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CAT 1991 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 · 16
  • Verbal Ability · 8

DILR

Data Interpretation & Logical Reasoning

22 questions · 22 MCQ · 0 TITA

  • Data Interpretation · 15
  • Logical Reasoning · 7

QA

Quantitative Ability

22 questions · 22 MCQ · 0 TITA

  • Arithmetic · 8
  • Algebra · 6
  • Geometry · 3
  • Modern Math · 3
  • Number System · 2

Sample questions with solutions

11 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 fact is often obscured by the widespread confusion about the nature and role of emotions in man’s life. One frequently hears the statement, “Man is not merely a rational being, he is also an emotional being”, which implies some sort of dichotomy, as if, in effect, man possessed a dual nature, with one part in opposition to the other. In fact, however, the content of man’s emotions is the product of his rational faculty; his emotions are a derivative and a consequence, which, like all of man’s other psychological characteristics, cannot be understood without reference to the conceptual power of his consciousness.

As man’s tool of survival, reasons has two basic functions: cognition and evaluation. The process of cognition consists of discovering what things are, of identifying their nature, their attributes and properties. The process of evaluation consists of man discovering the relationship of things to himself, of identifying what is beneficial to him and what is harmful, what should be sought and what should be avoided.

“A ‘value’ is that which one acts to gain and/or keep.” It is that which one regards as conducive to one’s welfare. A value is the object of an action. Since man must act in order to live, and since reality confronts him with many possible goals, many alternative courses of action, he cannot escape the necessity of selecting values and making value judgements.

“Value” is a concept pertaining to a relation – the relation of some aspect of reality to man (or to some other living entity). If a man regards a things (a person, an object, an event, mental state, etc.) as good for him, as beneficial in some way, he values it and, when possible and appropriate, seeks to acquire, retain and use or enjoy it; if a man regards a thing as bad for him, as inimical or harmful in some way, he disvalues it – and seeks to avoid or destroy it. If he regards a thing as of no significance to him, as neither beneficial nor harmful, he is indifferent to it – and takes no action in regard to it.

Although his life and well-being depend on a man selecting values that are in fact good for him, i.e., consonant with his nature and needs, conducive to his continued efficacious functioning, there are no internal or external forces compelling him to do so. Nature leaves him free in this matter. As a being of volitional consciousness, he is not biologically “programmed” to make the right value-choices automatically. He may select values that are incompatible with his needs and inimical to his well-being, values that lead him to suffering and destruction. But whether his values are life-serving or life-negating, it is a man’s values that direct his actions. Values constitute man’s basic motivational tie to reality.

In existential terms, man’s basic alternative of “for me” or “against me”, which gives rise to the issue of values, is the alternative of life or death. But this is an adult, conceptual identification. As a child, a human being first encounters the issue of values through the experience of physical sensations of pleasure and pain.

To a conscious organism, pleasure is experienced, axiomatically, as a value; pain, as disvalue. The biological reason for this is the fact that pleasure is a life-enhancing state and that pain is a signal of danger, of some disruption of the normal life process.

There is another basic alternative, in the realm of consciousness, through which a child encounters the issue of values, of the desirable and the undesirable. It pertains to his cognitive relations to reality. There are times when a child experiences a sense of cognitive efficacy in grasping reality, a sense of cognitive control, of mental clarity (within the range of awareness possible to his stage of development). There are times when he suffers from a sense of cognitive inefficacy, of cognitive helplessness, of mental chaos, the sense of being out of control and unable to assimilate the date entering his consciousness. To experience a state of efficacy is to experience it as a value; to experience a state of inefficacy is to experience it as a disvalue. The biological basis of this fact is the relationship of efficacy to survival.

The value of sense of efficacy as such, like the value of pleasure as such, is introspectively experienced by man as primary. One does not ask a man: “Why do you prefer pleasure to pain?” Nor does one ask him: “Why do you prefer a state of control to a state of helplessness?” It is through these two sets of experiences that man first acquires preferences, i.e. values.

A man may choose, as a consequence of his errors and/or evasions, to pursue pleasure by means of values that in fact can result only in pain; and he can pursue a sense of efficacy by means of values that can only render him impotent. But the value of pleasure and the disvalue of pain, as well as the value of efficacy and the disvalue of helplessness, remain the psychological base of the phenomenon of valuation.

Question 1 · MCQ

The author subtly suggests that
  1. A.
    there is a dual nature in man.
  2. B.
    there is dichotomy between man as an emotional being and man as a rational being.
  3. C.
    there should be no dichotomy between man as a rational being and man as an emotional being.
    ✓ Correct
  4. D.
    man’s emotions cannot be understood.
Solution
The passage calls the common claim that man is both rational and emotional a form of confusion and says emotions are a product of the rational faculty, not an opposing part. This implies there should be no dichotomy between man as rational and man as emotional. Hence option 3.

Question 2 · MCQ

The biological basis of choosing efficacy as value
  1. A.
    cannot be understood easily.
  2. B.
    is the relationship of efficacy to survival.
    ✓ Correct
  3. C.
    is the association of efficacy to pleasure.
  4. D.
    is the biological relationship to cognition.
Solution
The passage explicitly states: "The biological basis of this fact is the relationship of efficacy to survival." Therefore, option 2 is correct.

Question 3 · MCQ

The author defines value as
  1. A.
    something that results as good.
  2. B.
    something that is chosen by man.
    ✓ Correct
  3. C.
    that which gives pleasure over pain.
  4. D.
    that which increases efficacy.
Solution
The author defines value as "that which one acts to gain and/or keep" and calls it "the object of an action." He also says man cannot escape selecting values and making value judgements, so a value is essentially something chosen by man. Hence option 2.

Question 4 · MCQ

The basic theme of the passage is that
  1. A.
    man can choose his own values, irrespective of whether they are life sustaining or not.
    ✓ Correct
  2. B.
    man chooses values that are life sustaining.
  3. C.
    values are given to man on account of his emotive process.
  4. D.
    emotions and rationality are derived from each other.
Solution
The passage says values direct man's actions, but nature leaves him free in this matter. He may select values that are incompatible with his needs and inimical to his well-being. Thus the central theme is that man can choose his own values, whether or not they are life sustaining. Hence option 1.

DILR · Data Interpretation & Logical Reasoning

Set

Each of these items has a question followed by two statements. As the answer,
Mark (a), If the question can be answered with the help of statement I alone,
Mark (b), If the question can be answered with the help of statement II alone,
Mark (c), If both the statement I and statement II are needed to answer the question, and
Mark (d), If the question cannot be answered even with the help of both the statements.

Question 1 · MCQ

What is the area under the line GHI – JKL in the given quadrilateral OPQR, knowing that all the small spaces are squares of the same area? (Refer to the provided grid diagram with points P, Q, E, C, D, A, B, G, H, K, L, O, I, J, R)
I. Length ABCDEQ is greater than or equal to 60.
II. Area OPQR is less than or equal to 1512.
  1. A.
    Mark (a)
  2. B.
    Mark (b)
  3. C.
    Mark (c)
    ✓ Correct
  4. D.
    Mark (d)
Solution
Let the side of each small square be \(s\).
From the grid, path \(ABCDEQ\) spans 10 square-side lengths, so \(ABCDEQ = 10s\).
Statement I gives \(10s \ge 60 \Rightarrow s \ge 6\).
The quadrilateral \(OPQR\) contains 42 small squares, so its area is \(42s^2\).
Statement II gives \(42s^2 \le 1512 = 42 \times 36 \Rightarrow s \le 6\).
Thus, only together, \(s = 6\).
Once the side length is fixed, the area under \(GHI-JKL\) is fixed by the grid count. Neither statement alone fixes \(s\). Hence both statements are needed.

Question 2 · MCQ

Mr. Murthy takes the morning train to his office from station A to station B, and his colleague Mr. Rahman joins him on the way. There are three stations C, D and E on the way not necessarily in that sequence. What is the sequence of stations?
I. Mr. Rahman boards the train at D.
II. Mr. Thomas, who travels between C & D has two segments of journey in common with Mr. Murthy but none with Mr. Rahman.
  1. A.
    Mark (a)
  2. B.
    Mark (b)
  3. C.
    Mark (c)
    ✓ Correct
  4. D.
    Mark (d)
Solution
From statement II, Thomas travels between C and D and covers exactly two journey segments. So C and D must have exactly one station between them. Since the only remaining station is E, the order is either \(C-E-D\) or \(D-E-C\).

From statement I, Rahman boards at D and then travels onward toward B.
If the order were \(D-E-C\), Rahman's journey would include \(D-E\). Thomas, travelling between C and D, must also use \(D-E\), contradicting statement II that Thomas shares no segment with Rahman.

So the order must be \(C-E-D\), i.e. \(A-C-E-D-B\).
Each statement alone gives two possibilities or insufficient information; both are needed.

QA · Quantitative Ability

Question 1 · MCQ

Is it more profitable for Company M to produce Q?
I. Product R is sold at a price four times that of Q.
II. One unit of Q requires 2 units of labour, while one unit of R requires 5 units of labour. There is no other constraint on production.
  1. A.
    If the question can be answered with the help of statement I alone
  2. B.
    If the question can be answered with the help of statement II alone
  3. C.
    If both the statement I and statement II are needed to answer the question
    ✓ Correct
  4. D.
    If the question cannot be answered even with the help of both the statements
Solution
Let the price of Q be \(p\) and the labour cost per unit be \(c\).
From I, price of R is \(4p\).
From II, one unit of Q uses 2 units of labour, and one unit of R uses 5 units.
Profit per unit of labour:
  • Q: \(\frac{p}{2}-c\)
  • R: \(\frac{4p}{5}-c\)
Since \(\frac{4p}{5}>\frac{p}{2}\), R is more profitable per unit of labour; hence Q is not more profitable.
Both statements are needed, and neither alone is sufficient.

Question 2 · MCQ

A train started from Station A, developed engine trouble and reached Station B, 40 minutes late. What is the distance between Stations A and B?
I. The engine trouble developed after travelling 40 km from Station A and the speed reduced to \(\frac{1}{4}\)th of the original speed.
II. The engine trouble developed after travelling 40 km from station A in two hours and the speed reduced to \(\frac{1}{4}\)th of the original speed.
  1. A.
    If the question can be answered with the help of statement I alone
  2. B.
    If the question can be answered with the help of statement II alone
    ✓ Correct
  3. C.
    If both the statement I and statement II are needed to answer the question
  4. D.
    If the question cannot be answered even with the help of both the statements
Solution
From II, the first 40 km took 2 hours, so original speed \(v=20\) km/h.
After the fault, speed becomes \(\frac{v}{4}=5\) km/h.
If total distance is \(D\), the extra time is only from the remaining \(D-40\) km:
\[ \frac{D-40}{5}-\frac{D-40}{20}=\frac{2}{3} \]
\[ \frac{3(D-40)}{20}=\frac{2}{3} \]
\[ D=40+\frac{40}{9}=\frac{400}{9}\text{ km} \]
Statement I alone does not give the original speed. Hence statement II alone is sufficient.

Question 3 · MCQ

What is the value of prime number x?
I. \(x^2 + x\) is a two digit number greater than 50.
II. \(x^3\) is a three digit number.
  1. A.
    If the question can be answered with the help of statement I alone
    ✓ Correct
  2. B.
    If the question can be answered with the help of statement II alone
  3. C.
    If both the statement I and statement II are needed to answer the question
  4. D.
    If the question cannot be answered even with the help of both the statements
Solution
Statement I: \(x^2+x=x(x+1)\) is a two-digit number > 50.
For prime \(x\), check \(x=2,3,5,7,11\):
\(x=7\): \(56\); \(x=11\): \(132\) (three-digit). Only \(x=7\).
So I alone sufficient.
Statement II: \(x^3\) three-digit gives \(x=5\) (\(125\)) or \(x=7\) (\(343\)), not unique.
Answer: option 1.

Question 4 · MCQ

The average of three unequal quotations for a particular share is Rs. 110. If all are quoted in integral values of rupee, does the highest quotation exceed Rs. 129?
I. The lowest quotation is Rs. 100.
II. One of the quotations is Rs. 115.
  1. A.
    If the question can be answered with the help of statement I alone
    ✓ Correct
  2. B.
    If the question can be answered with the help of statement II alone
  3. C.
    If both the statement I and statement II are needed to answer the question
  4. D.
    If the question cannot be answered even with the help of both the statements
Solution
Sum of three unequal integer quotes = \(3\times110=330\). Let quotes be \(a<b<c\).
Statement I: \(a=100\), so \(b+c=230\). Smallest possible \(b=101\) gives largest possible \(c=129\). Thus \(c\) never exceeds 129; answer is No. I sufficient.
Statement II: one quote is 115.
If quotes are \(85,115,130\), highest 130 > 129.
If quotes are \(86,115,129\), highest 129, not exceeding.
Different answers, so II not sufficient.
Answer: option 1.

Question 5 · MCQ

X says to Y, “I am 3 times as old as you were 3 years ago”. How old is X?
I. Y’s age 17 years from now will be same as X’s present age.
II. X’s age nine years from now is 3 times Y’s present age.
  1. A.
    If the question can be answered with the help of statement I alone
    ✓ Correct
  2. B.
    If the question can be answered with the help of statement II alone
  3. C.
    If both the statement I and statement II are needed to answer the question
  4. D.
    If the question cannot be answered even with the help of both the statements
Solution
Let X's present age be \( x \) and Y's present age be \( y \).
Given: \( x = 3(y-3) \).

Statement I:
\( y + 17 = x \).
Substitute \( x = 3(y-3) \):
\( y + 17 = 3y - 9 \)
\( 2y = 26 \Rightarrow y = 13 \), so \( x = 30 \).
Thus statement I alone is sufficient.

Statement II:
\( x + 9 = 3y \).
But the given equation is \( x = 3y - 9 \), which is exactly \( x + 9 = 3y \).
So statement II gives no new information, and is not sufficient alone.

Answer: Statement I alone.

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