Aptitude - Numbers

Exercise :: Numbers - General Questions

11. 

5358 x 51 = ?

A. 273258
B. 273268
C. 273348
D. 273358

Answer: Option A

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

Answer: Option D

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

Answer: Option B

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

Answer: Option A

Explanation:

Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62

15. 

72519 x 9999 = ?

A. 725117481
B. 674217481
C. 685126481
D. 696217481
E. None of these

Answer: Option A

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.
B. 1
C. 2
D. None of these

Answer: Option C

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

Answer: Option A

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

Answer: Option D

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

Answer: Option A

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

Answer: Option A

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