# Number Theory Previous Year Questions (CAT) - Set 0023

• Previous years`s CAT questions: Number Theory

Post your solutions as reply to respective questions below.

• Question 1

For real numbers x, y, let

f(x, y) = Positive square-root of (x + y), if (x + y)0.5 is real

= (x + y)2, otherwise

g(x, y) = (x + y)2, if (x + y)0.5 is real

= –(x + y), otherwise

Under which of the following conditions is f(x, y) necessarily greater than g(x, y)?

(1) Both x and y are less than –1

(2) Both x and y are positive

(3) Both x and y are negative

(4) y > x                 (CAT 2000)

• Answer: Option 1

• Question 2

For a real number x,

let f(x) = 1/(1 + x), if x is non-negative

= 1+ x, if x is negative

f n(x) = f(f n – 1(x)), n = 2, 3, ....

r is an integer > 2. Then, what is the value of f r – 1(–r) + f r(–r) + f r + 1 (–r) ?

(1) -1

(2) 0

(3) 1

(4) None of these   (CAT 2000)

• Answer: Option 2

• Question 3

For two positive integers a and b define the function h(a,b) as the greatest common factor (G.C.F) of a, b. Let A be a set of n positive integers. G(A), the G.C.F of the elements of set A is computed by repeatedly using the function h. The minimum number of times h is required to be used to compute G is

a. n/2

b. (n – 1)

c. n

d. None of these         (CAT 1999)

• Question 4

• Question 5

• Question 6

• Question 7

I have one-rupee coins, 50-paisa coins and 25-paisa coins.

The number of coins are in the ratio 2.5 : 3 : 4

If the total amount with me is Rs. 210, find the number of one-rupee coins.

a. 90

b. 85

c. 100

d. 105Â Â Â  (CAT 1998 )

• Question 8

In a locality, there are five small cities: A, B, C, D and E. The distances of these cities from each other are as follows.

AB = 2 km AC = 2km AD > 2 km AE > 3 km BC = 2 km

BD = 4 km BE = 3 km CD = 2 km CE = 3 km DE > 3 km

If a ration shop is to be set up within 2 km of each city, how many ration shops will be required?

a. 2

b. 3

c. 4

d. 5  (CAT 1996)

• Question 9

In a locality, there are five small cities: A, B, C, D and E. The distances of these cities from each other are as follows.

AB = 2 km AC = 2km AD > 2 km AE > 3 km BC = 2 km

BD = 4 km BE = 3 km CD = 2 km CE = 3 km DE > 3 km

If a ration shop is to be set up within 3 km of each city, how many ration shops will be required?

a. 1

b. 2

c. 3

d. 4  (CAT 1996)

• Question 10

A student gets an aggregate of 60% marks in five subjects in the ratio 10 : 9 : 8 : 7 : 6. If the passing marks are 50% of the maximum marks and each subject has the same maximum marks, in how many subjects did he pass the examinaiton?

a. 2

b. 3

c. 4

d. 5 Â  (CAT 1997)

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