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CAT 1993 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 · 16
  • Logical Reasoning · 6

QA

Quantitative Ability

22 questions · 22 MCQ · 0 TITA

  • Arithmetic · 8
  • Algebra · 7
  • Geometry · 3
  • Modern Math · 2
  • Number System · 2

Sample questions with solutions

12 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

Emile Durkheim, the first person to be formally recognized as a sociologist and the most scientific of the pioneers, conducted a study that stands as a research model for sociologists today. His investigation of suicide was, in fact, the first sociological study to use statistics. In suicide (1964, originally published in 1897) Durkheim documented his contention that some aspects of human behaviour – even something as allegedly individualistic as suicide – can be explained without reference to individuals.

Like all of Durkheim’s work, suicide must be viewed within the context of his concern for social integration. Durkheim wanted to see if suicide rates within a social entity (for example, a group, organization, or society) are related to the degree to which individuals are socially involved (integrated and regulated). Durkheim describes three types of suicide: egoistic, anomic, and altruistic. Egoistic suicide is promoted when individuals do not have sufficient social ties. Since single (never married) adults, for example, are not heavily involved with the family life, they are more likely to commit suicide than are married adults. Altruistic suicide on the other hand, is more likely to occur when social integration is too strong. The ritual suicide of Hindu widows on their husbands funeral pyres is one example. Military personnel, trained to lay down their lives for their country, provide another illustration.

Durkheim’s third type of suicide – anomic suicide increases when the social regulation of individuals is disrupted. For example, suicide rates increase during economic depressions. People who suddenly find themselves without a job or without hope of finding one are more prone to kill themselves. Suicides may also increase during period of prosperity. People may loosen their social ties by taking new jobs, moving to new communities, or finding new mates.

Using data from the government population reports of several countries (much of it from the French Government Statistical Office), Durkheim found strong support for his line reasoning. Suicide rates were higher among single than married people, among military personnel than civilians, among divorced than married people, and among people involved in nationwide economic crises.

It is important to realize that Durkheim’s primary interest was not in the empirical (observations) indicators he used such as suicide rates among military personnel, married people, and so forth. Rather, Durkheim used the following indicators to support several of his contentions: (1) Social behavior can be explained by social rather than psychological factors; (2) suicide is affected by the degree of integration and regulation within social entities; and (3) Since society can be studied scientifically, sociology is worthy of recognition in the academic world. Durkheim was successful on all three counts.

Question 1 · MCQ

Higher suicide rate during rapid progress in a society is a manifestation of
  1. A.
    altruistic suicide.
  2. B.
    anomic suicide.
    ✓ Correct
  3. C.
    egoistic suicide.
  4. D.
    None of the above.
Solution
The passage states that suicides may also increase during periods of prosperity. People loosen their social ties by taking new jobs, moving, or finding new mates. This reflects disrupted social regulation, which Durkheim classifies as anomic suicide.

Question 2 · MCQ

In his study of suicide Durkheim’s main purpose was
  1. A.
    to document that suicide can be explained without reference to the individual.
    ✓ Correct
  2. B.
    to provide an explanation of the variation in the rate of suicide across societies.
  3. C.
    to categorize various types of suicides.
  4. D.
    to document that social behavior can be explained by social rather than psychological factors.
Solution
The opening paragraph states that Durkheim documented the contention that some aspects of human behaviour—even something as individualistic as suicide—can be explained without reference to individuals. Thus, the specific purpose of the suicide study was to show suicide can be explained without reference to the individual.

Question 3 · MCQ

Increase in the suicide rate during economic depression is an example of
  1. A.
    altruistic suicide.
  2. B.
    anomic suicide.
    ✓ Correct
  3. C.
    egoistic suicide.
  4. D.
    Both a and c.
Solution
The passage explains that anomic suicide increases when social regulation is disrupted, and it gives economic depression as an example. People who suddenly lose jobs or hope become more prone to suicide.

Question 4 · MCQ

Single adults not heavily involved with family life are more likely to commit suicide. Durkheim categorized this as
  1. A.
    anomic suicide.
  2. B.
    altruistic suicide.
  3. C.
    egoistic suicide.
    ✓ Correct
  4. D.
    Both (b) and (c)
Solution
Durkheim classifies egoistic suicide as arising from insufficient social ties. Since single adults are not heavily involved in family life, they have weaker social integration and are therefore more likely to commit egoistic suicide.

DILR · Data Interpretation & Logical Reasoning

Set

Read the text and the numbered statements carefully and answer the questions given at the end.

Four people of different nationalities live on the same side of a street in four houses each of different color. Each person has a different favorite drink. The following additional information is also known:
The Englishman lives in the red house.
The Italian drinks tea.
The Norwegian lives in the first house on the left.
In the second house from the right they drink milk.
The Norwegian lives adjacent to the blue house.
The Spaniard drinks fruit juice.
Tea is drunk in the blue house.
The white house is to the right of the red house.

Question 1 · MCQ

The color of the Norwegian’s house is
  1. A.
    yellow
    ✓ Correct
  2. B.
    white
  3. C.
    blue
  4. D.
    red
Solution
Number houses 1 to 4 from left to right.
Norwegian lives in house 1; since the Norwegian is adjacent to the blue house, house 2 is blue.
Tea is drunk in the blue house, so house 2 drinks tea. The Italian drinks tea, so house 2 is Italian.
House 3, second from the right, drinks milk.
The Spaniard drinks fruit juice, so the Spaniard must be in house 4; therefore house 3 is English.
The Englishman lives in the red house, so house 3 is red. White is to the right of red, so house 4 is white.
House1234
NationalityNorwegianItalianEnglishSpaniard
ColorYellowBlueRedWhite
DrinkCocoaTeaMilkFruit juice
Thus the Norwegian's house is yellow.

Question 2 · MCQ

Milk is drunk by
  1. A.
    Norwegian
  2. B.
    English
    ✓ Correct
  3. C.
    Italian
  4. D.
    None of the above
Solution
The completed arrangement is:
House1234
NationalityNorwegianItalianEnglishSpaniard
ColorYellowBlueRedWhite
DrinkCocoaTeaMilkFruit juice
Milk is in house 3, and house 3 belongs to the Englishman.
Hence milk is drunk by the Englishman.

Question 3 · MCQ

The Norwegian drinks
  1. A.
    milk
  2. B.
    cocoa
    ✓ Correct
  3. C.
    tea
  4. D.
    fruit juice.
Solution
From the arrangement:
House1234
NationalityNorwegianItalianEnglishSpaniard
ColorYellowBlueRedWhite
DrinkCocoaTeaMilkFruit juice
The Norwegian lives in house 1, whose drink is cocoa.
Thus the Norwegian drinks cocoa.

QA · Quantitative Ability

Question 1 · MCQ

Given that \(X\) and \(Y\) are non-negative. What is the value of \(X\)?
I. \(2X + 2Y \le 40\)
II. \(X - 2Y \ge 20\)
  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, 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
From statement II: \(X \ge 20 + 2Y\).
From statement I: \(X + Y \le 20\).
Together: \(20 + 2Y + Y \le 20 \Rightarrow 3Y \le 0\). Since \(Y \ge 0\), we get \(Y = 0\).
Then \(X \le 20\) from I and \(X \ge 20\) from II, so \(X = 20\).
Either statement alone allows many possible values of \(X\). Hence both statements are needed.

Question 2 · MCQ

Is the average of the largest and the smallest of four given numbers greater than the average of the four numbers?
I. The difference between the largest and the second largest numbers is greater than the difference between the second smallest and the smallest numbers.
II. The difference between the largest and the second largest numbers is less than the difference between the second largest and the second smallest numbers.
  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, 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 the four numbers in increasing order be \(a \le b \le c \le d\).
We need to check whether
\(\frac{a+d}{2} > \frac{a+b+c+d}{4}\), which simplifies to
\(d-c > b-a\).
Statement I says exactly that largest − second largest is greater than second smallest − smallest, i.e. \(d-c > b-a\). So statement I alone is sufficient.
Statement II says \(d-c < c-b\), which does not fix the comparison between \(d-c\) and \(b-a\).
Example with statement II: \(a=0,b=10,c=20,d=21\) gives \(d-c=1 < b-a=10\), so answer is no.
Another example: \(a=90,b=100,c=200,d=220\) gives \(d-c=20 > b-a=10\), so answer is yes.
Thus only statement I suffices.

Question 3 · MCQ

Two types of widgets, namely type A and type B, are produced on a machine. The number of machine hours available per week is 80. How many widgets of type A must be produced?
I. One unit of type A widget requires 2 machine hours and one unit of type B widget requires 4 machine hours.
II. The widget dealer wants supply of at least 10 units of type A widget per week and he would not accept less than 15 units of type B widget.
  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, 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 A and B be the units produced.

Statement I alone gives: \(2A + 4B \le 80\), i.e. \(A + 2B \le 40\). This does not determine A.

Statement II alone gives only \(A \ge 10\) and \(B \ge 15\), without relating them to the 80 machine hours.

Combining both: minimum B uses \(15 \times 4 = 60\) hours, leaving exactly 20 hours. Minimum A uses \(10 \times 2 = 20\) hours. Thus A must be exactly 10.

Both statements are needed.

Question 4 · MCQ

What is the area of a regular hexagon?
I. The length of the boundary line of the hexagon is 36 cm.
II. The area of the hexagon is 6 times the area of an equilateral triangle formed on one of the sides.
  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, 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 alone: perimeter of a regular hexagon is \(6s = 36\), so \(s = 6\) cm.

Area = \( \frac{3\sqrt{3}}{2} s^2 = \frac{3\sqrt{3}}{2} \times 36 = 54\sqrt{3} \) cm².

Statement II only restates a property of a regular hexagon and gives no side length, so it is not sufficient alone.

Hence, statement I alone is sufficient.

Question 5 · MCQ

The rate of increase of the price of sugar is observed to be two percent more than the inflation rate expressed in percentage. The price of sugar, on January 1, 1994, is Rs. 20 per kg. The inflation rate for the years 1994 and 1995 are expected to be 8% each. The expected price of sugar on January 1, 1996 would be
  1. A.
    Rs.23.60
  2. B.
    Rs.24.00
  3. C.
    Rs.24.20
    ✓ Correct
  4. D.
    Rs.24.60
Solution
Sugar price increase rate is 2 percentage points above inflation, so it is \(8% + 2% = 10%\) per year.

Price after 2 years:
\(20(1 + 0.10)^2 = 20 \times 1.21 = \text{₹}24.20\).

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