Number Theory Previous Year Questions (CAT)  Set 0009

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

Question 1
There are six persons sitting around a round table. Pankaj is sitting left of Dayananad who is facing Kundan. Ranjan is sitting right of Dayanand. Yash is sitting left of Pankaj and Abhishek is sitting right of Ranjan. If Pankaj and Ranjan swap their position and Yash and Abhishek also swap their position, then who will be to left of Abhishek?
(1) Kundan
(2) Yash
(3) Dayanand
(4) Pankaj (CAT 2002)

Answer: Option 1

Question 2
A transport company charges for its vehicles in the following manner If the driving is 5 hours or less, the company charges Rs. 60 per hour or Rs. 12 per km (which ever is larger) If driving is more than 5 hours, the company charges Rs. 50 per hour or Rs. 7.5 per km (which ever is larger). If Anand drove it for 30 km and paid a total of Rs. 300, then for how many hours does he drive?
(1) 4
(2) 5.5
(3) 7
(4) 6 (CAT 2002)

Answer: Option 4

Question 3
Number S is equal to the square of the sum of the digits of a 2 digit number D. If the difference between S and D is 27, then D is
(1) 32
(2) 54
(3) 64
(4) 52 (CAT 2002)

Answer: Option 2

Question 4
A boy finds the average of 10 positive integers. Each integer contains two digits. By mistake, the boy interchanges the digits of one number say ‘ba’ for ‘ab’. Due to this, the average becomes 1.8 less than the previous one. What was the difference of the two digits a and b?
(1) 4
(2) 2
(3) 6
(4) 8 (CAT 2002)

Answer: Option 2

Question 5
For all integers n > 0, 7^{6n} – 6^{6n} is divisible by
(1) 13
(2) 128
(3) 549
(4) None of these (CAT 2002)

Answer: Option 1

Question 6
The sum of 3^{rd }and 15^{th }elements of an arithmetic progression is equal to the sum of 6^{th}, 11^{th }and 13^{th }elements of the same progression. Then which element of the series should necessarily be equal to zero?
(1) 1^{st}
(2) 9^{th}
(3) 12^{th}
(4) None of the aboveÂ Â (CAT 2003 Leaked)

Answer: Option 3

Question 7
On a straight road XY, 100 metres in length, 5 stones are kept beginning from the end X. The distance between two adjacent stones is 2 metres. A man is asked to collect the stones one at a time and put at the end Y. What is the distance covered by him?
(1) 460 metres
(2) 540 metres
(3) 860 metres
(4) 920 metres (CAT 2002)

Answer: Option 3

Question 8
The remainder when 2^{256} is divided by 17 is
(1) 7
(2) 13
(3) 11
(4) 1 (CAT 2002)

Answer: Option 4

Question 9
A man received a cheque. The amount in Rs. has been transposed for paise and vice versa. After spending Rs. 5 and 42 paise, he discovered he now had exactly 6 times the value of the correct cheque amount. What amount he should have received?
(1) Rs. 5.30
(2) Rs. 6.44
(3) Rs. 60.44
(4) Rs. 16.44 (CAT 2002)

Answer: Option 2

Question 10
Suppose, for any real number x, [x] denotes the greatest integer less than or equal to x. Let L(x, y) = [x] + [y] + [x + y] and G(x, y) = [2x] + [2y]. Then it’s impossible to find any two positive real numbers x and y for which
(1) L(X, Y) > G(X, Y)
(2) L(X, Y) = G(X, Y)
(3) L(X, Y) < G(X, Y)
(4) None of these (CAT 2002)