# numbers aptitude questions

11.

5358 x 51 = ?
A.     273258    B.     273268
C.     273348    D.     273358

Explanation:

5358 x 51     = 5358 x (50 + 1)
= 5358 x 50 + 5358 x 1
= 267900 + 5358
= 273258.
12.

The sum of first five prime numbers is:
A.     11    B.     18
C.     26    D.     28

Explanation:

Required sum = (2 + 3 + 5 + 7 + 11) = 28.

Note: 1 is not a prime number.

Definition: A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself.

13.

The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?
A.     240    B.     270
C.     295    D.     360

Explanation:

Let the smaller number be x. Then larger number = (x + 1365).

x + 1365 = 6x + 15

5x = 1350

x = 270

Smaller number = 270.

14.

(12)3 x 64 ÷ 432 = ?
A.     5184    B.     5060
C.     5148    D.     5084
E.     None of these
15.

72519 x 9999 = ?
A.     725117481    B.     674217481
C.     685126481    D.     696217481
E.     None of these

Explanation:

72519 x 9999     = 72519 x (10000 – 1)
= 72519 x 10000 – 72519 x 1
= 725190000 – 72519
= 725117481.
16.

If the number 517*324 is completely divisible by 3, then the smallest whole number in the place of * will be:
A.     0     B.     1
C.     2    D.     None of these

Explanation:

Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x), which must be divisible by 3.

x = 2.

17.

The smallest 3 digit prime number is:
A.     101    B.     103
C.     109    D.     113

Explanation:

The smallest 3-digit number is 100, which is divisible by 2.

100 is not a prime number.

101 < 11 and 101 is not divisible by any of the prime numbers 2, 3, 5, 7, 11.

101 is a prime number.

Hence 101 is the smallest 3-digit prime number.

18.

Which one of the following numbers is exactly divisible by 11?
A.     235641    B.     245642
C.     315624    D.     415624

Explanation:

(4 + 5 + 2) – (1 + 6 + 3) = 1, not divisible by 11.

(2 + 6 + 4) – (4 + 5 + 2) = 1, not divisible by 11.

(4 + 6 + 1) – (2 + 5 + 3) = 1, not divisible by 11.

(4 + 6 + 1) – (2 + 5 + 4) = 0, So, 415624 is divisible by 11.

19.

(?) – 19657 – 33994 = 9999
A.     63650    B.     53760
C.     59640    D.     61560
E.     None of these

Explanation:

19657         Let x – 53651  = 9999
33994         Then, x = 9999 + 53651 = 63650
—–
53651
—–

20.

The sum of first 45 natural numbers is:
A.     1035    B.     1280
C.     2070    D.     2140

Explanation:

Let Sn =(1 + 2 + 3 + … + 45). This is an A.P. in which a =1, d =1, n = 45.

Sn =     n     [2a + (n – 1)d]     =     45     x [2 x 1 + (45 – 1) x 1]     =         45     x 46         = (45 x 23)
2     2     2

= 45 x (20 + 3)

= 45 x 20 + 45 x 3

= 900 + 135

= 1035.

Shorcut Method:

Sn =     n(n + 1)     =     45(45 + 1)     = 1035.
2     2