numbers - basic test - cat level

8/3/2019 Numbers - Basic Test - CAT Level

1/6

1.

For any natural number n, n4+n2+1 is

a) odd

b) even

c) either odd or even

d) cant be determined

e) none of these

Given 3 consecutive whole numbers, which of the following statements is/are true?

I. Two of the numbers are even

II. One of the numbers is divisible by 3

III. The sum of numbers is never divisible by 5

a) 1b) 11c) 1 and 11d) 11 and 111e) 111

3.

If x, y and z are integers and (xy) = z then

a) both x and y must be the perfect square.

b) either x is a perfect square or y is a perfect square

c) z cannot be a perfect square

d) None of these

e) All of these

4.

If n is any positive integer, which of the following must be true?

a) 3n+1 is odd

b) n(n+2) is even

c) n(3n+3) is divisible by 6

d) n(n+1) is divisible by 3

e) n(n+1) is divisible by 5

5.


2/6

If A = 441 x 484 x 529 x 576 x 625, then what is the number of the factors in A?

a) 607

b) 5706

c) 1024

d) 6075

e) 595

6.

Which of the following fractions is greater than 1/2 but less than 2/3?

a) 19/39

b) 23/47

c) 29/57

d) 36/54

e) None of these

7.

If m and n are integers and (mn)1/2 = 10, then which of the following cannot be the

value of (m+n)?

a) 29

b) 25c) 52

d) 50

e) Can't be determined

8.

If the approximate square root of (a2+b) , when (a>b), is equal to a +b/2a, then what

is the approximate square root of 66?

a) 6.3b) 8.4

c) 6.5

d) 8.125

e) 9.125


3/6

9.

The number plate on a car shows that its number is a perfect square and when the

number plate is turned upside down, the number is still a perfect square. What is the

possible value of the car plate number?

a)

169b) 36

c) 196

d) 625

e) 125

10.

How many natural numbers are there between 500 and 1300 which are divisible by

8?a) 95

b) 100

c) 105

d) 110

e) 115

11.

Which one is an invalid number?a) (325)7

b) (345)5

c) (543)6

d) (CB7)16

e) None of these

12.

The last three digits in the binary representation of (365247728)10 is:

a) 000

b) 100

c) 110

d) 010


4/6

e) 101

13.

If (25)n x (31)n = (1015)n then the value of (13)n x (52)n is when n > 0:

a) (626)4

b) (462)n

c) (716)n

d) (676)n

e) (816)n

14.

When a two digit number is reversed, the new number is reduced by 63 and the

sum of digits of these individual numbers is 9. Now, if these same numbers are

converted into base x the larger number becomes 5 times that of smaller one the

value of x is:

a) 36

b) 13

c) 15

d) 18

e) 23

15.

If the decimal number 2111 is written in the octal system, then what is its unit place

digit?

a) 0

b) 1

c) 2

d) 3

e) 7

17.


5/6

The product of any two integers is 25, then the minimum possible sum is:

a) 5

b) 10

c) 26

d) 1

e) None of these

16.

How many 3s you have to write down while writing the numbers from 3301 to

3401?

a) 220

b) 218

c) 120

d) 198

e) 100

18.

If 4 p 5 and 10 q -9, then the least value is given by the expression:

a) p.q

b) pq6

c) p6q

d) (pq)5

e) pq2

19.

If (x 5)(y + 6)(z 8) = 1331, then the minimum value of x + y + + z is:

a) 40

b) 33c) 19

d) 45

e) Not unique


6/6

20.

If x + y + z = 21, then the maximum value of (x 6)(y + 7) (z 4) is:

a) 343

b) 216

c) 125

d) 64

e) None of these

numbers - basic test - cat level

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