. Price after 25% increase = 125.

Price after 20% decrease will be 125 × 0.8 = 100.

Again, price after 10% increase 110. So, final value (110) increased by 10% with respect to the initial value (100).

**Directions for the following 3 (three) items:**

Read the following two passages and answer the items that follow the passages. Your answers to these items should be based on the passages only.

**Passage — 1**

The main threat to maintaining progress in human development comes from the increasingly evident unsustainability of production and consumption patterns. Current production models rely heavily on fossil fuels. We now know that this is unsustainable because the resources are finite. The close link between economic growth and greenhouse gas emissions needs to be severed for human development to become truly sustainable. Some developed countries have begun to alleviate the worst effects by expanding recycling and investing in public transport and infrastructure. But most developing countries are hampered by the high costs and low availability of clean energy sources. Developed countries need to support developing countries' transition to sustainable human development.

**31.**Unsustainability in production pattern is due to which of the following?

- Heavy dependence on fossil fuels
- Limited availability of resources
- Expansion of recycling

Select the correct answer using the code given below.

- 1 and 2 only
- 2 only
- 1 and 3 only
- 1, 2 and 3

**32.**Consider the following statements:

Developed countries can support developing countries’ transition to sustainable human development by

- making clean energy sources available at low cost
- providing loans for improving their public transport at nominal interest rates
- encouraging them to change their production and consumption patterns

Which of the statements given above is/are correct?

- 1 only
- 1 and 2 only
- 2 and 3 only
- 1, 2 and 3

**Sol 31. Ans.(a). The passage is about the unsustainable models of global production (environmental sustainability).**

Expansion of recycling is not a cause for unsustainability in production pattern, in fact it is opposite of it. So, 3 can’t be true. As per passage 1 and 2 clearly are the causes of unsustainability in production pattern. So answer is (a).

**Sol 32. Ans.(d). ** The passage talks of all the three things, low-cost clean energy sources, investing in public transport and unsustainability of production and consumption patterns.

**Passage — 2**

Unless the forces and tendencies which are responsible for destroying the country's environment are checked in the near future and afforestation of denuded areas is taken up on a massive scale, the harshness of the climatic conditions and soil erosion by wind and water will increase to such an extent that agriculture, which is the mainstay of our people, will gradually become impossible. The desert countries of the world and our own desert areas in Rajasthan are a grim reminder of the consequences of large-scale deforestation. Pockets of desert-like landscape are now appearing in other parts of the country including the Sutlej-Ganga Plains and the Deccan Plateau. Where only a few decades back there used to be lush green forests with perennial streams and springs, there is only brown earth, bare of vegetation, without any water in the streams and springs except in the rainy season.

**33. **According to the passage given above, deforestation and denudation will ultimately lead to which of the following?

- Depletion of soil resource
- Shortage of land for the common man
- Lack of water for cultivation

Select the correct answer using the code given below.

- 1 and 2 only
- 2 and 3 only
- 1 and 3 only
- 1, 2 and 3

**Sol 33. Ans.(c). ** According to the passage, both 1 and 3 are given, but 2 is wrong (there would not be shortage of land for common man). Only possible option is (c).

**34.**What is the value of X in the sequence
20, 10, 10, 15. 30, 75, X?

- 105
- 120
- 150
- 225

**Sol. Ans.(d). A simple coding decoding question.**

Now, 20 × 0.5 = 10. 10 × 1 = 10. 10 × 1.5 = 15. 15 × 2 = 30. 30 × 2.5 = 75. So, correct answer is 75 × 3 = 225.

**35.**An Identity Card has the number ABCDEFG, not necessarily in that order, where each letter represents a distinct digit (1, 2, 4, 5, 7, 8. 9 only). The number is divisible by 9. After deleting the first digit from the right, the resulting number is divisible by 6. After deleting two digits from the right of original number, the resulting number is divisible by 5. After deleting three digits from the right of original number, the resulting number is divisible by 4. After deleting four digits from the right of original number, the resulting number is divisible by 3. After deleting five digits from the right of original number, the resulting number is divisible by 2. Which of the following is a possible value for the sum of the middle three digits of the number?

- 8
- 9
- 11
- 12

**Sol. Ans.(a). A tough question that can be left. **

The number is in the form ABCDEFG.

We have to use digits from 1, 2, 4, 5, 7, 8 and 9.

So, since the last digit of number divisible by 5 must be 5. So, E = 5.

Now recall the rule for divisibility by 9, similar to divisibility rule for 3. That is, if the sum of digits of the number is divisible by 9, then the number itself is divisible by 9.

Numbers which are divisible by both 2 and 3 are divisible by 6. That is, if the last digit of the given number is even and the sum of its digits is a multiple of 3, then the given number is also a multiple of 6.

We have three even numbers (2, 4 and 8) and these should be at places of F, B and D in any order. No other digit would be even. Possible value of CD are 12, 72 and 92. We have to find C + D + E.

If CD = 12, C + D + E = 1 + 2 + 5 = 8, if CD = 72, C + D + E = 7 + 2 + 5 = 14, if CD = 92, C + D + E = 9 + 2 + 5 = 16. Only matched option is (a).

**36.**Two friends X and Y start running and they run together for 50 m in the same direction and reach a point. X turns right and runs 60 m, while Y turns left and runs 40 m. Then X turns left and runs 50 m and stops, while Y .turns right and runs 50 m and then stops. How far are the two friends from each other now?

- 100 m
- 90 m
- 60 m
- 50 m

**Sol. Ans.(a). A simple diagram helps solve this. **

**37.**Which date of June 2099 among the following is Sunday?

- 4
- 5
- 6
- 7

**Sol. Ans.(d). A calendar-based question. **

We know that January 01, 2001 is Monday and December 31, 2000 is a Sunday (It is a fact).

Calculating total number of odd days between December 31, 2000 – Sunday to June 1 2099, we get the following 98 complete years + Jan 2099 to May 2099 + One day of June (i.e. June 1)

98 complete years have 24 leap years having 2 odd days each and 74 ordinary years having one odd day each.

So total number of odd days in 98 years = 24×2 + 74×1 = 48 + 74 = 122 (which is 3 odd days) (remainder when we divide 122 by 7).

In year 2099 (Ordinary Year, having Feb of 28 days) Jan to May we will get number of days as follows 3 (Jan) + 0 (Feb) + 3 (March) + 2 (April) + 3 (May) + 1 (June) = 3 + 3 + 2 + 3 + 1 = 12 = 5 odd days (remainder when we divide 12 by 7) So, total odd days = 3 + 5 = 8 = 1 (remainder when we divide 8 by 7)

So, in all we got 1 remainder considering Dec. 31, 2000 – Sunday as base date.

So, June 1, 2099 – Sunday + 1 day = Monday.

And first Sunday of June will be on 7^{th }.

**38.**A bill for Rs. 1,840 is paid in the denominations of Rs. 50, Rs. 20 and Rs.10 notes. 50 notes in all are used. Consider the following statements:

- 25 notes of Rs. 50 are used and the remaining arc in the denominations of Rs.20 and Rs. 10.
- 35 notes of Rs.20 are used and the remaining are in the denominations of Rs. 50 and Rs. 10.
- 20 notes of Rs.10 are used and the remaining are in the denominations of Rs. 50 and Rs. 20.

Which of the above statements are not correct?

- 1 and 2 only
- 2 and 3 only
- 1 and 3 only
- 1, 2 and 3

**Sol. Ans.(d). **

Statement 1 – Total bill to be paid = Rs. 1840. Denominations – Rs. 10, Rs. 20 and Rs. 50. If 25 notes are Rs. 50 are used, it will give us 25 × 50 = Rs. 1250. Which means remaining 1840 – 1250 = Rs. 590 to be paid in Rs. 20 and Rs. 10 denominations. But we have remaining number of notes = 50 – 25 = 25. Now even if we take all these 25 notes of Rs. 20 we can pay maximum 25 × 20 = Rs. 500. So, Rs. 590 can’t be paid. Statement 1 is not correct.

Statement 2 – Total bill to be paid = Rs. 1840. Denominations – Rs. 10, Rs. 20 and Rs. 50. If 25 notes are Rs. 50 are used, it will give us 35 × 20 = Rs. 700. Which means remaining 1840 – 700 = Rs. 1140 to be paid in Rs. 50 and Rs. 10 denominations. Whereas we have remaining number of notes = 50 – 35 = 15. Now even if we take all these 15 notes of Rs. 50 we can pay maximum 15 × 50 = Rs. 750. So, Rs. 1140 can’t be paid. Statement 2 is not correct.

Statement 3 – Total bill to be paid = Rs. 1840. Denominations – Rs. 10, Rs. 20 and Rs. 50. If 25 notes are Rs. 50 are used, it will give us 10 × 20 = Rs. 200. Which means remaining 1840 – 200 = Rs. 1640 to be paid in Rs. 50 and Rs. 20 denominations. Whereas we have remaining number of notes = 50 – 20 = 30. Now even if we take all these 30 notes of Rs. 50 we can pay maximum 30 × 50 = Rs. 1500. So, Rs. 1640 can’t be paid. Statement 3 is not correct.

All three are NOT correct.

**39.**Which number amongst 240, 321, 418 and 812 is the smallest?

- 2
40 - 3
21 - 4
18 - 8
12

**Sol. Ans.(b). A question based on indices.**

We have to compare 2^{40}, 3^{21}, 4^{18} and 8^{12} which can be rewritten as 2^{40}, 3^{21}, 2^{36} and 2^{36}.

Which means 4^{18} = 8^{12}. So they can’t be smallest, otherwise two answers (option c and d) would be correct. Again 2^{40} = 4^{20} > 4^{18} , so this also can’t be smallest. Smallest will be 3^{21}.

**40.**The digits 1 to 9 are arranged in three rows in such a way that each row contains three digits, and the number formed in the second row is twice the number formed in the first row; and the number formed in the third row is thrice the number formed in the first row. Repetition of digits is not allowed. If only three of the four digits 2,3,7 and 9 are allowed to use in the first row, how many such combinations are possible to be arranged in the three rows?

- 4
- 3
- 2
- 1

**Sol. Ans.(c). ** Digits used in the first row are 2, 3, 7 and 9. Possible numbers 237, 239, 273, 279, 293, 297, 327, 329, 372 … and so on 24 numbers are possible. But you see, answer of thrice the number greater 329 would be in four digits (372×3 = 1116), that is not our case. So, we have possible numbers for the first row are 237, 239, 273, 279, 293, 297, 327, 329.

Repetition of digits is not allowed. So, if we will take 237, 476 (two times).. 7 is repeated, failed. 239 – two time is 478 and three time is 717, repetition error. 273 – two time = 546, three time = 819, no digit is repeated, so 273 is a valid number. 279 – two times = 558, repetition error. 293 – two times = 586, three times 879, repetition error. 297 – two times = 594, repetition error. 327 – two times 654 and three times = 981 is a valid number. 329 – two times = 658, but three times = 851, will have repeated digit.

So, only two such cases are possible

**Case I** - First row – 273; Second row – 546 and Third row - 819

**Case II** – First row – 327; Second row – 654 and Third row – 981.

**Directions for the following 3 (three) items: **

**Passage — 1**

To encourage research is one of the functions of a university. Contemporary universities have encouraged research, not only in those cases where research is necessary, but on all sorts of entirely unprofitable subjects as well. Scientific research is probably never completely valueless. However silly and insignificant it may seem, however mechanical and unintelligent the labours of the researchers, there is always a chance that the results may be of value to the investigator of talent, who can use the facts collected for him by uninspired but industrious researchers as the basis of some fruitful generalization. But where research is not original, but consists in the mere rearrangement of existing materials, where its object is not scientific but literary or historical, then there is a risk of the whole business becoming merely futile.

**41.** The author's assumption about scientific research is that

- it is never very valuable
- it is sometimes very valuable
- it is never without some value
- it is always very valuable

**42.** According to the author

- not many research results can be of value to an intelligent investigator
- a research result is always valuable to an intelligent investigator
- any research result can be of value to an intelligent investigator
- a research result must always be of some value to an intelligent investigator

**Sol 41. Ans.(c). ** A passage that talks of the value of original research in universities.

Correct answer is option (c), which is evident from the words *“Scientific research is probably never completely valueless”* given in the passage. The four options are quite close, and you have to be careful

**Sol42. Ans.(c). ** The correct answer is option (c) “ …there is always a chance that the results may be of value to investigator of talent…” indicates the same.

**Passage — 2 **

How best can the problems of floods and droughts be addressed so that the losses are minimal and the system becomes resilient? In this context, one important point that needs to be noted is that India gets too much' water (about 75% of annual precipitation) during 120 days (June to September) and too little' for the remaining 245 days. This skewed water availability has to be managed and regulated for its consumption throughout the year.

**43.**Which one of the following best reflects the practical, rational and lasting solution?

- Constructing huge concrete storage tanks and canals across the country
- Changing the cropping patterns and farming practices
- Interlinking of rivers across the country
- Buffer stocking of water through dams and recharging aquifers

**Sol. Ans.(d). ** **The passage talks about skewed rainfall distribution over India.** As it talks about ‘floods and droughts’ and ‘resilience of system’, option (d) becomes the best fit. **Interlinking of rivers is not referred to at all in this passage, hence (c) is incorrect.** The wording of (a) sound a bit awkward.

**44.**If 15X14X13x…….X3X2X1=3^{m}Xn

where m and n are positive integers, then what is the maximum value of m?

- 7
- 6
- 5
- 4

**Sol. Ans.(b). **

15 × 14 × 13 × ….. × 3 × 2 × 1 = 15!

We have to find maximum power of 3 in 15!

**That will be in 15/3 (= 5) + 5/3 (= 1) = 6 – Short-cut.**

Otherwise, in the multiplication of 15 × 14… 2 × 1, 3 is present 15 (one time), 12 (one time), 9 (two times), 6(one time) and 3 (one time). So, total 1 + 1 + 2 + 1 + 1 = 6 times. So, maximum power of 3 will be 6 in 15!

**45.**What is the value of X in the sequence 2, 12, 36, 80, 150, X?

- 248
- 252
- 258
- 262

**Sol. Ans.(b). **

1^{2} + 1^{3} = 2. 2^{2} + 2^{3} = 12. 3^{2} + 3^{3} = 36. 4^{2} + 4^{3} = 80. 5^{2} + 5^{3} = 150. So, correct answer is 6^{2} + 6^{3} = 252.

**46.**One non-zero digit, one vowel and one consonant from English alphabet (in capital) are to be used in forming passwords, such that each password has to start with a vowel and end with a consonant. How many such passwords can be generated?

- 105
- 525
- 945
- 1050

**Sol. Ans.(c). **

Non-zero digits = 9 (1, 2, 3, 4, 5, 6, 7, 8, 9); Vowels = 5 (A, E, I, O, U); Consonants = 21.

Total number of ways in which password can be made = 5 × 9 × 21 = 945.

**47.**There are 9 cups placed on a table arranged in equal number of rows and columns out of which 6 cups contain coffee and 3 cups contain tea. In how many ways can they be arranged so that each row should contain at least one cup of coffee?

- 18
- 27
- 54
- 81

**Sol. Ans.(b). **

9 cups are arranged into 3 × 3 grid - 6 cups of coffee and 3 cups of tea.

Case I - Each row contains one cup of tea.

First row can be arranged in three ways – CCT, CTC, TCC. Similarly, the next two rows.

So, total possibilities = 3 × 3 × 3 = 27.

Case II – In one row there are three coffee cups like CCC, in other two coffee cups like CCT or CTC or TCC (3 ways) and in the last, one coffee cup and two tea cups like CTT or TCT or TTC. In this case these three rows can be arranged in 3! = 6 ways. Total possible ways to arrange in this case = 6 × 3 × 3 = 54.

Desired answer = Case I + Case II = 27 + 54 = 81

**48.**The sum of three consecutive integers is equal to their product- How many such possibilities are there?

- Only one
- Only two
- Only three
- No such possibility is there

**Sol. Ans.(c). **

Possibility I – (-)1, 0, 1, product = 0, sum = 0.

Possibility II – 1, 2, 3, product = 6, sum = 6.

Possibility III – -1, -2, -3, product = - 6, sum = - 6.

There are three possibilities where the sum and product are same.

**49.**What is the number of numbers of the form 0.XY, where X and Y are distinct non-zero digits?

- 72
- 81
- 90
- 100

**Sol. Ans.(a). A simple combinatorial question.**

Distinct non-zero digits (9 in total) can be arranged at two places in 9 × 8 = 72 ways (without repetition).

**50.**The average weight of A, B, 0 is 40 kg, the average weight of B, D, B is 42 kg and the weight of F is equal to that of R What is the average weight of A, B, C, D. E and F?

- 40.5 kg
- 40.8 kg
- 41 kg
- Cannot be determined as data is Inadequate

**Sol. Ans.(c). A question from averages.**

Given, B = F. Given, average weight of B, D, E is 42. Replace B by F here. We have, average weight of F, D and E is 42. Again, given that average weight of A, B, C is 40. So, total of A, B, C = 120 and total of D, E, F = 126. Total of A to F = 120 + 126 = 246. So, average = 246/6 = 41. Alternately you can do it by allegation method.

**Directions for the following 3 (three) items:**

Read the following two passages and answer the items that follow the passages. Your answers to these items should be based on the passages only

**Passage — 1**

The majority of people who fail to accumulate money sufficient for their needs, are generally, easily influenced by the opinions of others. They permit the newspapers and the gossiping neighbours to do their thinking for them. Opinions are the cheapest commodities on the earth. Everyone has a flock of opinions ready to be wished upon by anyone who will accept them. If you are influenced by opinions when you reach decisions, you will not succeed in any undertaking.

**51.**Which one of the following is implied by the passage?

- Most of the people do not accumulate money for their needs.
- Most of the people never fail to accumulate money for their needs.
- There are people who fail to accumulate money for their needs.
- There is no need to accumulate money.

**52.**What is the main idea of the passage?

- People should not be influenced by the opinions of others.
- People should accumulate as much money as they can
- People should neither give nor accept the opinions.
- People will succeed in any undertaking if they do not accept any opinion at all.

**Sol 51. Ans.(a). ** The first line of passage itself indicates the same – “The majority of people who fail to accumulate money sufficient for their needs…” - this means there surely are some people who fail to accumulate money. Do not get confused with (a).

**Sol 52. Ans.(a). ** Options (b), (c) and (d) are absurd! The last line of the passage, “If you are influenced by opinions when you reach…”, indicates that failure awaits you if your decisions are not your own. Hence, (a).

**Passage — 2**

The social order is a sacred right which is the basis of all other rights. Nevertheless, this right does not come from nature, and must therefore be founded on conventions."

**53.**With reference to the above passage, which of the following statements is/are correct?

- Conventions are the sources of rights of man.
- Rights of man can be exercised only when there is a social order.

Select the correct answer using the code given below.

- 1 only
- 2 only
- Both 1 and 2
- Neither 1 nor 2

**Sol. Ans.(c). ** Clearly both the statements are true. **If there would be no conventions, social order won’t form (which is itself a right). Without that, there would be none of the other rights as well.**

**54.**Two candidates X and Y contested an election. 80% of voters cast their vote and there were no invalid votes. There was no NOTA (None of the above) option. X got 56% of the votes cast and won by 1440 votes. What is the total number of voters in the voters list?

- 15000
- 12000
- 9600
- 5000

**Sol. Ans.(a). **

Let the total number of votes = T.

As per the condition given in question, Numbers of votes received by X = 0.8 × 0.56 × T.

Numbers of votes received by Y = 0.8 × 0.44 × T.

Again = 0.8 × 0.56 × T - 0.8 × 0.44 × T = 1440 or 0.8 × 0.12 × T = 1440 or T = 12,000/0.8 or T = 15,000.

**55.**What is the smallest number greater than 1000 that when divided by any one of the numbers 6, 9. 12, 15, 18 leaves a remainder of 3?

- 1063
- 1073
- 1083
- 1183

**Sol. Ans.(c). A question based on number-theory.**

LCM of 6, 9, 12, 15, 18 is equal to 180. It means it is the smallest number which will be completely divided by the given numbers. Such number just above 1000 = 180 × 6 = 1080. Now, we need the remainder as 3. So, desired number = 1083. Or you can directly try the options, and work backwards.

**56.**Let p be a two-digit number and q be the number consisting of same digits written in reverse order. If p × q = 2430, then what is the difference between p and q?

- 45
- 27
- 18
- 9

**Sol. Ans.(d). **

The product of two, two digits numbers has one 0 in it. That means the unit digit of one of the numbers must be equal to 5 (0 is not possible as the other number is formed reversing the digits).

And 5 will be the ten’s digit of the other number.

So, the number would be in the form 5_ × _ 5 = 2430. The other digit must be even.

So, possible cases 52 × 25 = 1300, 54 × 45 = 2430. So, desired answer = 54 – 45 = 9

**57.**Consider the following statements in respect of two natural numbers p and q such that p is a prime number and q is a composite number:

- p×q can be an odd number.
- q/p can be a prime number.
- p + q can be a prime number.

Which of the above statements are correct?

- 1 and 2 only
- 2 and 3 only
- 1 and 3 only
- 1, 2 and 3

**Sol. Ans.(d). **

Statement 1 – p is a prime number, let’s take 3. q is a composite number let’s take 9. So, p × q = 3 × 9 = 27 is an odd number. So, statement 1 can be true.

Statement 2 - p is a prime number, let’s take 3. q is a composite number let’s take 6. So, q/p = 6/3 = 2 is a prime number. So, statement 2 can be true.

Statement 3 - p is a prime number, let’s take 3. q is a composite number let’s take 4. So, p + q = 7 is a prime number. So, statement 3 can be true.

**58.**Consider the following statements:

- Between 3:16 p.m. and 3:17 p.m., both hour hand and minute hand coincide.
- Between 4:58 p.m. and 4:59 p.m., both minute hand and second hand coincide.

Which of the above statements is/are correct?

- 1 only
- 2 only
- Both 1 and 2
- Neither 1 nor 2

**Sol. Ans.(c). **

Between 3 and 4, hour and minute hand coincide at 3:164/11. So, statement, 1 is true.

Hour hand and second hand coincide in once in every minute. So, statement, 2 is true.

Use formula – Angle between minute hand and hour hand = θ= 11/2 M~30H. Where M is number of Minutes and H is number of Hours. Put θ = 0, and H = 3 to find M between 3 and 4, when both hands coincide.

**59.**There are two containers X and Y. X contains 100 ml of milk and y contains 100 ml of water. 20 ml of milk from X is transferred to Y. After mixing well, 20 ml of the mixture in y is transferred back to X. If m denotes the proportion of milk in X and n denotes the proportion of water in Y, then which one of the following is correct?

- m = n
- m>n
- m < n
- Cannot be determined due to insufficient data

**Sol. Ans.(a). **

Container X has 100 ml milk, and Container Y has 100 ml water.

When 20 ml milk goes from X to Y, X is left with 80 ml milk, and Y now has 100 ml water plus 20 ml milk. So the ratio is 5:1 (w : m). Now, 20 ml of mixture in Y is taken out and put into X.

Of this 20 ml, water : milk = 5 : 1

So, 5/6x 20 ml water and 1/6x 20 ml milk.

Or 50/3 ml water, and 10/3 ml milk.

So in Y = water left = 100 - 50/3 and milk left = 20 - 10/3.

So ratio of water in Y = (100 - 50/3) / 100 = 5/6 = n (given)

Now container X got 20 ml of mixture. So milk = 80 + 10/3 = 250/3 ml and water = 50/3

So ratio of milk m in X = 250/3 / 100 = 5/6

Hence, m = n.

**60.**A pie chart gives the expenditure on five different items A, B, C, D and. E in a household. If B, C, D and E correspond to 90°, 50°, 45° and 75° respectively, then what is the percentage of expenditure on item A?

- 112/9
- 125/6
- 155/9 < n
- 250/9

**Sol. Ans.(d). **

In a pie-chart, there is a total of 360°.

B = 90°, C = 50°, D = 45° and E = 75°. So, A = 360 – (90 + 50 + 45 + 75) = 100.

**So, required percentage 100 × 100/360 = 250/9**

**Directions for the following 3 (three) items:**

**Passage — 1**

In an economic organization, allowing mankind to benefit by the productivity of machines should lead to a very good life of leisure, and much leisure is apt to be tedious except to those who have intelligent activities and interests. If a leisured population is to be happy, it must be an educated population. and must be educated with a view to enjoyment as well as to the direct usefulness of technical knowledge.

**61.**Which of the following statements best reflects the underlying tone of the passage?

- Only an educated population can best make use of the benefits of economic progress.
- All economic development should be aimed at the creation of leisure.
- An increase in the educated population of a country leads to an increase in the happiness of its people.
- Use of machines should be encouraged in order to create a large leisured population.

**Sol. Ans.(a). ** Option (b) is ruled out being silly. Option (c) is not wrong, assuming the country is having economic prosperity. Option (d) is creating a cause and effect that’s not established directly. So best is (a).

“ … much leisure is apt to be tedious except to those who have intelligent activities and interests.” indicates the same.

**Passage — 2**

If presents bring less thrill now that we are grown up, perhaps it is because we have too much already; or perhaps it is because we have lost the fullness of the joy of giving, and with it the fullness of the joy of receiving. Children's fears are poignant, their miseries are acute, but they do not look too forward nor too far backward. Their joys are clear and complete. because they have not yet learnt always to add 'but’ to every proposition. Perhaps we are too cautious, too anxious, too sceptical. Perhaps. some of our cares would shrink if we thought less about them and entered with more single-minded enjoyment into the happiness that come our way.

**62.**With reference to the passage, which one of the following statements is correct?

- It is not possible for adults to feel thrilled by presents.
- There can be more than one reason why adults feel less thrilled by presents.
- The author does not know why adults feel less thrilled by presents.
- Adults have less capacity to feel the joy of loving or being loved.

**63.**The author of the passage is against

- worrying too much about the past and future
- being in the habit of thinking about presents
- not being thrilled by new things
- giving and receiving joy only partially

**Sol 62. Ans.(b). ** “… perhaps it is because we have too much already; or perhaps it is because we have ..” indicates the same.

**Sol 63. Ans.(a). ** “Perhaps some of our cares would shrink if we thought less about them.” indicates the same.

**64.**Let A, B and C represent distinct non- zero digits. Suppose x is the sum of all possible 3-digit numbers formed by A, B and C without repetition.

Consider the following statements:

- The 4-digit least value of x is 1332.
- The 3-digit greatest value of x is 888.

Which of the above statements is/are correct?

- 1 only
- 2 only
- Both 1 and 2
- Neither 1 nor 2

**Sol. Ans.(a). ** A, B and C are three distinct non-zero digits. Least such value would be possible for A, B and C as 1, 2 and 3.
So, number formed would be 123, 132, 213, 231, 312, 321 (Sum = 1332). So, statement 1 is true. As the least number is in four-digit, no such number of 3 digit would be possible. So, statement 2 is not true.

**65.**There is a numeric lock which has a 3-digit PIN. The PIN contains digits 1 to 7. There is no repetition of digits. The digits in the PIN from left to right are in decreasing order. Any two digits in the PIN differ by at least 2. How many maximum attempts does one need to find out the PIN with certainty?

- 8
- 8
- 10
- 12

**Sol. Ans.(c). ** The possible PINs are 753, 752, 751, 742, 741, 731, 642, 641, 631 and 531. Total 10.

**66.**There are eight equidistant points on a circle. How many right-angled triangles can be drawn sing these points as vertices and taking the diameter as one side of the triangle?

- 24
- 16
- 12
- 8

**Sol. Ans.(a). ** The angle in semi-circle is of 90°. Total four diameters can be made on 8 equidistant points. Each diameter can form 6 right-angle triangles (as shown in figure). So, total 4 × 6 = 24 right angled-triangles are possible.

**67.**24 men and 12 women can do a piece of work in 30 days. In how many days can 12 men and 24 women do the same piece of work?

- 30 days
- More than 30 days
- Less than 30 days or more than 30 days
- Data is inadequate to draw any conclusion

**Sol. Ans.(d). ** The given data is inadequate to answer the question, as we do not know relation between efficiencies of men and women.

**68.**What is the remainder when

91 × 92× 93 ×94 ×95 ×96 ×97 ×98 ×99 is divided by 1261?

- 3
- 2
- 1
- 0

**Sol. Ans.(d). ** First of all, prime factorize 1261 . We get 1261 = 13 × 97.

13 and 97 both are prime, so can’t be further factorized.

Both 13 × 97 are available in the given product. So, 1261 will divide the given product completely. Hence remainder 0.

**69.**Consider the following statements in respect of a rectangular sheet of length 20 cm and breadth 8 cm:

- It is possible to cut the sheet exactly into 4 square sheets.
- It is possible to cut the sheet into 10 triangular sheets of equal area.

Which of the above statements is/are correct?

- 1 only
- 2 only
- Both I and 2
- Neither 1 nor 2

**Sol. Ans.(b). ** Area of given rectangle = 8 × 20 = 160.

Statement 1 If you will divide into four parts, each part would have area of 160/4 = 40, which is not a complete square number. So, 1 is not correct.

Statement 2 If we will rectangle into 10 equal triangles. Area of each triangle would be 160/10 = 16. 10 triangles of area 16 can be made (see figure). So statement 2 is correct.

**70.**When 70% of a number x is added to another number y, the sum becomes 165% of the value of y. When 60% of the number x is added to another number z, then the sum becomes 165% of the value of z. Which one of the following is correct?

- z < x < y
- x < y < z
- y < x < z
- z < y < x

**Sol. Ans.(a). **

**Directions for the following 4 (four) items:**

**Passage — 1**

For two or three generations past, ever- increasing numbers of individuals have been living as workers merely, not as human beings. An excessive amount of labour is rule today in every circle of society, with the result that man's spiritual element cannot thrive. He finds it very difficult to spend his little leisure in serious activities. He does not want to think; or he cannot even if he wants to. He seeks not self-improvement, but entertainment which would enable him to be mentally idle and to forget his usual activities. Therefore, the so-called culture of cur age is dependent more on cinema than on theatre, more on newspapers, magazines and crime stories than on serious literature.

**71.**The passage is based on the idea that

- man should not work hard
- the great evil of our age us overstrain
- man cannot think well
- man cannot care for his spiritual welfare

**72.**Man does not seek self-improvement because he

- is not intellectually capable
- has no time to do so
- is distracted by materialism
- loves amusement and is mentally idle

**Sol 71. Ans.(b). ** The passage talks about nature of modern life, that makes a common man escape deep thinking.

Answer will be (b) – “An excessive amount of labour is rule today in every circle of society..” hints the same.

**Sol 72. Ans.(b). ** “He find it very difficult to spend his little leisure…” indicates the same.

**Passage — 2**

The demographic dividend, which has begun in India and is expected to last another few decades, is a great window of opportunity. The demographic dividend is basically a swelling in the working age population, which conversely means that the relative ratio of very young and very old will, for a while, be on the decline. From the experience of Ireland and China, we know that this can be a source of energy and an engine of economic growth. The demographic dividend tends to raise a nation's savings rate since in any nation, it is the working age population that is the main saver. And since the savings rate is an important driver of growth, this should help elevate our growth rate. However, the benefits of demographic dividend depend on the quality of the working age population. And this implies bringing back the importance of education, acquisition of skills and human capital.

**73.**Which of the following would invariably happen in a country, when the demographic dividend has begun to operate?

- The number of illiterate people will decrease.
- The ratio of very old and very young will decrease for a while
- Population growth rate will quickly stabilize. <

Select the correct answer using the code given below.

- 1 and 2 only
- 2 only
- 1 and 3 only
- 1, 2 and 3

**Sol. Ans.(b). The passage is based on the nature of so-called demographic dividend. **

“ .. which conversely means that the relative ratio of very young and very old will, for a while, be on the decline.”, proposes the same. Only 2 is correct, but 1 and 3 are not.

**74.**With reference to the passage, which of the following inferences can be drawn?

- Demographic dividend is an essential condition for a country to rapidly increase its economic growth rate.
- Promotion of higher education is an essential condition for a country for its rapid economic growth.

Select the correct answer using the code given below.

- 1 only
- 2 only
- Both 1 and 2
- Neither 1 nor 2

**Sol. Ans.(a). ** “The demographic dividend tends to raise a nation’s saving rate….. saving rate is an important driver of growth…” indicates the same. The passage doesn’t talk about higher education.

**75.**Five friends P, Q, X, Y and Z purchased some notebooks. The relevant information is given below:

- Z purchased 8 notebooks more than X did.
- P and Q together purchased 21 notebooks.
- Q purchased 5 notebooks less than P did.
- X and Y together purchased 28 notebooks.
- P purchased 5 notebooks more than X did.

If each notebook is priced f40, then what is the total cost of all the notebooks?

- Rs. 2,600
- Rs. 2,400
- Rs. 2,360
- Rs. 2,320

**Sol. Ans.(a). ** Given, Z = X + 8, P + Q = 21, Q = P – 5, X + Y = 28, P = X + 5. By these equations we have Z = 16. So total number of books P + Q + X + Y + Z = 21 + 28 + 16 = 65. Each book cost 40, total cost = 65 × 40 = 2600.

**76.**A man started from home at 14:30 hours and drove to village, arriving there when the village clock indicated 15:15 hours. After staying for 25 minutes, he drove back by a different route of length 1-25 times the first route at a rate twice as fast reaching home at 16:00 hours. As compared to the clock at home, the village clock is

- 10 minutes slow
- 5 minutes slow
- 10 minutes fast
- 5 minutes fast

**Sol. Ans.(d). ** Working backwards with options –

Considering option D – Village clock is 5 minutes fast then Home clock

So, option (d) satisfies all the conditions.

**77.**A person X wants to distribute some pens among six children A, B, C, D, E and F. Suppose A gets twice the number of pens received by B, three times that of C, four times that of D, five times that of E and six times that of F. What is the minimum number of pens X should buy so that the number of pens each one gets is an even number?

- 147
- 150
- 294
- 300

**Sol. Ans.(c). ** A = 2B, A = 3C, A = 4D, A = 5E and A = 6F. We have B = A/2, C = A/3, D = A/4, E = A/5, F = A/6.

Total number of pens = A + B + C + D + E + F = A + A/2 + A/3 + A/4 + A/5 + A/6 = 147A/60. Out of the given options, if we will take 147A/60 = 294 i.e., A = 120, we get B = 60, C = 40, D = 30, E = 24 and F = 20 all even.

**78.**Six persons A, B, C, D, E and F are sitting equidistant from each other around a circular table (facing the centre of the table).

Consider the Question and two Statements given below:

Question: Who is sitting on the immediate left of A?

Statement-1: B is sitting opposite to C and D is sitting opposite to E.

Statement-2 : F is sitting on the immediate left of B.

Which one of the following is correct in respect of the Question and the Statements?

- Statement-1 alone is sufficient to answer the Question
- Statement-2 alone is sufficient to answer the Question
- Both Statement-1 and Statement-2 are sufficient to answer the Question
- Both Statement-1 and Statement-2 are not sufficient to answer the Question

**Sol. Ans.(d). **

Considering statement 1 any of B, C, D or E can be immediate left of A.

Statement 2 provides information only about F and B, which is not sufficient to answer the question. Even if we combined both the statements, we can have multiple possibilities for the person immediate left of A (Refer to the figure given).

So, correct answer is (d).

**79.**Consider the Question and two Statements given below:

Question: What is the age of Manisha?

Statement-1: Manisha is 24 years younger than her mother.

Statement-2 : 5 years later, the ages of Manisha and her mother will be in the ratio 3:5.

Which one of the following is correct in respect of the Question and the Statements?

- Statement-1 alone is sufficient to answer the Question
- Statement-2 alone is sufficient to answer the Question
- Both Statement-1 and Statement-2 are sufficient to answer the Question
- Both Statement-1 and Statcment-2 are not sufficient to answer the Question

**Sol. Ans.(c). ** Statements 1 and 2 alone are not sufficient to answer the question.

If you combine both the statements then we have ratio of ages of Manisha and her mother, five years hence as 3 : 5.

So, present ages of Manisha and Mother can be written as 3x – 5 and 5x – 5.

By statement 1, 5x – 5 = 3x – 5 + 24 or x = 12.

So, we can find the age of Manisha. So both statements combined are sufficient to answer the question.

**80.**Six lectures A, B, C, D, E and F, each of one hour duration, are scheduled between 8:00 a.m. and 2:00 p.m.

Consider the Question and two Statements given below:

Question : Which lecture is in the third period?

Statement-1 : Lecture F is preceded by A and followed by C.

Statcment-2 : There is no lecture after lecture B.

Which one of the following is correct in respect of the Question and the Statements?

- Statement-1 alone is sufficient to answer the Question
- Statement-2 alone is sufficient to answer the Question
- Both Statement-1 and Statemcnt-2 are sufficient to answer the Question
- Both Statement-1 and Statement-2 are not sufficient to answer the Question

**Sol. Ans.(d). ** Statement 1 – Order of the lecture would be FAC _ _ _ or F _ A _ C _ or _ _ F A C _.

Here in the first case, the third lecture is C, in the second case it is A and in third case it is F. So, statement 1 is not sufficient to answer the question.

Statement 2 – Statement 2 gives us that B is the last lecture. First 5 lectures can be arranged in various orders. So, we didn’t get the answer by using statement 2 alone.

Even by combining both the statements, we can have FAC_ _ B, or F _ A _ C B or _ _ F A C B, different lectures in third period. So, answer is (d).

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