Number Theory Previous Year Questions (CAT)  Set 0017

Previous years`s CAT questions: Number Theory
Post your solutions as reply to respective questions below.

Question 1
Three bells chime at an interval of 18 min, 24 min and 32 min. At a certain time they begin to chime together. What length of time will elapse before they chime together again?
a. 2 hr and 24 min
b. 4 hr and 48 min
c. 1 hr and 36 min
d. 5 hr (CAT 1995)

Question 2
The number of votes not cast for the Praja Party increased by 25% in the National General Election over those not cast for it in the previous Assembly Polls, and the Praja Party lost by a majority twice as large as that by which it had won the Assembly Polls. If a total 2,60,000 people voted each time. How many voted for the Praja Party in the Assembly Elections.
(a) 1,10,000
(b) 1,50,000
(c) 1,40,000
(d) 1,20,000 Â Â Â (CAT 1994)

Question 3
If the harmonic mean between two positive numbers is to their geometric mean as 12 : 13; then the numbers could be in the ratio
(a) 12 : 13
(b) 1/12 : 1/13
(c) 4 : 9
(d) 2 : 3 (CAT 1994)

Question 4
Fourth term of an arithmetic progression is 8. What is the sum of the first 7 terms of the arithmetic progression?
(a) 7
(b) 64
(c) 56
(d) Cannot be determinedÂ (CAT 1994)

Question 5

Question 6
Along a road lie an odd number of stones placed at intervals of 10m. These stones have to be assembled around the middle stone. A person can carry only one stone at a time. A man carried out the job starting with the stone in the middle, carrying stones in succession, thereby covering a distance of 4.8 km. Then the number of stones is
(a) 35
(b) 15
(c) 29
(d) 31 (CAT 1994)

Question 7
What is the smallest number which when increased by 5 is completely divisible by 8, 11 and 24?
(a) 264
(b) 259
(c) 269
(d) None of these (CAT 1994)

Question 8
Which is the least number that must be subtracted from 1856, so that the remainder when divided by 7, 12, and 16 is 4.
(a) 137
(b) 1361
(c) 140
(d) 172 (CAT 1994)

Question 9
Two oranges three bananas and four apples cost Rs. 15. Three oranges, two bananas and one apple cost Rs. 10. I bought 3 oranges, 3 bananas and 3 apples. How much did I pay?
(a) Rs. 10
(b) Rs. 8
(c) Rs 15
(d) cannot be determinedÂ (CAT 1993)

Question 10
An intelligence agency decides on a code of 2 digits selected from 0, 1, 2, âŚ. , 9. But the slip on which the code is handâwritten allows confusion between top and bottom, because these are indistinguishable. Thus, for example, the code 91 could be confused with 16. How many codes are there such that there is no possibility of any confusion?
(a) 25
(b) 75
(c) 80
(d) None of theseÂ (CAT 1993)