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CAT 1997 Question Paper with Solutions

68 questions in 120 minutes, in three timed sections. Below: how the paper is built, the topics each section tested, and a solved sample from every section. Take the whole paper in the simulator to get your Score Waterfall, Topic ROI Map and Strategic IQ.

Paper structure and topics

VARC

Verbal Ability & Reading Comprehension

24 questions · 24 MCQ · 0 TITA

  • Reading Comprehension · 20
  • Verbal Ability · 4

DILR

Data Interpretation & Logical Reasoning

22 questions · 22 MCQ · 0 TITA

  • Data Interpretation · 18
  • Algebra · 2
  • Logical Reasoning · 1
  • Number System · 1

QA

Quantitative Ability

22 questions · 22 MCQ · 0 TITA

  • Arithmetic · 8
  • Algebra · 7
  • Geometry · 3
  • Number System · 3
  • Modern Math · 1

Sample questions with solutions

14 of the 68 questions: the first passage, the first DILR set and the first QA questions of the paper.

VARC · Verbal Ability & Reading Comprehension

Passage

I think that it would be wrong to ask whether 50 years of India's Independence are an achievement or a failure. It would be better to see things as evolving. It's not an either-or question. My idea of the history of India is slightly contrary to the Indian idea. India is a country that, in the north, outside Rajasthan, was ravaged and intellectually destroyed to a large extent by the invasions that began in about AD 1000 by forces and religions that India had no means of understanding.

The invasions are in all the schoolbooks. But I don't think that people understand that every invasion, every war, every campaign, was accompanied by slaughter, a slaughter always of the most talented people in the country. So these wars, apart from everything else led to a tremendous intellectual depletion of the country. I think that in the British period, and in the 50 years after the British period, there has been a kind of regrouping or recovery, a very slow revival of energy and intellect. This isn't an idea that goes with the vision of the grandeur of old India and all that sort of rubbish. That idea is a great simplification and it occurs because it is intellectually, philosophically easier for Indians to manage.

What they cannot manage, and what they have not yet come to terms with, is that ravaging of all the north of India by various conquerors. That was ruined not by the act of nature, but by the hand of man. It is so painful that few Indians have begun to deal with it. It is much easier to deal with British imperialism. That is a familiar topic, in India and Britain. What is much less familiar is the ravaging of India before the British. What happened from AD 1000 onwards, really, is such a wound that it is almost impossible to face. Certain wounds are so bad that they can't be written about. You deal with that kind of pain by hiding from it. You retreat from reality. I do not think, for example, that the Incas of Peru or the native people of Mexico have ever got over their defeat by the Spaniards. In both places the head was cut off. I think the pre-British ravaging of India was as bad as that.

In the place of knowledge of history, you have various fantasies about the village republic and the Old Glory. There is one big fantasy that Indians have always found solace in: about India having the capacity for absorbing its conquerors. This is not so. India was laid low by its conquerors. I feel the past 150 years have been years of every kind of growth. I see the British period and what has continued after that as one period. In that time, there has been a very slow intellectual recruitment. I think every Indian should make the pilgrimage to the site of the capital of the Vijayanagar empire, just to see what the invasion of India led to. They will see a totally destroyed town. Religious wars are like that. People who see that might understand what the centuries of slaughter and plunder meant. War isn't a game. When you lost that kind of war, your town was destroyed, the people who built the towns were destroyed. You are left with a headless population. That's where modern India starts from. The Vijayanagar capital was destroyed in 1565. It is only now that the surrounding region has begun to revive.

A great chance has been given to India to start up again, and I feel it has started up again. The questions about whether 50 years of India since Independence have been a failure or an achievement are not the questions to ask.

In fact, I think India is developing quite marvelously, people thought — even Mr Nehru thought — that development and new institutions in a place like Bihar, for instance, would immediately lead to beauty. But it doesn't happen like that. When a country as ravaged as India, with all its layers of cruelty, begins to extend justice to people lower down, it's a very messy business. It's not beautiful, it's extremely messy. And that's what you have now, all these small politicians with small reputations and small parties. But this is part of growth, this is part of development. You must remember that these people, and the people they represent, have never had rights before. When the oppressed have the power to assert themselves, they will behave badly. It will need a couple of generations of security, and knowledge of institutions, and the knowledge that you can trust institutions — it will take at least a couple of generations before people in that situation begin to behave well.

People in India have known only tyranny. The very idea of liberty is a new idea. The rulers were tyrants. The tyrants were foreigners. And they were proud of being foreign. There's a story that anybody could run and pull a bell and the emperor would appear at his window and give justice. This is a child's idea of history — the slave's idea of the ruler's mercy. When the people at the bottom discover that they hold justice in their own hands, the earth moves a little. You have to expect these earth movements in India. It will be like this for a hundred years. But it is the only way. It's painful and messy and primitive and petty, but it’s better that it should begin. It has to begin. If we were to rule people according to what we think fit, that takes us back to the past when people had no voices.

With self-awareness all else follows. People begin to make new demands on their leaders, their fellows, on themselves. They ask for more in everything. They have a higher idea of human possibilities. They are not content with what they did before or what their fathers did before. They want to move. That is marvellous. That is as it should be.

I think that within every kind of disorder now in India there is a larger positive movement. But the future will be fairly chaotic. Politics will have to be at the level of the people now. People like Nehru were colonial — style politicians. They were to a large extent created and protected by the colonial order. They did not begin with the people. Politicians now have to begin with the people. They cannot be too far above the level of the people. They are very much part of the people.

It is important that self-criticism does not stop. The mind has to work, the mind has to be active, there has to be an exercise of the mind. I think it's almost a definition of a living country that it looks at itself, analyses itself at all times. Only countries that have ceased to live can say it's all wonderful.

Question 1 · MCQ

The central thrust of the passage is that
  1. A.
    India is gearing up for a new awakening.
    ✓ Correct
  2. B.
    India is going back to its past status.
  3. C.
    India is yet to understand itself.
  4. D.
    India's glorious past is a figment of the imagination.
Solution
The author rejects the achievement/failure framing and describes a slow recovery: 'a kind of regrouping or recovery', 'India is developing quite marvelously', and 'within every kind of disorder now in India there is a larger positive movement'. The central thrust is forward-looking revival, making option 1 the best fit.

Question 2 · MCQ

The writer's attitude is
  1. A.
    excessively critical of India.
  2. B.
    insightful.
    ✓ Correct
  3. C.
    cynical.
  4. D.
    cold.
Solution
The writer is critical of romanticised history but gives a reasoned, penetrating diagnosis of India's wounds and messy growth. That measured, perceptive stance is best called 'insightful' rather than excessively critical, cynical, or cold.

Question 3 · MCQ

The writer has given the example of the Vijayanagar kingdom in order to drive home the point that
  1. A.
    Indians should know their historical sites.
  2. B.
    Indians should be aware of the existence of such a historic past.
  3. C.
    it is time that India came to terms with the past.
    ✓ Correct
  4. D.
    All of these
Solution
The Vijayanagar example follows the statement that Indians have not come to terms with the pre-British ravaging. The destroyed capital makes that unacknowledged wound concrete, so the point is that India needs to come to terms with its past.

Question 4 · MCQ

The writer is against
  1. A.
    the child's view of history.
    ✓ Correct
  2. B.
    taking a critical stand on history.
  3. C.
    indulging in the details of the past.
  4. D.
    None of these
Solution
The writer explicitly calls the emperor's bell story 'a child's idea of history — the slave's idea of the ruler's mercy'. Thus he is against such a naive, child's view of history.

Question 5 · MCQ

According to the writer, India's regeneration and revival took place
  1. A.
    in the British period.
  2. B.
    after the British period.
  3. C.
    during and after the British period.
    ✓ Correct
  4. D.
    a long time after the British left.
Solution
The passage states that 'in the British period, and in the 50 years after the British period, there has been a kind of regrouping or recovery' and treats the British period and what followed as one continuous period of growth. Hence the revival took place during and after the British period.

DILR · Data Interpretation & Logical Reasoning

Set

Each of these items has a question followed by two statements, I and II. Mark the answer
a. if the question can be answered with the help of one statement alone.
b. if the question can be answered with the help of any one statement independently.
c. if the question can be answered with the help of both statements together.
d. if the question cannot be answered even with the help of both statements together.

Question 1 · MCQ

What is the value of \(a^3 + b^3\)?
I. \(a^2 + b^2 = 22\)
II. \(ab = 3\)
  1. A.
    Statement I alone is sufficient
  2. B.
    Either statement alone is sufficient
  3. C.
    Both statements together are sufficient
  4. D.
    Both statements together are not sufficient
    ✓ Correct
Solution
Using both statements:

\((a+b)^2 = a^2 + b^2 + 2ab = 22 + 2(3) = 28\)
So \(a+b = \pm 2\sqrt7\).

Now,
\(a^3+b^3 = (a+b)(a^2 - ab + b^2)\)
\(= (a+b)(22 - 3) = 19(a+b)\).

Since \(a+b\) can be either \(2\sqrt7\) or \(-2\sqrt7\), \(a^3+b^3\) can be either \(38\sqrt7\) or \(-38\sqrt7\).
Thus the value is not unique even after using both statements.

Therefore, both statements together are not sufficient.

Question 2 · MCQ

Is the number completely divisible by 99?
I. The number is divisible by 9 and 11 simultaneously.
II. If the digits of the number are reversed, the number is divisible by 9 and 11.
  1. A.
    Statement I alone is sufficient
  2. B.
    Either statement alone is sufficient
    ✓ Correct
  3. C.
    Both statements together are sufficient
  4. D.
    Both statements together are not sufficient
Solution
A number divisible by both 9 and 11 is divisible by their product 99, since 9 and 11 are coprime.

Statement I directly says the number is divisible by both 9 and 11, so it is sufficient.

Statement II says the reversed number is divisible by both 9 and 11.
Divisibility by 9 depends only on the digit sum, which does not change on reversing the digits, so the original number is also divisible by 9.
Divisibility by 11 uses the alternating digit-sum test; reversing the digits at most changes the sign of the alternating sum, so divisibility by 11 is preserved. Hence the original number is also divisible by 11.
Thus the original number is divisible by both 9 and 11, and hence by 99.

Therefore either statement alone is sufficient.

Question 3 · MCQ

A person is walking from Mali to Pali, which lies to its north-east. What is the distance between Mali and Pali?
I. When the person has covered \(\frac{1}{3}\) the distance, he is 3 km east and 1 km north of Mali.
II. When the person has covered \(\frac{2}{3}\) the distance, he is 6 km east and 2 km north of Mali.
  1. A.
    Statement I alone is sufficient
  2. B.
    Either statement alone is sufficient
    ✓ Correct
  3. C.
    Both statements together are sufficient
  4. D.
    Both statements together are not sufficient
Solution
Let the straight-line displacement from Mali to Pali be \((E, N)\).

From I:
\(\frac{1}{3}(E,N)=(3,1)\), so \(E=9, N=3\).
Distance \(= \sqrt{9^2+3^2}=\sqrt{90}=3\sqrt{10}\) km. Hence I alone is sufficient.

From II:
\(\frac{2}{3}(E,N)=(6,2)\), which again gives \(E=9, N=3\).
Same distance; hence II alone is also sufficient.

So the question can be answered using either statement alone.

Question 4 · MCQ

What is the value of x and y?
I. \(3x + 2y = 45\) II. \(10.5x + 7y = 157.5\)
  1. A.
    Statement I alone is sufficient
  2. B.
    Either statement alone is sufficient
  3. C.
    Both statements together are sufficient
  4. D.
    Both statements together are not sufficient
    ✓ Correct
Solution
I: \(3x+2y=45\).

II: \(10.5x+7y=157.5\).

Divide II by \(3.5\):
\(3x+2y=45\), which is exactly the same as I.

So the two statements provide only one independent equation in two unknowns. There are infinitely many \((x,y)\) pairs, so the values cannot be determined even using both statements together.

QA · Quantitative Ability

Question 1 · MCQ

What is the average weight of the students in group D?
  1. A.
    More than the average weight of A
  2. B.
    More than the average weight of C
  3. C.
    Less than the average weight of C
  4. D.
    Cannot be determined
    ✓ Correct
Solution
Let average weights of groups A and C be \(a\) and \(c\).

Group D has \(15+25=40\) students, and its average is:

\[d=\frac{15a+25c}{40}\].

This is a weighted average of \(a\) and \(c\). Its value depends on the actual weights of A and C, which are not given.

For example, if \(c>a\), then \(d>a\); if \(a>c\), then \(d<c\). So no definite comparison can be made.

Question 2 · MCQ

A student gets an aggregate of 60% marks in five subjects in the ratio 10 : 9 : 8 : 7 : 6. If the passing marks are 50% of the maximum marks and each subject has the same maximum marks, in how many subjects did he pass the examination?
  1. A.
    2
  2. B.
    3
  3. C.
    4
    ✓ Correct
  4. D.
    5
Solution
Let the maximum marks in each subject be \(M\).

Total maximum marks \(=5M\).

Aggregate \(60%\) means total marks obtained:

\[0.6 \times 5M = 3M\].

Marks in the five subjects are in the ratio \(10:9:8:7:6\), so let them be \(10x, 9x, 8x, 7x, 6x\).

\[40x = 3M \Rightarrow x = \frac{3M}{40}\].

Subject-wise percentages:

\[10x=75%,\quad 9x=67.5%,\quad 8x=60%,\quad 7x=52.5%,\quad 6x=45%\].

Passing marks are \(50%\). Therefore, the student passed in 4 subjects.

Question 3 · MCQ

In how many ways can eight directors, the vice chairman and chairman of a firm be seated at a round table, if the chairman has to sit between the vice chairman and a director?
  1. A.
    9! \(\times 2\)
  2. B.
    2 \(\times 8\)!
    ✓ Correct
  3. C.
    2 \(\times 7\)!
  4. D.
    None of these
Solution
Fix the chairman at a reference position. His two neighbours must be the vice-chairman on one side and one of the 8 directors on the other.
Choose the side for the vice-chairman: \(2\) ways.
Choose the neighbouring director: \(8\) ways.
Arrange the remaining 7 directors in the remaining seats: \(7!\) ways.
Total \(= 2 \times 8 \times 7! = 2 \times 8!\).
Hence option 2.

Question 4 · MCQ

If \(\log_2 [\log_7 (x^2 - x + 37)] = 1\), then what could be the value of ‘x’?
  1. A.
    3
  2. B.
    5
  3. C.
    4
    ✓ Correct
  4. D.
    None of these
Solution
\(\log_2[\log_7(x^2 - x + 37)] = 1\)
So \(\log_7(x^2 - x + 37) = 2\).
Thus \(x^2 - x + 37 = 49\).
\(x^2 - x - 12 = 0\)
\((x - 4)(x + 3) = 0\)
So \(x = 4\) or \(x = -3\).
Among the options, \(x = 4\). Hence option 3.

Question 5 · MCQ

After allowing a discount of 11.11%, a trader still makes a gain of 14.28%. At how many percentage above the cost price does he mark on his goods?
  1. A.
    28.56%
    ✓ Correct
  2. B.
    35%
  3. C.
    22.22%
  4. D.
    None of these
Solution
Let cost price be \(C\).

Given gain \(14.28% = \frac{1}{7}\), so
\(SP = \frac{8}{7}C\).

After discount \(11.11% = \frac{1}{9}\),
\(SP = \frac{8}{9}MP\).

Thus,
\(\frac{8}{9}MP = \frac{8}{7}C\)
\(MP = \frac{9}{7}C\).

So markup above cost price is \(\frac{2}{7} = 28.57%\).

The other 54 questions are in the simulator

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