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CAT 2006 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 · 15
  • Verbal Ability · 9

DILR

Data Interpretation & Logical Reasoning

22 questions · 22 MCQ · 0 TITA

  • Logical Reasoning · 12
  • Data Interpretation · 10

QA

Quantitative Ability

22 questions · 22 MCQ · 0 TITA

  • Algebra · 8
  • Arithmetic · 5
  • Geometry · 5
  • 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

Our propensity to look out for regularities, and to impose laws upon nature, leads to the psychological phenomenon of dogmatic thinking or, more generally, dogmatic behaviour: we expect regularities everywhere and attempt to find them even where there are none; events which do not yield to these attempts we are inclined to treat as a kind of ‘background noise’; and we stick to our expectations even when they are inadequate and we ought to accept defeat. This dogmatism is to some extent necessary. It is demanded by a situation which can only be dealt with by forcing our conjectures upon the world. Moreover, this dogmatism allows us to approach a good theory in stages, by way of approximations: if we accept defeat too easily, we may prevent ourselves from finding that we were very nearly right.

It is clear that this dogmatic attitude, which makes us stick to our first impressions, is indicative of a strong belief; while a critical attitude, which is ready to modify its tenets, which admits doubt and demands tests, is indicative of a weaker belief. Now according to Hume’s theory, and to the popular theory, the strength of a belief should be a product of repetition; thus it should always grow with experience, and always be greater in less primitive persons. But dogmatic thinking, an uncontrolled wish to impose regularities, a manifest pleasure in rites and in repetition as such, is characteristic of primitives and children; and increasing experience and maturity sometimes create an attitude of caution and criticism rather than of dogmatism.

My logical criticism of Hume’s psychological theory, and the considerations connected with it, may seem a little removed from the field of the philosophy of science. But the distinction between dogmatic and critical thinking, or the dogmatic and the critical attitude, brings us right back to our central problem. For the dogmatic attitude is clearly related to the tendency to verify our laws and schemata by seeking to apply them and to confirm them, even to the point of neglecting refutations, whereas the critical attitude is one of readiness to change them — to test them; to refute them; to falsify them, if possible. This suggests that we may identify the critical attitude with the scientific attitude, and the dogmatic attitude with the one which we have described as pseudo-scientific. It further suggests that genetically speaking the pseudo-scientific attitude is more primitive than, and prior to, the scientific attitude: that it is a pre-scientific attitude. And this primitivity or priority also has its logical aspect. For the critical attitude is not so much opposed to the dogmatic attitude as super-imposed upon it: criticism must be directed against existing and influential beliefs in need of critical revision — in other words, dogmatic beliefs. A critical attitude needs for its raw material, as it were, theories or beliefs which are held more or less dogmatically.

Thus, science must begin with myths, and with the criticism of myths; neither with the collection of observations, nor with the invention of experiments, but with the critical discussion of myths, and of magical techniques and practices. The scientific tradition is distinguished from the pre-scientific tradition in having two layers. Like the latter, it passes on its theories; but it also passes on a critical attitude towards them. The theories are passed on, not as dogmas, but rather with the challenge to discuss them and improve upon them.

The critical attitude, the tradition of free discussion of theories with the aim of discovering their weak spots so that they may be improved upon, is the attitude of reasonableness, of rationality. From the point of view here developed, all laws, all theories, remain essentially tentative, or conjectural, or hypothetical, even when we feel unable to doubt them any longer. Before a theory has been refuted we can never know in what way it may have to be modified.

Question 1 · MCQ

In the context of science, according to the passage, the interaction of dogmatic beliefs and critical attitude can be best described as:
  1. A.
    A duel between two warriors in which one has to die.
  2. B.
    The effect of a chisel on a marble stone while making a sculpture.
    ✓ Correct
  3. C.
    The feedshare (natural gas) in fertilizer industry being transformed into fertilizers.
  4. D.
    A predator killing its prey.
  5. E.
    The effect of fertilizers on a sapling.
Solution
The passage says: “A critical attitude needs for its raw material, as it were, theories or beliefs which are held more or less dogmatically” and that criticism is “super-imposed upon” dogmatic beliefs. This suggests a shaping/refining interaction, like a chisel (critical attitude) working on raw marble (dogmatic beliefs) to produce a sculpture (refined scientific theory). Option 2 captures this exactly.

Question 2 · MCQ

According to the passage, the role of a dogmatic attitude or dogmatic behaviour in the development of science is
  1. A.
    critical and important, as, without it, initial hypotheses or conjectures can never be made.
    ✓ Correct
  2. B.
    positive, as conjectures arising out of our dogmatic attitude become science.
  3. C.
    negative, as it leads to pseudo-science.
  4. D.
    neutral, as the development of science is essentially because of our critical attitude.
  5. E.
    inferior to critical attitude, as a critical attitude leads to the attitude of reasonableness and rationality.
Solution
The passage states that dogmatism is “to some extent necessary. It is demanded by a situation which can only be dealt with by forcing our conjectures upon the world.” It also says “science must begin with myths” (dogmatic beliefs) and that a critical attitude needs such raw material. Without initial dogmatic conjectures, there would be nothing to criticise, so dogmatic behaviour is critical for forming initial hypotheses. Option 1 matches.

Question 3 · MCQ

Dogmatic behaviour, in this passage, has been associated with primitives and children. Which of the following best describes the reason why the author compares primitives with children?
  1. A.
    Primitives are people who are not educated, and hence can be compared with children, who have not yet been through school.
  2. B.
    Primitives are people who, though not modern, are as innocent as children.
  3. C.
    Primitives are people without a critical attitude, just as children are.
    ✓ Correct
  4. D.
    Primitives are people in the early stages of human evolution; similarly, children are in the early stages of their lives.
  5. E.
    Primitives are people who are not civilized enough, just as children are not.
Solution
The author writes: “dogmatic thinking… is characteristic of primitives and children; and increasing experience and maturity sometimes create an attitude of caution and criticism rather than of dogmatism.” The inherent link is the lack of a critical attitude. Option 3 states this: “Primitives are people without a critical attitude, just as children are,” which explains the comparison most directly.

Question 4 · MCQ

Which of the following statements best supports the argument in the passage that a critical attitude leads to a weaker belief than a dogmatic attitude does?
  1. A.
    A critical attitude implies endless questioning, and, therefore, it cannot lead to strong beliefs.
  2. B.
    A critical attitude, by definition, is centred on an analysis of anomalies and “noise”.
  3. C.
    A critical attitude leads to questioning everything, and in the process generates “noise” without any conviction.
  4. D.
    A critical attitude is antithetical to conviction, which is required for strong beliefs.
  5. E.
    A critical attitude leads to questioning and to tentative hypotheses.
    ✓ Correct
Solution
The passage directly explains that a dogmatic attitude “is indicative of a strong belief” while a critical attitude “is indicative of a weaker belief” because it involves doubt and readiness to modify. Later it stresses that all theories remain “essentially tentative, or conjectural, or hypothetical” under a critical attitude. Option 5 reflects this by stating that a critical attitude leads to “tentative hypotheses,” i.e., weaker beliefs.

Question 5 · MCQ

According to the passage, which of the following statements best describes the difference between science and pseudo-science?
  1. A.
    Scientific theories or hypotheses are tentatively true whereas pseudo-sciences are always true.
  2. B.
    Scientific laws and theories are permanent and immutable whereas pseudo-sciences are contingent on the prevalent mode of thinking in a society.
  3. C.
    Science always allows the possibility of rejecting a theory or hypothesis, whereas pseudo-sciences seek to validate their ideas or theories.
    ✓ Correct
  4. D.
    Science focuses on anomalies and exceptions so that fundamental truths can be uncovered, whereas pseudo-sciences focus mainly on general truths.
  5. E.
    Science progresses by collection of observations or by experimentation, whereas pseudo-sciences do not worry about observations and experiments.
Solution
The passage identifies the critical attitude (scientific) with readiness “to test; to refute; to falsify” theories, while the dogmatic attitude (pseudo‑scientific) seeks “to verify… to confirm… neglecting refutations.” This means science allows rejection of theories, while pseudo‑science tries to validate them. Option 3 directly aligns: “Science always allows the possibility of rejecting a theory or hypothesis, whereas pseudo‑sciences seek to validate their ideas.”

DILR · Data Interpretation & Logical Reasoning

Set

K, L, M, N, P, Q, R, S, U and W are the only ten members in a department. There is a proposal to form a team from within the members of the department, subject to the following conditions:
  1. A team must include exactly one among P, R, and S.
  2. A team must include either M or Q, but not both.
  3. If a team includes K, then it must also include L, and vice versa.
  4. If a team includes one among S, U, and W, then it must also include the other two.
  5. L and N cannot be members of the same team.
  6. L and U cannot be members of the same team.
The size of a team is defined as the number of members in the team.

Question 1 · MCQ

Who cannot be a member of a team of size 3?
  1. A.
    L
    ✓ Correct
  2. B.
    M
  3. C.
    N
  4. D.
    P
  5. E.
    Q
Solution
Size 3 analysis: If S in → U,W in → at least 3, but then need M or Q (condition 2), so size ≥4. Hence S out. So SUW out. Condition 1: exactly one of P,R in. Condition 2: exactly one of M,Q in. These two use two slots. The third slot from remaining {K,L,N}. K↔L, so including one forces both (needs 2 slots), impossible. So K,L both out. Thus third slot is N. Possible teams: {P,M,N}, {P,Q,N}, {R,M,N}, {R,Q,N}. L never appears. So L cannot be a member.

Question 2 · MCQ

Who can be a member of a team of size 5?
  1. A.
    K
  2. B.
    L
  3. C.
    M
    ✓ Correct
  4. D.
    P
  5. E.
    R
Solution
Size 5 analysis: Case with S in: SUW in (3), plus one of M/Q (1), need 1 more. Only N available (K,L would need 2 together, exceeding 5). Check conditions: L‑N conflict (L not in), L‑U conflict (L not in) OK. So teams: {S,U,W,M,N} and {S,U,W,Q,N}. Case with S out: SUW out, so exactly one of P,R (1), one of M,Q (1), need 3 from {K,L,N}. K↔L, so to reach 3 must take both K and L, forcing N also, but L and N cannot coexist (condition 5). Impossible. Thus only possible size‑5 teams contain M or Q. So M can be a member; K, L, P, R cannot.

Question 3 · MCQ

What would be the size of the largest possible team?
  1. A.
    8
  2. B.
    7
  3. C.
    6
  4. D.
    5
    ✓ Correct
  5. E.
    Cannot be determined
Solution
Conditions simplify the member blocks:
  • Condition 4: {S, U, W} together (all or none).
  • Condition 1: exactly one of P, R, S.
  • Condition 2: exactly one of M, Q.
  • Condition 3: {K, L} together (both or none).
  • Condition 5: L and N cannot both be in.
  • Condition 6: L and U cannot both be in.
Two cases:

Case S included
→ U, W included (cond. 4); P, R excluded (cond. 1). L and U conflict → L out, so K out (cond. 3).
Remaining: M, N, Q. Need exactly one of M, Q. N can be included or not.
Max size = 3 (S,U,W) + 1 (M/Q) + 1 (N) = 5.

Case S excluded
→ U, W excluded (if any in, S forced). Exactly one of P, R included.
To maximise: include K, L (both in), then N out (cond. 5), include one of P/R, one of M/Q → size = 4.

Largest possible team size is 5.

Answer: 5 (option 4).

Question 4 · MCQ

What could be the size of a team that includes K?
  1. A.
    2 or 3
  2. B.
    2 or 4
  3. C.
    3 or 4
  4. D.
    Only 2
  5. E.
    Only 4
    ✓ Correct
Solution
K in → L in (cond. 3).
L and U conflict (cond. 6) → U out.
If U out, S and W must also be out (cond. 4: all or none of {S, U, W}).
Exactly one of P, R, S required (cond. 1); S out → exactly one of P, R in.
L and N cannot both be in (cond. 5) → N out.
Exactly one of M, Q required (cond. 2).

Team = {K, L, one of P/R, one of M/Q} → size exactly 4.

Answer: Only 4 (option 5).

QA · Quantitative Ability

Question 1 · MCQ

If \(\frac{a}{b} = \frac{1}{3}\), \(\frac{b}{c} = 2\), \(\frac{c}{d} = \frac{1}{2}\), \(\frac{d}{e} = 3\) and \(\frac{e}{f} = \frac{1}{4}\), then what is the value of \(\frac{abc}{def}\)?
  1. A.
    \(\frac{3}{8}\)
    ✓ Correct
  2. B.
    \(\frac{27}{8}\)
  3. C.
    \(\frac{3}{4}\)
  4. D.
    \(\frac{27}{4}\)
  5. E.
    \(\frac{1}{4}\)
Solution
From \(\frac{a}{b} = \frac{1}{3}\) we get \(b = 3a\).
From \(\frac{b}{c} = 2\) we get \(c = \frac{b}{2} = \frac{3a}{2}\).
From \(\frac{c}{d} = \frac{1}{2}\) we get \(d = 2c = 3a\).
From \(\frac{d}{e} = 3\) we get \(e = \frac{d}{3} = a\).
From \(\frac{e}{f} = \frac{1}{4}\) we get \(f = 4e = 4a\).
Then \(\frac{abc}{def} = \frac{a \cdot 3a \cdot \frac{3a}{2}}{3a \cdot a \cdot 4a} = \frac{\frac{9}{2}}{12} = \frac{3}{8}\).

Question 2 · MCQ

If \(x = -0.5\), then which of the following has the smallest value?
  1. A.
    \(\frac{1}{2^x}\)
  2. B.
    \(\frac{1}{x}\)
    ✓ Correct
  3. C.
    \(\frac{1}{x^2}\)
  4. D.
    \(2^x\)
  5. E.
    \(\frac{1}{\sqrt{-x}}\)
Solution
Substitute \(x = -0.5 = -\frac{1}{2}\) into each option:
\(2^x = 2^{-0.5} = \frac{1}{\sqrt{2}} \approx 0.707\)
\(\frac{1}{2^x} = 2^{0.5} = \sqrt{2} \approx 1.414\)
\(\frac{1}{x} = \frac{1}{-0.5} = -2\)
\(\frac{1}{x^2} = \frac{1}{0.25} = 4\)
\(\frac{1}{\sqrt{-x}} = \frac{1}{\sqrt{0.5}} = \sqrt{2} \approx 1.414\)
The smallest value is \(-2\), which is option 2.

Question 3 · MCQ

Consider a sequence where the nth term, \(t_n = \frac{n}{(n+2)}\), \(n = 1, 2, \dots\). The value of \(t_3 \times t_4 \times t_5 \times \dots \times t_{53}\) equals:
  1. A.
    \(\frac{2}{495}\)
    ✓ Correct
  2. B.
    \(\frac{2}{477}\)
  3. C.
    \(\frac{12}{55}\)
  4. D.
    \(\frac{1}{1485}\)
  5. E.
    \(\frac{1}{2970}\)
Solution
Product = \(\displaystyle\prod_{n=3}^{53} t_n = \frac{3}{5} \cdot \frac{4}{6} \cdot \frac{5}{7} \cdot \frac{6}{8} \cdots \frac{52}{54} \cdot \frac{53}{55}\).
Numerator: \(3\cdot4\cdot5\cdot6\cdots53\), denominator: \(5\cdot6\cdot7\cdots55\).
Cancel common factors \(5\cdot6\cdots53\) to leave \(\frac{3\cdot4}{54\cdot55} = \frac{12}{2970} = \frac{2}{495}\).
Hence, the value is \(\frac{2}{495}\), corresponding to option 1.

Question 4 · MCQ

The length, breadth and height of a room are in the ratio \(3 : 2 : 1\). If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will
  1. A.
    remain the same
  2. B.
    decrease by 13.64%
  3. C.
    decrease by 15%
  4. D.
    decrease by 18.75%
  5. E.
    decrease by 30%
    ✓ Correct
Solution
Let original length, breadth, height be \(3x, 2x, x\) respectively.
Original total area of four walls = \(2(\text{length}+\text{breadth})\times\text{height} = 2(3x+2x)x = 10x^2\).
New dimensions: length = \(6x\), breadth = \(x\), height = \(x/2\).
New wall area = \(2(6x+x)(x/2) = 7x^2\).
Decrease = \(10x^2 - 7x^2 = 3x^2\).
Percentage decrease = \(\frac{3x^2}{10x^2} \times 100% = 30%\).
Thus, the total area of the four walls decreases by 30% (option 5).

Question 5 · MCQ

A survey was conducted of 100 people to find out whether they had read recent issues of Golmal, a monthly magazine. The summarized information regarding readership in 3 months is given below:
Only September: 18;
September but not August: 23;
September and July: 8;
September: 28;
July: 48;
July and August: 10;
None of the three months: 24.

What is the number of surveyed people who have read exactly two consecutive issues (out of the three)?
  1. A.
    7
  2. B.
    9
    ✓ Correct
  3. C.
    12
  4. D.
    14
  5. E.
    17
Solution
Let J, A, S be sets for July, August, September.

From "Only September": \(|S \setminus (J \cup A)| = 18\)
"September but not August": \(|S \cap A^c| = 23\)
So \(|S \cap J \cap A^c| = 23 - 18 = 5\)
"September and July": \(|S \cap J| = 8\)
Hence all three \(|S \cap J \cap A| = 8 - 5 = 3\)
"July and August": \(|J \cap A| = 10 = |J \cap A \cap S^c| + 3\)
Thus exactly July & August (no Sept) = 7

Breakdown of S: \(|S| = 28 = 18 + 5 + |A \cap S \cap J^c| + 3\)
So exactly August & September (no July) = \(28 - 26 = 2\)

Exactly two consecutive issues = \(7 + 2 = 9\).

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