CAT 1998 Question Paper


For the following questions answer them individually

Question 31

Find $$2 \circledast 3$$, where $$2\circledast 3$$ need not be equal to $$3\circledast2$$

I. $$1 \circledast 2$$=3

II. $$a \circledast b=\frac{a+b}{a}$$, where a and b are positive.

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Question 32

Radha and Rani appeared in an examination. What was the total number of questions?

I. Radha and Rani together solved 20% of the paper.

II. Radha alone solved 5/3 rd of the paper solved by Rani.

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Question 33

What is the price of tea?

I. Price of coffee is Rs. 5 more than that of tea.

II. Price of coffee was Rs. 5 less than the price of a cold drink which cost three times the price of tea.

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Question 34

What is the value of ‘a’?

I. Ratio of a and b is 3 : 5, where b is positive.

II. Ratio of 2a and b is 10 12 , where a is positive.

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Question 35

In a group of 150 students, find the number of girls.

I. Each girl was given 50 paise, while each boy was given 25 paise to purchase goods totaling Rs. 49.

II. Girls and boys were given 30 paise each to buy goods totalling Rs. 45.

Video Solution
Question 36

There are four envelopes — E1, E2, E3 and E4 — in which one was supposed to put letters L1, L2, L3 and L4 meant for persons C1, C2, C3 and C4 respectively, but by mistake the letters got jumbled up and went in wrong envelopes. Now if C2 is allowed to open an envelope at random, then how will he identify the envelope containing the letter for him?

I. L2 has been put in E1.

II. The letter belonging to C3 has gone in the correct envelope.

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Question 37

There are four racks numbered 1, 2, 3, 4 and four books numbered 1, 2, 3, 4. If an even rack has to contain an odd-numbered book and an odd rack contains an even-numbered book, then what is the position of book 4?

I. Second book has been put in third rack.

II. Third book has been put in second rack.

Video Solution
Question 38

Find the value of X in terms of ‘a’.

I. Arithmetic mean of X and Y is ’a’ while the geometric mean is also ‘a’.

II. Y X = R; X - Y = D.

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Question 39

There are two concentric circles C1 and C2 with radii r1 and r2. The circles are such that C1 fully encloses C2. Then what is the radius of C1?

I. The difference of their circumference is k cm.

II. The difference of their areas is m sq. cm.

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Question 40

A circle circumscribes a square. What is the area of the square?

I. Radius of the circle is given.

II. Length of the tangent from a point 5 cm away from the centre of the circle is given.

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