The Hindu Business Line : Walk the CAT

A confused bank teller transposed the rupees and paise when he cashed a cheque for Shailaja, giving her rupees instead of paise and paise instead of rupees. After buying a toffee for 50 paise, Shailaja noticed that she was left with exactly three times as much as the amount on the cheque. Which of the following is a valid statement about the cheque amount?

1) Over Rs 22 but less than Rs 23;

2) Over Rs 18 but less than Rs 19;

3) Over Rs 4 but less than Rs 5;

4) Over Rs 13 but less than Rs 14;

5) Over Rs 7 but less than Rs 8.

This question appeared in the Quantitative Section of this year’s CAT (Common Admission Test), which was held yesterday. Here are some more questions, see if you can crack them:

a) How many pairs of positive integers ‘m’, ‘n’ satisfy 1/m + 4/n = 1/12 where ‘n’ is an odd integer less than 60?

(1) 7; (2) 5; (3) 3; (4) 6; (5) 4.

b) Mr David manufactures and sells a single product at a fixed price in a niche market. The selling price of each unit is Rs 30. On the other hand, the cost in rupees, of producing ‘x’ units is 240 + bx + cx², where ‘b’ and ‘c’ are some constants. Mr David noticed that doubling the daily production from 20 to 40 units increases the daily production cost by 66-2/3 per cent. However, an increase in daily production from 40 to 60 units results in an increase of only 50 per cent in the daily production cost. Assume that demand is unlimited and that Mr David can sell as much as he can produce. His objective is to maximise the profit.

i) How many units should Mr David produce daily?

(1) 70; (2) 150; (3) 130; (4) 100; (5) Cannot be determined.

ii) What is the maximum daily profit, in rupees, that Mr David can realise from his business?

(1) 840; (2) 760; (3) 620; (4) 920; (5) Cannot be determined.

c) If p = 1/3 and q = 2/3, then what is the smallest odd ‘n’ such that a_n + b_n < 0.01?

(1) 11; (2) 9; (3) 15; (4) 7; (5) 13.

d) Consider four digit numbers for the first two digits are equal and the last two digits are also equal. How many such numbers are perfect squares?

(1) 4; (2) 0; (3) 1; (4) 3; (5) 2.

d) Shabnam is considering three alternatives to invest her surplus cash for a week. She wishes to guarantee maximum returns on her investment. She has three options, each of which can be utilised fully or partially in conjunction with others.

Option A: Invest in a public sector bank. It promises a return of +0. 10 per cent.

Option B: Invest in mutual funds of ABC Ltd. A rise in the stock market will result in a return of +5 per cent, while a fall will entail a return of -3 per cent.

Option C: Invest in mutual funds of CBA Ltd. A rise in the stock market will result in a return of -2.5 per cent, while a fall will entail a return of +2 per cent.

The maximum guaranteed return to Shabnam in percentage terms is: (1) 0.20; (2) 0.15; (3) 0.30; (4) 0.25; (5) 0.10.

Edited extracts from CAT 2007 question paper.