Number Theory Previous Year Questions (CAT)  Set 0003

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

Question 1

Answer: Option 2 Option 4

Question 2
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) 6
(2) 4
(3) 7
(4) 5
(5) 3 (CAT 2007)

Answer: Option 5

Question 3
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 Rupees 13 but less than Rupees 14
(2) Over Rupees 7 but less than Rupees 8
(3) Over Rupees 22 but less than Rupees 23
(4) Over Rupees 18 but less than Rupees 19
(5) Over Rupees 4 but less than Rupees 5 (CAT 2007)

Answer: Option 4

Question 4
Consider the set S = {2, 3, 4, ...., 2n + 1}, where n is a positive integer larger than 2007. Define X as the average of the odd integers in S and Y as the average of the even integers in S. What is the value of X – Y?
(1) 0
(2) 1
(3) n/2
(4) n + 1/2n
(5) 2008 (CAT 2007)

Answer: Option 2

Question 5
All the page numbers from a book are added, beginning at page 1. However, one page number was mistakenly added twice. The sum obtained was 1000. Which page number was added twice?
(1) 44
(2) 45
(3) 10
(4) 12 (CAT 2001)

Answer: Option 3

Question 6
For a Fibonacci sequence, from the third term onwards, each term in the sequence is the sum of the previous two terms in that sequence. If the difference in squares of seventh and sixth terms of this sequence is 517, what is the tenth term of this sequence?
(1) 147
(2) 76
(3) 123
(4) Cannot be determinedÂ Â ( CAT 2001 )

Answer: Option 3

Question 7
A shop stores x kg of rice. The first customer buys half this amount plus half a kg of rice. The second customer buys half the remaining amount plus half a kg of rice. Then the third customer also buys half the remaining amount plus half a kg of rice. Thereafter, no rice is left in the shop. Which of the following best describes the value of x?
(1) 2 ≤ x ≤ 6
(2) 5 ≤ x ≤ 8
(3) 9 ≤ x ≤ 12
(4) 11≤ x ≤ 14
(5) 13 ≤ x ≤ 18 (CAT 2008 )

Answer: Option 2

Question 8
A test has 50 questions. A student scores 1 mark for a correct answer, −1/3 for a wrong answer, and −1/6 for not attempting a question. If the net score of a student is 32, the number of questions answered wrongly by that student cannot be less than
(1) 6
(2) 12
(3) 3
(4) 9 (CAT 2003 Leaked)

Answer: Option 3

Question 9
The number of common terms in the two sequences 17, 21, 25, … , 417 and 16, 21, 26, … , 466 is
(1) 78
(2) 19
(3) 20
(4) 77
(5) 22 (CAT 2008 )

Answer: Option 3

Question 10
The integers 1, 2, …, 40 are written on a blackboard. The following operation is then repeated 39 times: In each repetition, any two numbers, say a and b, currently on the blackboard are erased and a new number a + b – 1 is written. What will be the sum of the numbers left on the board at the end?
(1) 820
(2) 821
(3) 781
(4) 819
(5) 780 (CAT 2008 )