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Directions for the following 3 (three) items:
Read the following two passages and answer the items that follow. Your answers to these items should be based on the passages only.
Passage-1
Medieval merchants risked the hazards of the Silk Road to reach the markets of China; Portuguese caravels in the 15th century sailed beyond the bounds of the known world, searching less for knowledge than for gold and spices. Historically, the driver for opening frontiers has always been the search for resources. Science and curiosity are weaker drivers. The only way to open up space, whether the space of solar system or interstellar space is to create an economic engine and that engine is resource extraction.
Q 41. Which one of the following statements best sums up the passage given above?
(a) Wealth generation is the primary motive for any human endeavour.
(b) Space, whether space in solar system or interstellar space, will govern our future economy.
(c) Human beings are motivated to explore new frontiers principally by economic considerations.
(d) Wealth generation is based on the risk-behaviour of some men.
Ans. (c)
Solution
Option (a) is incorrect – This is an extreme statement. Primacy is not established, nor the passage discusses all or any human endeavor, it focuses on exploration.
Option (b) is incorrect – Future economy is not discussed in the passage.
Option (c) is correct - The passage emphasizes on this through several examples like exploration for gold, spice, and Chinese market.
Option (d) is incorrect - The passage does hint about this aspect but this does not capture the main message of the passage that is opening new frontiers needs economic engine.
Passage-2
"........ most people would agree that telling deliberate lies is wrong, except perhaps in certain special situations where more harm will be done by telling the truth. Even the most truthful people probably tell a good many more lies that might be regarded as semantic lies; their use of words contains some measure of falsehood, more or less deliberate."
Q 42. The idea which the first part of the passage mentions is
(a) agreement about telling lies.
(b) disagreement about telling lies.
(c) disagreement about telling the truth.
(d) disagreement about the harm in telling the truth.
Ans. (a)
Solution
Option (a) is correct – The passage’s first line hints that there is an agreement that in certain special situations where more harm will be done by telling the truth, it is okay to lie. Hence, we can say that agreement about telling lies is the correct option.
Option (b) is incorrect - The first part agrees on telling lies as telling the truth is not possible in special situations.
Option (c) is incorrect – Truth is not discussed directly.
Option (d) is incorrect - The passage actually supports an opposite idea.
Q 43. Which one of the following habits is found more often in good people?
(a) Mixing up the true and false
(b) Intentional mixing up of truth with the false.
(c) Falsification of facts
(d) Complete concealment of truth
Ans. (b)
Solution
Option (a) is incorrect – this statement broadly agrees with the passage but a better choice in option b is available which is better suited.
Option (b) is correct - The passage mentions "…….their use of falsehood, more or less deliberate….". Good people use lies deliberately/intentionally to reduce the harm from the truth. Hence this option is correct.
Option (c) is incorrect – Falsification of facts is not stated as a good habit.
Option (d) is incorrect – The usage of “complete” makes this unsuitable choice, the passage talks about some falsehood not complete concealment.
Q 44. A pie diagram shows the percentage distribution of proteins, water and on the dry elements in the human body. Given that proteins correspond to 16% and water corresponds to 70%. If both proteins and the other dry elements correspond to p%, then what is the central angle of the sector representing p on the pie diagram?
(a) 54°
(b) 96°
(c) 108°
(d) 120°
Ans. (c)
Solution
Percentage of Other Dry Elements in the human body = 100 – (% of Proteins + % of Water) = 100 – (16 + 70) = 100 – 86 = 14%
So, % of both Proteins and Other Dry Elements, i.e. p = 16 + 14 = 30%
In a pie diagram, 100% corresponds to 360o.
So, by unitary method, 30% will correspond to (360/100) × 30 = 108o
That is, the central angle of the sector representing p (30%) on the pie diagram = 108o
Q 45. Joseph visits the club on every 5th day, Harsh visits on every 24th day, while Sumit visits on every 9th day. If all three of them met at the club on a Sunday, then on which day will all three of them meet again ?
(a) Monday
(b) Wednesday
(c) Thursday
(d) Sunday
Ans. (b)
Solution
Joseph visits the club every 5th day.
Harsh visits the club every 24th day.
Sumit visits the club every 9th day.
To find out when is the next time they will meet again, we will take the LCM of these time-periods.
LCM (5, 24, 9) = (5, 2x2x2x3, 3x3) = 5x2x2x2x2x3x3 = 360
To calculate the day of the week, we divide the days by 7 (days in a week, Sunday will be repeated)
So, 357th day is Sunday again, so they meet next on Sunday +3 days = Wednesday (Remainder when 360 is divided by 7 is 3)
Q 46. The difference between a 2-digit number and the number obtained by interchanging the positions of the digits is 54.
1. The sum of the two digits of a number can be determined only if the product of the two digits is known.
2. The difference between the two digits of the number can be determined.
Which of the above statements is/are correct?
(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2
Ans. (b)
Solution
Let the number be xy, i.e. 10x + y
The number obtained on interchanging the positions of the digits will be yx, i.e. 10y + x
Difference between these two numbers = (10x + y) – (10y + x) = 9x – 9y = 9 (x – y) = 54
So, 9 (x – y) = 54
Or x – y = 6
So, statement 2 is correct.
The “only if” condition stands invalidated as we can find out the sum of the digits using other available information like one of the numbers, x or y.
So, statement 1 is incorrect.
Q 47. X said to Y, "At the time of your birth I was twice as old as you are at present." If the present age of X is 42 years, then consider the following statements:
1. 8 years ago, the age of X was five times the age of Y.
2. After 14 years, the age of X would be two times the age of Y.
Which of the above statements is/are correct?
(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2
Ans. (b)
Solution
Present age of X is 42 years. Let the present age of Y be y years.
As per the question, 42 – y = 2y
Or 3y = 42
Or y = 14 years
So, at present the ages of X and Y are 42 and 14 respectively.
Statement 1:
Eight years ago, the ages of X and Y must have been 34 and 6 respectively.
We can see that the age of X was not 5 times the age of Y. Hence, this statement is incorrect.
Statement 2:
After fourteen years, the ages of X and Y will be 56 and 28 respectively.
We can see that the age of X would indeed be two times the age of Y. Hence, this statement is correct.
Q 48. If the price of an article is decreased by 20% and then the new price is increased by 25%, then what is the net change in the price?
(a) 0%
(b) 5% increase
(c) 5% decrease
(d) Cannot be determined due to insufficient data
Ans. (a)
Solution
Let the initial price be Rs. 100
New price on decreasing the original price by 20% = 100 – 20% of 100 = 100 – 20 = Rs. 80
Now, the final price on increasing the previous price by 25% = 80 + 25% of 80 = 80 + 20 = Rs. 100
So, there is no net change in price.
Q 49. When a certain number is multiplied by 7, the product entirely comprises ones only (1111...). What is the smallest such number?
(a) 15713
(b) 15723
(c) 15783
(d) 15873
Ans. (d)
Solution
Method I:
As the number comprising of all 1’s is obtained on multiplication by 7, so it means that 7 is the factor of that number.
Our answer will the smallest number comprising of all 1’s that will be divisible by 7. So, let’s check.
Is 1 divisible by 7? – No
Is 11 divisible by 7? – No
Is 111 divisible by 7? – No
Is 1111 divisible by 7? – No
Is 11111 divisible by 7? – No
Is 111111 divisible by 7? – Yes
So, 111111/7 = 15,873
Method II:
Multiply the numbers given in the options by 7, and see which multiplication gives you a resultant comprising of all 1’s.
Checking option (d):
15873 × 7 = 111111
Q 50. A man completes 7/8 of a job in 21 days. How many more days will it take him to finish the job if quantum of work is further increased by 50%
(a) 24
(b) 21
(c) 18
(d) 15
Ans. (d)
Solution
Initial units of work = 8 units
Out of which, 7 units are completed in 21 days.
So, the number of days that man takes in completing one unit of work = 21/7 = 3 days
Now, amount of new work = 8 + 50% of 8 = 8 + 4 = 12 units
Work remaining = 12 – 7 = 5 units
So, the time taken by the man to complete the rest of the work = 5 × 3 = 15 days
Directions for the following 2 (two) items :
Read the following two passages and answer the items that follow. Your answers to these items should be based on the passages only.
Passage-1
Can a democracy avoid being a welfare state for long? Why cannot mass welfare be left entirely to the markets? There is a built-in tension between markets and democracy. Markets do not work on a one-person-one-vote principle as democracies do. What one gets out of the market place depends on one's endowments, skills, purchasing power and the forces of demand and supply. Markets reward individual initiative and skill, and may also lift many from the bottom rungs of society, but some people never get the opportunity to develop skills that markets demand; they are simply too poor and too handicapped; or skill formation takes too long. By creating jobs, markets may be able to help even unskilled people, but capitalism has always witnessed bursts of unemployment.
Q 51. With reference to the above passage, the following assumptions have been made :
1. Modern democracies rely on the market forces to enable them to be welfare states.
2. Markets ensure sufficient economic growth necessary for democracies to be effective.
3. Government programmes are needed for those left behind in economic growth.
Which of the above assumptions is/are valid ?
(a) 1 and 3 only
(b) 3 only
(c) 2 and 3 only
(d) 1, 2 and 3
Ans. (b)
Solution
Statement 1 is incorrect: The passage mentions that "there is a built-in tension between markets and democracy." The passage further goes on to elaborate, how. Here "built-in" refers to the systemic aspects of each.
Statement 2 is incorrect: The last few lines of the passage invalidate the claim made in statement 2. The passage mentions that "some people never get the opportunity to develop skills that markets demand" and that "capitalism has always witnessed bursts of unemployment". Therefore, we can assume that democracies are not efficient if the market runs strong.
Statement 3 is correct: As the markets cannot ensure equity (as understood from the various lines of the passage), government programs are needed to complement the market outcomes, to help those who have not benefited by the "efficient distribution of resources" of the markets.
Passage-2
In our schools, we teach our children all that is there to know no about Physics, maths and history and what-have you. But do we teach them about the bitter caste divide that plagues the country, about the spectre of famine that stalks large part of our land, about gender sensitivity, about the possibility of atheism as a choice, etc.? Equally important, do we teach them to ask question, or do we teach them only to passively receive our wisdom? From the cocooned world of school, suddenly, the adolescent finds himself/herself in the unfettered world of university. Here he/she is swept up in a turmoil of ideas and influences and ideologies. For someone who has been discouraged from asking questions and forming an opinion, this transition can be painful.
Q 52. Which one of the following best reflects the central idea of the passage given above?
(a) School curriculum is not compatible with the expectations of children and parents.
(b) Emphasis on academic achievements does give time for development of personality and skills.
(c) Preparing the children to be better citizens should be the responsibility of the education system.
(d) To be a better citizen, the present world order demands societal and life-coping skills in addition to academic content.
Ans. (d)
Solution
Option (a) is incorrect: The passage makes no mention of the expectations of either parents or children. Hence it is beyond the scope of the passage.
Option (b) is incorrect: The time factor, i.e. allocation of time between academics and skill development activities, is not discussed in the passage.
Option (c) is close but incorrect: The passage does not discuss the aspect of holistic education of children in terms of whose responsibility it should be. Though it asserts that the schools do not fulfill this important role and it is important that these values and such education are not received straightaway at the time of college, but also at the time of school, the author does not make any conclusive judgments about where the ultimate responsibility should lie.
Option (d) is the best answer: The passage explicitly mentions, both the present world order demands, as well as the societal and life-coping skills in addition to academic content. The present world order is mentioned in the lines, "But do we teach them about the bitter caste divide that plagues the country, about the specter of famine that stalks large parts of our land, about gender sensitivity, about the possibility of atheism as a choice, etc.?". Societal and life coping skills are discussed as "Equally important, do we teach them to ask questions, or do we teach them only to passively receive our wisdom?". Further, the author asserts "From the cocooned world of school", making the assertion made in the statement a valid one.
Q 53. There are three points P,Q and R on a straight line such that PQ:QR-3:5. If n is the number of possible values of PQ:PR, then what is n equal to ?
(a) 1
(b) 2
(c) 3
(d) 4
Ans. (b)
Solution
We have to arrange three points P, Q, and R on a straight line, such that PQ : QR = 3 : 5
Three points can be arranged in 3!, i.e. 6 ways.
However, the number of possible values of PQ : PR will be only 2, i.e. n = 2. They have been represented below.
Q 54. On a chess board, in how many different ways can 6 consecutive squares be chosen on the diagonals along a straight path ?
(a) 4
(b) 6
(c) 8
(d) 12
Ans. (b)
Solution
Here’s a typical 8 × 8 chess board:
There are two diagonals, each having 8 squares.
On one diagonal, 6 consecutive squares can be chosen in 3 ways.
So, total number of ways of choosing 6 consecutive squares on the diagonals along a straight path = 3 + 3 = 6
Q 55. In the series_b_a_ba_b_abab_aab; fill in the six blanks (_) using one of the following given four choices such that the series follows a specific order.
(a) bababa
(b) baabba
(c) bbaabb
(d) ababab
Ans. (d)
Solution
The given series is: _b_a_ba_b_abab_aab
The pattern being followed in the above series is: abb, then aab. Again abb, and then aab, and so on.
The blanks have been highlighted below:
a b b / a a b / a b b / a ab / ab b / aab
Q 56. Using 2, 2, 3, 3, 3 as digits, how many distinct numbers greater than 30000 can be formed?
(a) 3
(b) 6
(c) 9
(d) 12
Ans. (b)
Solution
For the number to be greater than 30000, it must start with the digit 3. Also, as only 5 digits are given to us, all must be used.
3 _ _ _ _
The 4 blanks have to be filled by two 2’s and two 3’s.
Number of ways to do so = 4!/(2! 2!) = 6
These numbers are: 33322, 33232, 33223, 32332, 32323, and 32233.
Q 57. Consider the following statements :
1. The sum of 5 consecutive integers can be 100.
2. The product of three consecutive natural numbers can be equal to their sum.
which of the above statements is/are correct?
(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2
Ans. (c)
Solution
Considering statement 1:
Let the 5 consecutive numbers be x-2, x-1, x, x+1, x+2
Their sum = 5x = 100
Or x = 20
So, the numbers are 18, 19, 20, 21, and 22. Statement 1 is correct.
Considering statement 2:
We know that, 1 + 2 + 3 = 6
And 1 × 2 × 3 = 6
So, Statement 2 is correct too.
Q 58. A cubical vessel of side 1 m is filled completely with water. How many millilitres of water is contained in it (neglect thickness of the vessel) ?
(a) 1000
(b) 10000
(c) 100000
(d) 1000000
Ans. (d)
Solution
Volume of the cube = Side × Side × Side = 1 × 1 × 1 = 1 cubic meter
Now, 1 cubic meter = 1000000 mililiters
Q 59. There are 6 persons arranged in a row. Another person has to shake hands with 3 of them so that he should not shake hands with two consecutive persons. In how many distinct possible combinations can the handshakes take place?
(a) 3
(b) 4
(c) 5
(d) 6
Ans. (b)
Solution
Method I:
We just need to choose 3 persons out of 6, such that no two of them are together.
Number of ways to choose 3 out of 6 people, without any constraints = 6C3 = (6 × 5 × 4)/(3 × 2 × 1) = 20
Number of ways to choose 3 out of 6 people, such that all of them are together = 4
Number of ways to choose 3 out of 6 people, such that two of them are together = 3 + 2 + 2 + 2 + 3 = 12
So, required answer = 20 – (4 + 12) = 4
Method II:
Let the six individuals be numbered 1, 2, 3, 4, 5, and 6.
So, another person can shake hands with:
1, 3, 5
1, 4, 6
1, 3, 6
2, 4, 6
Hence, he can shake hands in 4 ways.
Q 60. An amount of money was distributed among A, B and c in the ratio p : q : r.
Consider the following statements :
1. A gets the maximum share if p is greater than (q+r).
2. C gets the minimum share if r is less than (p+q).
Which of the above statements is/are correct ?
(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2
Ans. (a)
Solution
Ratio of distribution of money among A, B and C is p : q : r.
Considering statement 1:
If p > (q + r), then p is definitely the largest number.
So, A must have got the maximum share. Hence, statement 1 is correct.
Considering statement 2:
If r < (p + q), then r may or may not be the smallest number.
For example, 5 < (2 + 4)
So, C may or may not have got the minimum share. Hence, statement 2 is incorrect.
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