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CAT 2008 Question Paper with Solutions

65 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 · 21
  • Verbal Ability · 3

DILR

Data Interpretation & Logical Reasoning

19 questions · 19 MCQ · 0 TITA

  • Data Interpretation · 10
  • Logical Reasoning · 9

QA

Quantitative Ability

22 questions · 22 MCQ · 0 TITA

  • Algebra · 8
  • Geometry · 6
  • Number System · 4
  • Modern Math · 3
  • Data Sufficiency · 1

Sample questions with solutions

15 of the 65 questions: the first passage, the first DILR set and the first QA questions of the paper.

VARC · Verbal Ability & Reading Comprehension

Passage

When I was little, children were bought two kinds of ice cream, sold from those white wagons with cano-pies made of silvery metal: either the two-cent cone or the four-cent ice-cream pie. The two-cent cone was very small, in fact it could fit comfortably into a child's hand, and it was made by taking the ice cream from its container with a special scoop and piling it on the cone. Granny always suggested I eat only a part of the cone, then throw away the pointed end, because it had been touched by the vendor's hand (though that was the best part, nice and crunchy, and it was regularly eaten in secret, after a pretence of discarding it).

The four-cent pie was made by a special little machine, also silvery, which pressed two disks of sweet biscuit against a cylindrical section of ice cream. First you had to thrust your tongue into the gap between the biscuits until it touched the central nucleus of ice cream; then, gradually, you ate the whole thing, the biscuit surfaces softening as they became soaked in creamy nectar. Granny had no advice to give here: in theory the pies had been touched only by the machine; in practice, the vendor had held them in his hand while giving them to us, but it was impossible to isolate the contaminated area.

I was fascinated, however, by some of my peers, whose parents bought them not a four-cent pie but two two-cent cones. These privileged children advanced proudly with one cone in their right hand and one in their left; and expertly moving their head from side to side, they licked first one, then the other. This liturgy seemed to me so sumptuously enviable, that many times I asked to be allowed to celebrate it. In vain. My elders were inflexible: a four-cent ice, yes; but two two-cent ones, absolutely no.

As anyone can see, neither mathematics nor economy nor dietetics justified this refusal. Nor did hygiene, assuming that in due course the tips of both cones were discarded. The pathetic, and obviously menda-cious, justification was that a boy concerned with turning his eyes from one cone to the other was more inclined to stumble over stones, steps, or cracks in the pavement. I dimly sensed that there was another secret justification, cruelly pedagogical, but I was unable to grasp it.

Today, citizen and victim of a consumer society, a civilization of excess and waste (which the society of the thirties was not), I realize that those dear and now departed elders were right. Two two-cent cones instead of one at four cents did not signify squandering, economically speaking, but symbolically they surely did. It was for this precise reason, that I yearned for them: because two ice creams suggested excess. And this was precisely why they were denied to me: because they looked indecent, an insult to poverty, a display of fictitious privilege, a boast of wealth. Only spoiled children ate two cones at once, those children who in fairy tales were rightly punished, as Pinocchio was when he rejected the skin and the stalk. And parents who encouraged this weakness, appropriate to little parvenus, were bringing up their children in the foolish theatre of "I'd like to but I can't." They were preparing them to turn up at tourist-class check-in with a fake Gucci bag bought from a street peddler on the beach at Rimini.

Nowadays the moralist risks seeming at odds with morality, in a world where the consumer civilization now wants even adults to be spoiled, and promises them always more, from the wristwatch in the box of detergent to the bonus bangle sheathed, with the magazine it accompanies, in a plastic envelope. Like the parents of those ambidextrous gluttons I so envied, the consumer civilization pretends to give more, but actually gives, for four cents, what is worth four cents. You will throwaway the old transistor radio to purchase the new one, that boasts an alarm clock as well, but some inexplicable defect in the mecha-nism will guarantee that the radio lasts only a year. The new cheap car will have leather seats, double side mirrors adjustable from inside, and a panelled dashboard, but it will not last nearly so long as the glorious old Fiat 500, which, even when it broke down, could be started again with a kick.

The morality of the old days made Spartans of us all, while today's morality wants all of us to be Sybarites.

Question 1 · MCQ

Which of the following cannot be inferred from the passage?
(1) Today's society is more extravagant than the society of the 1930s.
(2) The act of eating two ice cream cones is akin to a ceremonial process.
(3) Elders rightly suggested that a boy turning eyes from one cone to the other was more likely to fall.
(4) Despite seeming to promise more, the consumer civilization gives away exactly what the thing is worth.
(5) The consumer civilization attempts to spoil children and adults alike.
  1. A.
    Today's society is more extravagant than the society of the 1930s.
  2. B.
    The act of eating two ice cream cones is akin to a ceremonial process.
  3. C.
    Elders rightly suggested that a boy turning eyes from one cone to the other was more likely to fall.
    ✓ Correct
  4. D.
    Despite seeming to promise more, the consumer civilization gives away exactly what the thing is worth.
  5. E.
    The consumer civilization attempts to spoil children and adults alike.
Solution
The passage calls the justification 'pathetic, and obviously mendacious' (lying). Therefore, it cannot be inferred that the elders' suggestion was right.

Question 2 · MCQ

In the passage, the phrase “little parvenus” refers to
  1. A.
    naughty midgets.
  2. B.
    old hags.
  3. C.
    arrogant people.
  4. D.
    young upstarts.
    ✓ Correct
  5. E.
    foolish kids.
Solution
'Parvenu' means a person of obscure origin who has gained wealth and acts pretentiously. 'Little parvenus' refers to the spoilt children acting like young upstarts.

Question 3 · MCQ

The author pined for two two-cent cones instead of one four-cent pie because
  1. A.
    it made dietetic sense.
  2. B.
    it suggested intemperance.
    ✓ Correct
  3. C.
    it was more fun.
  4. D.
    it had a visual appeal.
  5. E.
    he was a glutton.
Solution
The author states: 'It was for this precise reason, that I yearned for them: because two ice creams suggested excess.' Excess is intemperance.

Question 4 · MCQ

What does the author mean by “nowadays the moralist risks seeming at odds with morality"?
  1. A.
    The moralists of yesterday have become immoral today.
  2. B.
    The concept of morality has changed over the years.
    ✓ Correct
  3. C.
    Consumerism is amoral.
  4. D.
    The risks associated with immorality have gone up.
  5. E.
    The purist's view of morality is fast becoming popular.
Solution
The moralist's traditional stance against excess seems outdated because consumer civilization has redefined what is considered moral. Hence, the concept of morality has changed.

Question 5 · MCQ

According to the author, the justification for refusal to let him eat two cones was plausibly
  1. A.
    didactic.
    ✓ Correct
  2. B.
    dietetic.
  3. C.
    dialectic.
  4. D.
    diatonic.
  5. E.
    diastolic.
Solution
The author sensed a 'secret justification, cruelly pedagogical.' Pedagogical means didactic, intended to teach a moral lesson.

DILR · Data Interpretation & Logical Reasoning

Set

Abdul, Bikram and Chetan are three professional traders who trade in shares of a company XYZ Ltd. Abdul follows the strategy of buying at the opening of the day at 10 am and selling the whole lot at the close of the day at 3 pm. Bikram follows the strategy of buying at hourly intervals: 10 am, 11 am, 12 noon, 1 pm, and 2 pm, and selling the whole lot at the close of the day. Further, he buys an equal number of shares in each purchase. Chetan follows a similar pattern as Bikram but his strategy is somewhat different. Chetan's total investment amount is divided equally among his purchases. The profit or loss made by each investor is the difference between the sale value at the close of the day less the investment in purchase. The “return” for each investor is defined as the ratio of the profit or loss to the investment amount expressed as a percent-age.
One day, two other traders, Dane and Emily joined Abdul, Bikram and Chetan for trading in the shares of XYZ Ltd. Dane followed a strategy of buying equal numbers of shares at 10 am. 11 am and 12 noon, and selling the same numbers at 1 pm, 2 pm and 3 pm. Emily, on the other hand, followed the strategy of buying shares using all her money at 10 am and selling all of them at 12 noon and again buying the shares for all the money at 1 pm and again selling all of them at the close of the day at 3 pm. At the close of the day the following was observed.
i. Abdul lost money in the transactions.
ii. Both Dane and Emily made profits.
iii. There was an increase in share price during the closing hour compared to the price at 2 pm.
iv. Share price at 12 noon was lower than the opening price

Question 1 · MCQ

On a day of fluctuating market prices, the share price of XYZ Ltd. ends with a gain, i.e, it is higher at the close of the day compared to the opening value. Which trader got the maximum return on that day?
  1. A.
    Bikram
  2. B.
    Chetan
  3. C.
    Abdul
  4. D.
    Bikram or Chetan
  5. E.
    cannot be determined
    ✓ Correct
Solution
Let the hourly prices be \(P_{10}, P_{11}, P_{12}, P_{1}, P_{2}\) and closing price \(P_3\).

Abdul buys at \(P_{10}\); return \(= \frac{P_3}{P_{10}}-1\).
Bikram buys equal numbers; return \(= \frac{P_3}{\text{AM}}-1\), where AM is arithmetic mean of the five prices.
Chetan buys equal amounts; return \(= \frac{P_3}{H}-1\), where \(H\) is harmonic mean.

For any set of positive numbers, \(H \leq \text{AM}\) (equality only when all are equal). Since the market fluctuates, \(H < \text{AM}\) and so Chetan’s return > Bikram’s.

Comparing Chetan with Abdul: if \(P_{10} < H\), Abdul’s return > Chetan’s; if \(P_{10} > H\), Chetan’s return > Abdul’s. Both are possible, so the maximum cannot be determined.

Hence option (5).

Question 2 · MCQ

Which one of the following statements is always true?
(1) Abdul will not be one with the minimum return
(2) Return for Chetan will be higher than that of Bikram
(3) Return for Bikram will be higher than that of Chetan
(4) Return for Chetan cannot be higher than that of Abdul
(5) none of the above
  1. A.
    Abdul will not be one with the minimum return
  2. B.
    Return for Chetan will be higher than that of Bikram
  3. C.
    Return for Bikram will be higher than that of Chetan
  4. D.
    Return for Chetan cannot be higher than that of Abdul
  5. E.
    none of the above
    ✓ Correct
Solution
Evaluate each statement:

(1) Abdul can be the one with minimum return (e.g., open high, intraday prices lower, close slightly below open) → false.
(2) Chetan’s return ≥ Bikram’s; equality possible when all five purchase prices are equal (flat market), so “higher than” is not always true → false.
(3) Opposite of (2), false.
(4) Abdul’s return can be lower than Chetan’s (e.g., \(P_{10} > H\) leads to Abdul’s return < Chetan’s) → false.

Therefore none of (1)–(4) is always true. Answer (5).

Question 3 · MCQ

On a "boom" day the share price of XYZ Ltd. keeps rising throughout the day and peaks at the close of the day. Which trader got the minimum return on that day?
  1. A.
    Bikram
    ✓ Correct
  2. B.
    Chetan
  3. C.
    Abdul
  4. D.
    Abdul or Chetan
  5. E.
    cannot be determined
Solution
On a boom day, prices strictly rise: \(P_{10} < P_{11} < P_{12} < P_{1} < P_{2} < P_3\).

Abdul buys at the lowest price (\(P_{10}\)) and sells at the highest; his return is highest.
Chetan’s effective buy price is the harmonic mean \(H\), which satisfies \(P_{10} < H < \text{AM}\) (AM = arithmetic mean).
Bikram’s effective buy price is AM, so Bikram’s return is \(\frac{P_3}{\text{AM}}-1\), the smallest among the three.

Hence Bikram gets the minimum return. Option (1).

Question 4 · MCQ

Share price was at its highest at
  1. A.
    10 am
    ✓ Correct
  2. B.
    11 am
  3. C.
    12 noon
  4. D.
    1 pm
  5. E.
    cannot be determined
Solution
Let the share prices at 10 am, 11 am, 12 noon, 1 pm, 2 pm, 3 pm be \(p_{10}, p_{11}, p_{12}, p_{13}, p_{14}, p_{15}\).

Given:
  • Abdul lost money ⇒ \(p_{15} < p_{10}\)
  • Closing hour increase ⇒ \(p_{15} > p_{14}\)
  • 12 noon < opening ⇒ \(p_{12} < p_{10}\)
  • Dane’s profit: \(p_{13} + p_{14} + p_{15} > p_{10} + p_{11} + p_{12}\)
  • Emily’s profit: \(p_{12}p_{15} > p_{10}p_{13}\) ⇒ \(p_{13} < \frac{p_{12}}{p_{10}} p_{15}\)
From Emily, since \(p_{15} < p_{10}\), we get \(p_{13} < p_{12}\). Also, using Dane’s inequality with \(p_{14} < p_{15} < p_{10}\) and \(p_{13} < p_{10}\), we can bound:
\[p_{10} + p_{11} + p_{12} < p_{13} + p_{14} + p_{15} < 3p_{10}\]
This forces \(p_{11} < p_{10}\).

Thus:
  • \(p_{15} < p_{10}\)
  • \(p_{14} < p_{15} < p_{10}\)
  • \(p_{13} < p_{15} < p_{10}\)
  • \(p_{12} < p_{10}\)
  • \(p_{11} < p_{10}\)
All prices except possibly \(p_{10}\) are strictly less than \(p_{10}\). Hence the highest price is at 10 am.

Question 5 · MCQ

Which of the following is necessarily false?
(1) Share price was at its lowest at 2 pm
(2) Share price was at its lowest at 11 am
(3) Share price at 1 pm was higher than the share price at 2 pm
(4) Share price at 1 pm was higher than the share price at 12 noon
(5) none of the above
  1. A.
    Share price was at its lowest at 2 pm
  2. B.
    Share price was at its lowest at 11 am
  3. C.
    Share price at 1 pm was higher than the share price at 2 pm
  4. D.
    Share price at 1 pm was higher than the share price at 12 noon
    ✓ Correct
  5. E.
    none of the above
Solution
From Emily’s profit condition:
\[p_{12}p_{15} > p_{10}p_{13}\]
\(\Rightarrow p_{13} < \frac{p_{12}}{p_{10}}\, p_{15}\)

Abdul lost money ⇒ \(p_{15} < p_{10}\), so \(\frac{p_{15}}{p_{10}} < 1\).
Therefore \(p_{13} < p_{12}\).

Thus the statement “Share price at 1 pm was higher than the share price at 12 noon” (\(p_{13} > p_{12}\)) is impossible. It must be false.

Other options can be true. For example:
  • Option (2): \(p_{11}\) can be the minimum (e.g., \(p_{10}=100, p_{11}=10, p_{12}=90, p_{13}=80, p_{14}=89, p_{15}=90\) satisfies all conditions).
  • Option (3): \(p_{13} > p_{14}\) is possible (e.g., \(p_{10}=100, p_{11}=10, p_{12}=80, p_{13}=70, p_{14}=50, p_{15}=90\)).
Option (1) is also necessarily false, but option (4) is the most direct contradiction derived from the given data.

QA · Quantitative Ability

Question 1 · MCQ

The integers 1, 2, ..., 40 are written on a blackboard. The following operation is then repeated 39 times: In each repetition, any two numbers, say a and b, currently on the blackboard are erased and a new number a + b - 1 is written. What will be the number left on the board at the end?
  1. A.
    820
  2. B.
    821
  3. C.
    781
    ✓ Correct
  4. D.
    819
  5. E.
    780
Solution
Initial sum = \(1+2+\cdots+40 = \frac{40\times41}{2}=820\).
Each operation reduces the sum by 1 because replacing \(a\) and \(b\) with \(a+b-1\) changes the sum by \((a+b-1)-(a+b) = -1\).
After 39 operations, the sum decreases by 39, so final sum = \(820-39 = 781\).
Only one number remains, so the answer is 781.

Question 2 · MCQ

What are the last two digits of \(7^{2008}\)?
  1. A.
    21
  2. B.
    61
  3. C.
    01
    ✓ Correct
  4. D.
    41
  5. E.
    81
Solution
We need \(7^{2008} \pmod{100}\).
Since \(\gcd(7,100)=1\) and Euler's totient \(\phi(100)=40\), we have \(7^{40} \equiv 1 \pmod{100}\).
\(2008 = 40\times50 + 8\), so \(7^{2008} \equiv 7^8 \pmod{100}\).
Now \(7^2 = 49\), \(7^4 = 49^2 = 2401 \equiv 1 \pmod{100}\).
Thus \(7^8 = (7^4)^2 \equiv 1^2 = 1 \pmod{100}\).
Last two digits are 01.

Question 3 · MCQ

If the roots of the equation \(x^3 – ax^2 + bx − c = 0\) are three consecutive integers, then what is the smallest possible value of b?
  1. A.
    \(-\frac{1}{\sqrt{3}}\)
  2. B.
    -1
    ✓ Correct
  3. C.
    0
  4. D.
    1
  5. E.
    \(\frac{1}{\sqrt{3}}\)
Solution
Let the roots be \(n-1\), \(n\), \(n+1\).
Sum of roots = \(3n\), sum of pairwise products = \((n-1)n + n(n+1) + (n+1)(n-1) = 3n^2 - 1\).
Given equation: \(x^3 - ax^2 + bx - c = 0\), so coefficient of \(x\) is \(b = 3n^2 - 1\).
\(b\) is minimum when \(n=0\) giving \(b = -1\).

Question 4 · MCQ

A shop stores x kg of rice. The first customer buys half this amount plus half a kg of rice. The second customer buys half the remaining amount plus half a kg of rice. Then the third customer also buys half the remaining amount plus half a kg of rice. Thereafter, no rice is left in the shop. Which of the following best describes the value of x?
  1. A.
    \(2 \le x \le 6\)
  2. B.
    \(5 \le x \le 8\)
    ✓ Correct
  3. C.
    \(9 \le x \le 12\)
  4. D.
    \(11 \le x \le 14\)
  5. E.
    \(13 \le x \le 18\)
Solution
Let initial rice = \(x\) kg.
After 1st: buys \(\frac{x}{2} + \frac{1}{2}\), remains \(R_1 = \frac{x}{2} - \frac{1}{2}\).
After 2nd: buys \(\frac{R_1}{2} + \frac{1}{2} = \frac{x}{4} + \frac{1}{4}\), remains \(R_2 = \frac{x}{4} - \frac{3}{4}\).
After 3rd: buys \(\frac{R_2}{2} + \frac{1}{2} = \frac{x}{8} + \frac{1}{8}\), remains \(R_3 = \frac{x}{8} - \frac{7}{8} = 0 \Rightarrow x = 7\).
Thus \(x = 7\) lies in the range \(5 \le x \le 8\).

Question 5 · MCQ

Let \(f(x)=ax^2+bx+c\), where \(a\), \(b\), and \(c\) are certain constants and \(a\ne0\). It is known that \(f(5)=-3f(2)\) and that \(3\) is a root of \(f(x)=0\).

What is the other root of \(f(x) = 0\)?
  1. A.
    -7
  2. B.
    -4
    ✓ Correct
  3. C.
    2
  4. D.
    6
  5. E.
    cannot be determined
Solution
Since \(3\) is a root of the quadratic, let the other root be \(r\). Then

\[ f(x)=a(x-3)(x-r), \]

where \(a\neq0\).

Using the given condition,

\[ f(5)=-3f(2). \]

Evaluate each side:

\[ f(5)=a(5-3)(5-r)=2a(5-r), \]

\[ f(2)=a(2-3)(2-r)=-a(2-r). \]

Substituting these into the given equation,

\[ 2a(5-r)=3a(2-r). \]

Since \(a\neq0\), divide both sides by \(a\):

\[ 2(5-r)=3(2-r). \]

Expanding both sides,

\[ 10-2r=6-3r. \]

Rearranging,

\[ 10+r=6, \]

\[ r=-4. \]

Hence, the other root of \(f(x)=0\) is

\[ \boxed{-4}. \]

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