Number Theory Previous Year Questions (CAT)  Set 0021

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

Question 1
Every ten years the Indian government counts all the people living in the country. Suppose that the director of the census has reported the following data on two neighbouring villages Chota hazri and Mota hazri:
Chota hazri has 4,522 fewer males than Mota hazri.
Mota hazri has 4,020 more females than males.
Chota hazri has twice as many females as males.
Chota hazri has 2,910 fewer females than Mota hazri.
What is the total number of males in Chota hazri?
(1) 11264
(2) 14174
(3) 5632
(4) 10154Â Â (CAT 2001)Â

Answer: Option 3

Question 2
At a certain fast food restaurant, Brian can buy 3 burgers, 7 shakes, and one order of fries for Rs. 120 exactly. At the same place it would cost Rs. 164.5 for 4 burgers, 10 shakes, and one order of fries. How much would it cost for an ordinary meal of one burger, one shake, and one order of fries?
(1) Rs. 31
(2) Rs. 41
(3) Rs. 21
(4) Cannot be determinedÂ (CAT 2001)Â

Answer: Option 1

Question 3
If a, b, c and d are four positive real numbers such that abcd = 1, what is the minimum value of (1 + a) (1 + b) (1 + c) (1 + d) ?
(1) 4
(2) 1
(3) 16
(4) 18Â (CAT 2001)Â

Answer: Option 3

Question 4

Answer: Option 1

Question 5

Answer: Option 3

Question 6
Ashish is given Rs. 158 in one rupee denominations. He has been asked to allocate them into a number of bags such that any amount required between Re. 1 and Rs. 158 can be given by handing out a certain number of bags without opening them. What is the minimum number of bags required?
(1) 11
(2) 12
(3) 13
(4) None of theseÂ (CAT 2001)Â

Answer: Option 4

Question 7
In some code, letters, a, b, c, d and e represent numbers 2, 4, 5, 6 and 10. However, we don’t know which letter represent which number.
Consider the following relationships:
i. a + c = e
ii. b – d = d
iii. e + a = b
(1) b = 4, d = 2
(2) a = 4, e = 6
(3) b = 6, e = 2
(4) a = 4, c = 6 (CAT 2001)

Answer: Option 2

Question 8
A change making machine contains 1 rupee, 2 rupee and 5 rupee coins. The total number of coins is 300. The amount is Rs. 960. If the number of 1 rupee coins and the number of 2 rupee coins are interchanged, the value comes down by Rs. 40. The total number of 5 rupee coins is
(1) 100
(2) 140
(3) 60
(4) 150Â (CAT 2001)Â

Answer: Option 2

Question 9
Let n be the number of different 5 digit numbers, divisible by 4 with the digits 1, 2, 3, 4, 5 and 6, no digit being repeated in the numbers. What is the value of n?
(1) 144
(2) 168
(3)192
(4) None of theseÂ Â (CAT 2001)Â

Answer: Option 3

Question 10
New Age Consultants have three consultants Gyani, Medha and Buddhi. The sum of the number of projects handled by Gyani and Buddhi individually is equal to the number of projects in which Medha is involved. All three consultants are involved together in 6 projects. Gyani works with Medha in 14 projects. Buddhi has 2 projects with Medha but without Gyani and 3 projects with Gyani but without Medha. The total number of projects for New Age Consultants is one less than twice the number of projects in which more than one consultant is involved.
What is the number of projects in which Gyani alone is involved?
(1) Uniquely equal to zero
(2) Uniquely equal to 1
(3) Uniquely equal to 4
(4) Cannot be determined uniquely
What is the number of projects in which Medha alone is involved?
(1) Uniquely equal to zero
(2) Uniquely equal to 1
(3) Uniquely equal to 4
(4) Cannot be determined uniquely (CAT 2003 Leaked)