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