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CAT 2001 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 · 22
  • Verbal Ability · 2

DILR

Data Interpretation & Logical Reasoning

22 questions · 22 MCQ · 0 TITA

  • Data Interpretation · 12
  • Logical Reasoning · 10

QA

Quantitative Ability

22 questions · 22 MCQ · 0 TITA

  • Arithmetic · 8
  • Algebra · 6
  • Number System · 4
  • Geometry · 3
  • Logical Reasoning · 1

Sample questions with solutions

15 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

The Union Government’s present position vis-a-vis the upcoming United Nations conference on racial and related discrimination world-wide seems to be the following: discuss race please, not caste; caste is our very own and not at all as bad as you think. The gross hypocrisy of that position has been lucidly underscored by Kancha Ilaiah. Explicitly, the world community is to be cheated out of considering the matter on the technicality that caste is not, as a concept, tantamount to a racial category. Internally, however, allowing the issue to be put on agenda at the said conference would, we are patriotically admonished, damage the country’s image. Somehow, India’s virtual beliefs elbow out concrete actualities. Inverted representations, as we know, have often been deployed in human histories as balm for the forsaken — religion being the most persistent of such inversions. Yet, we would humbly submit that if globalising our markets is thought as good for the ‘national’ pocket, globalising our social inequities might not be so bad for the mass of our people. After all, racism was as uniquely institutionalised in South Africa as caste discrimination has been within our society; why then can’t we permit the world community to express itself on the latter with a fraction of the zeal with which, through the years, we pronounced on the former?

As to the technicality about whether or not caste is admissible into an agenda about race (that the conference is also about ‘related discriminations’ tends to be forgotten), a reputed sociologist has recently argued that where race is a ‘biological’ category caste is a ‘social’ one. Having earlier fiercely opposed implementation of the Mandal Commission Report, the said sociologist is at least to be complemented now for admitting, however tangentially, that caste discrimination is a reality, although, in his view, incompatible with racial discrimination. One would like quickly to offer the hypothesis that biology, in important ways that affect the lives of many millions, is in itself perhaps a social construction. But let us look at the matter in another way.

If it is agreed — as per the position today at which anthropological and allied scientific determinations rest — that the entire race of homo sapiens derived from an originary black African female (called ‘Eve’), then one is hard put to understand how, one some subsequent ground, ontological distinctions are to be drawn either between races or castes. Let us also underline the distinction between the supposition that we are all god’s children and the rather more substantiated argument about our descent from ‘Eve’, lest both positions are thought to be equally diversionary. It then stands to reason that all subsequent distinctions are, in modern parlance, ‘constructed’ ones, and like all ideological constructions, attributable to changing equations between knowledge and power among human communities through contested histories here, there, and elsewhere.

This line of thought receives, thankfully, extremely consequential buttress from the findings of the Human Genome project. Contrary to earlier (chiefly 19th-century colonial) persuasions on the subject of race, as well as, one might add, the somewhat infamous Jensen offerings in the 20th century from America, those finding deny genetic difference between ‘races’. If anything, they suggest that environmental factors impinge on gene-function, as a dialectic seems to unfold between nature and culture. It would thus seem that ‘biology’ as the constitution of pigmentation enters the picture first only as a part of that dialectic. Taken together, the originary mother stipulation and the Genome findings ought indeed to furnish ground for human equality across the board, as well as yield policy initiatives towards equitable material dispensations aimed at building a global order where, in Hegel’s stirring formulation, only the rational constitutes the right. Such, sadly, is not the case as everyday fresh arbitrary grounds for discrimination are constructed in the interests of sectional dominance.

Question 1 · MCQ

When the author writes ‘globalising our social inequities’, the reference is to
  1. A.
    going beyond an internal deliberation on social inequity.
    ✓ Correct
  2. B.
    dealing with internal poverty through the economic benefits of globalisation.
  3. C.
    going beyond an internal delimitation on social inequity.
  4. D.
    achieving disadvantaged people’s empowerment, globally.
Solution
The phrase appears in the context of the UN conference on racial discrimination: the author argues that if globalising markets is beneficial, then subjecting our domestic social inequities (like caste) to global scrutiny should also be acceptable. Thus, it refers to moving beyond internal debate and allowing international discussion of social inequity.
Option 1 matches this meaning exactly. Options 2 and 4 distort the intent; option 3 uses ‘delimitation’ which is less precise.

Question 2 · MCQ

According to the author, ‘inverted representations as balm for the forsaken’
  1. A.
    is good for the forsaken and often deployed in human histories.
  2. B.
    is good for the forsaken, but not often deployed historically for the oppressed.
  3. C.
    occurs often as a means of keeping people oppressed.
    ✓ Correct
  4. D.
    occurs often to invert the status quo.
Solution
The author states that ‘inverted representations… have often been deployed in human histories as balm for the forsaken — religion being the most persistent of such inversions.’ ‘Balm’ suggests a false comfort, not genuine good. Thus, such representations are a tool to pacify the oppressed, keeping them in subjugation.
Option 3 captures this function correctly. Option 1 misinterprets ‘balm’ as genuinely good; option 2 incorrectly says ‘not often deployed’; option 4 misses the oppressive purpose.

Question 3 · MCQ

Based on the passage, which broad areas unambiguously fall under the purview of the UN conference being discussed?
A. Racial prejudice
B. Racial pride
C. Discrimination, racial or otherwise
D. Caste-related discrimination
E. Race-related discrimination
  1. A.
    A and E
    ✓ Correct
  2. B.
    C and E
  3. C.
    A, C and E
  4. D.
    B, C and D
Solution
The conference is explicitly on ‘racial and related discrimination.’ Thus, racial prejudice (A) and race-related discrimination (E) clearly fall within its scope. ‘Discrimination, racial or otherwise’ (C) is too broad—the conference is only about related discrimination, not all forms. Caste-related discrimination (D) is exactly what the Indian government wants to exclude, so it is not unambiguously included. Hence, only A and E are certain.

Question 4 · MCQ

According to the author, the sociologist who argued that race is a ‘biological’ category and caste is a ‘social’ one,
  1. A.
    generally shares the same orientation as the author’s on many of the central issues discussed.
  2. B.
    tangentially admits to the existence of ‘caste’ as a category.
    ✓ Correct
  3. C.
    admits the incompatibility between the people of different race and caste.
  4. D.
    admits indirectly that both caste-based prejudice and racial discrimination exist.
Solution
The author says the sociologist, who earlier opposed the Mandal Commission, now ‘admits, however tangentially, that caste discrimination is a reality.’ The sociologist’s argument that caste is a ‘social’ category implies he recognises the existence of caste as a category. Option 2 captures this indirect admission precisely. Option 4 adds ‘racial discrimination,’ which the sociologist does not explicitly admit; options 1 and 3 are unsupported.

Question 5 · MCQ

An important message in the passage, if one accepts a dialectic between nature and culture, is that
  1. A.
    the results of the Human Genome Project reinforces racial differences.
  2. B.
    race is at least partially a social construct.
    ✓ Correct
  3. C.
    discrimination is at least partially a social construct.
  4. D.
    caste is at least partially a social construct.
Solution
The passage argues that biology, including pigmentation, is part of a dialectic between nature and culture. The Human Genome Project shows no genetic basis for race; environmental factors influence gene function. Hence, race emerges as a social construct, not a fixed biological category. Option 2 states this directly. Options 3 and 4 are broader or less central, while option 1 contradicts the Genome findings.

DILR · Data Interpretation & Logical Reasoning

Set

Each question is followed by two statements, I and II.
Mark
a. if the question can be answered by one of the statements alone and not by the other.
b. if the question can be answered by using either statement alone.
c. if the question can be answered by using both the statements together, but cannot be answered by using either statement alone.
d. if the question cannot be answered even by using both statements together.

Question 1 · MCQ

What are the values of m and n?
I. n is an even integer, m is an odd integer, and m is greater than n.
II. Product of m and n is 30.
  1. A.
    a
  2. B.
    b
  3. C.
    c
  4. D.
    d
    ✓ Correct
Solution
Using both statements together:
  • I: n is even, m is odd, m > n.
  • II: m × n = 30.
Possible integer pairs for (m, n) with product 30 include (15, 2), (−1, −30), (−3, −10), (−5, −6), etc. Among these, satisfying I (m odd, n even, m > n) are (15, 2), (−1, −30), (−3, −10), and others. Since multiple solutions exist, the question cannot be answered even using both statements.

Question 2 · MCQ

Is Country X’s GDP higher than country Y’s GDP?
I. GDPs of the countries X and Y have grown over the past 5 years at compounded annual rate of 5% and 6% respectively.
II. Five years ago, GDP of country X was higher than that of country Y.
  1. A.
    a
  2. B.
    b
  3. C.
    c
  4. D.
    d
    ✓ Correct
Solution
Let initial GDPs 5 years ago be \(X_0\) and \(Y_0\). Statement II says \(X_0 > Y_0\). Statement I gives growth: \(X = X_0(1.05)^5\), \(Y = Y_0(1.06)^5\). To decide if \(X > Y\), we compare \(X_0(1.05)^5\) and \(Y_0(1.06)^5\). Since \(1.05^5 < 1.06^5\), the outcome depends on how much larger \(X_0\) is. If \(X_0\) is only slightly bigger, \(Y\) could overtake; if \(X_0\) is much bigger, \(X\) may still be larger. Thus both statements together are insufficient.

Question 3 · MCQ

What is the value of X?
I. X and Y are unequal even integers, less than 10, and \(\frac{X}{Y}\) is an odd integer.
II. X and Y are even integers, each less than 10, and product of X and Y is 12.
  1. A.
    a
    ✓ Correct
  2. B.
    b
  3. C.
    c
  4. D.
    d
Solution
Consider positive even integers less than 10: {2, 4, 6, 8}.
From I: X and Y are unequal, and X/Y is an odd integer.
Possible pairs: (6, 2) gives 6/2 = 3 (odd); no other pair works (e.g., 4/2 = 2 even; 8/2 = 4 even; 8/4 = 2 even). Hence X = 6 uniquely.
From II alone: X × Y = 12 with X, Y even < 10. Pairs: (2, 6) and (6, 2). X can be 2 or 6, not unique.
Thus statement I alone is sufficient, but II alone is not.

Question 4 · MCQ

On a given day a boat ferried 1,500 passengers across the river in 12 hr. How many round trips did it make?
I. The boat can carry 200 passengers at any time.
II. It takes 40 min each way and 20 min of waiting time at each terminal.
  1. A.
    a
    ✓ Correct
  2. B.
    b
  3. C.
    c
  4. D.
    d
Solution
Statement I alone gives only the boat's capacity (200 passengers per trip). Without time per trip, the number of round trips cannot be determined.

Statement II alone gives the time per round trip: 40 min each way + 20 min waiting at each terminal = 2 hours per round trip. Total time is 12 hours, so the boat made exactly \(12/2 = 6\) round trips. The passenger count is irrelevant.

Thus, statement II alone is sufficient, but statement I alone is not.

Question 5 · MCQ

What will be the time for downloading software?
I. Transfer rate is 6 kilobytes per second.
II. The size of the software is 4.5 megabytes.
  1. A.
    a
  2. B.
    b
  3. C.
    c
    ✓ Correct
  4. D.
    d
Solution
Time = size ÷ transfer rate.

Statement I gives the rate but not the size.
Statement II gives the size but not the rate.
Only with both statements can we compute the time: \( \frac{4.5 \text{ MB}}{6 \text{ KB/s}} = \frac{4.5 \times 1024 \text{ KB}}{6 \text{ KB/s}} = 768\) seconds.

QA · Quantitative Ability

Question 1 · MCQ

A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6 : 7 : 8 : 9 : 10. In all papers together, the candidate obtained 60% of the total marks. Then the number of papers in which he got more than 50% marks is
  1. A.
    2
  2. B.
    3
  3. C.
    4
    ✓ Correct
  4. D.
    5
Solution
Let full marks per paper = \(F\). Total marks = \(5F\).
Marks in papers: \(6k, 7k, 8k, 9k, 10k\). Total = \(40k\).
\(40k = 0.6 \times 5F = 3F\) ⇒ \(F = \frac{40k}{3}\).
50% marks = \(\frac{1}{2}F = \frac{20k}{3} \approx 6.67k\).
Papers with marks >50%: \(7k, 8k, 9k, 10k\) → 4 papers.

Question 2 · MCQ

Let x, y and z be distinct integers. x and y are odd and positive, and z is even and positive. Which one of the following statements cannot be true?
  1. A.
    \(y(x - z)^2\) is even
    ✓ Correct
  2. B.
    \(y^2(x - z)\) is odd
  3. C.
    \(y(x - z)\) is odd
  4. D.
    \(z(x - y)^2\) is even
Solution
Option 1: \(y\) is odd, \(x-z\) is odd (odd − even), so \((x-z)^2\) is odd. Product is odd, not even. Thus cannot be true.
Others: Option 2: \(y^2\) odd, \(x-z\) odd → odd. Option 3: odd × odd = odd. Option 4: \(z\) even → product even. Only option 1 cannot be true.

Question 3 · MCQ

If x > 5 and y < –1, then which of the following statements is true?
  1. A.
    (x + 4y) > 1
  2. B.
    x > –4y
  3. C.
    –4x < 5y
  4. D.
    None of these
    ✓ Correct
Solution
Given x > 5 and y < –1. Check the options with counterexamples:

(1) (x + 4y) > 1: Take x = 6, y = –100 → 6 – 400 = –394 ≯ 1. ❌

(2) x > –4y: Take x = 6, y = –2 → –4y = 8, so 6 > 8 is false. ❌

(3) –4x < 5y: Take x = 10, y = –100 → –40 < –500 is false. ❌

Hence none of the statements is always true.

Question 4 · MCQ

Of 128 boxes of oranges, each box contains at least 120 and at most 144 oranges. The number of boxes containing the same number of oranges is at least
  1. A.
    5
  2. B.
    103
  3. C.
    6
    ✓ Correct
  4. D.
    Cannot be determined
Solution
Possible numbers of oranges per box: from 120 to 144 inclusive → 144 – 120 + 1 = 25 distinct values.

With 128 boxes, by the pigeonhole principle, at least one value must occur in ⌈128 ÷ 25⌉ = 6 boxes.

Question 5 · MCQ

A certain city has a circular wall around it, and this wall has four gates pointing north, south, east and west. A house stands outside the city, 3 km north of the north gate, and it can just be seen from a point 9 km east of the south gate. What is the diameter of the wall that surrounds the city?
  1. A.
    6 km
  2. B.
    9 km
    ✓ Correct
  3. C.
    12 km
  4. D.
    None of these
Solution
Let the radius be \(r\) km.
Place centre at origin. N gate \((0,r)\), S gate \((0,-r)\).
House H: 3 km north of N → \((0, r+3)\).
Point P: 9 km east of S → \((9, -r)\).
For the house to be just visible, line PH is tangent to the circle.
Distance from centre to line = \(r\).

Slope of PH = \(-\frac{2r+3}{9}\).
Line equation: \((2r+3)x + 9y - 9(r+3)=0\).
Distance: \(\frac{9(r+3)}{\sqrt{(2r+3)^2+81}} = r\).
Square: \(81(r+3)^2 = r^2[(2r+3)^2+81]\).
Simplify to \(4r^4+12r^3+9r^2-486r-729=0\).

Testing \(r=\frac{9}{2}\) satisfies the equation, so \(r = 4.5\) km.
Diameter \(= 2r = 9\) km.

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