# Aptitude - Numbers

### Exercise :: Numbers - General Questions

81.

The difference of the squares of two consecutive even integers is divisible by which of the following integers ?

 A. 3 B. 4 C. 6 D. 7

Explanation:

Let the two consecutive even integers be 2n and (2n + 2). Then,

(2n + 2)2 = (2n + 2 + 2n)(2n + 2 - 2n)

= 2(4n + 2)

= 4(2n + 1), which is divisible by 4.

82.

Which one of the following is a prime number ?

 A. 119 B. 187 C. 247 D. 551 E. None of these

Explanation:

551 > 22

All prime numbers less than 24 are : 2, 3, 5, 7, 11, 13, 17, 19, 23.

119 is divisible by 7; 187 is divisible by 11; 247 is divisible by 13 and 551 is divisible by 19.

So, none of the given numbers is prime.

83.

The sum all even natural numbers between 1 and 31 is:

 A. 16 B. 128 C. 240 D. 512

Explanation:

Required sum = (2 + 4 + 6 + ... + 30)

This is an A.P. in which a = 2, d = (4 - 2) = 2 and l = 30.

Let the number of terms be n. Then,

tn = 30 a + (n - 1)d = 30 2 + (n - 1) x 2 = 30 n - 1 = 14 n = 15 Sn = n (a + l) = 15 x (2 + 30)   = 240. 2 2

84.

The difference between the place value and the face value of 6 in the numeral 856973 is

 A. 973 B. 6973 C. 5994 D. None of these

Explanation:

(Place value of 6) - (Face value of 6) = (6000 - 6) = 5994

85.

If a and b are odd numbers, then which of the following is even ?

 A. a + b B. a + b + 1 C. ab D. ab + 2 E. None of these

Explanation:

The sum of two odd number is even. So, a + b is even.

86.

Which one of the following numbers is completely divisible by 99?

 A. 3572404 B. 135792 C. 913464 D. 114345 E. None of these

Explanation:

99 = 11 x 9, where 11 and 9 are co-prime.

By hit and trial, we find that 114345 is divisibleby 11 as well as 9. So, it is divisible by 99.

87.

The sum of how many terms of the series 6 + 12 + 18 + 24 + ... is 1800 ?

 A. 16 B. 24 C. 20 D. 18 E. 22

Explanation:

This is an A.P. in which a = 6, d = 6 and Sn = 1800

 Then, n [2a + (n - 1)d] = 1800 2 n [2 x 6 + (n - 1) x 6] = 1800 2 3n (n + 1) = 1800 n(n + 1) = 600 n2 + n - 600 = 0 n2 + 25n - 24n - 600 = 0 n(n + 25) - 24(n + 25) = 0 (n + 25)(n - 24) = 0 n = 24

Number of terms = 24.

88.

(51+ 52 + 53 + ... + 100) = ?

 A. 2525 B. 2975 C. 3225 D. 3775

Explanation:

This is an A.P. in which a = 51, l = 100 and n = 50. Sum = n (a + l) = 50 x (51 + 100)   = (25 x 151)   = 3775. 2 2

89.

1904 x 1904 = ?

 A. 3654316 B. 3632646 C. 3625216 D. 3623436 E. None of these

Explanation:

 1904 x 1904 = (1904)2 = (1900 + 4)2 = (1900)2 + (4)2 + (2 x 1900 x 4) = 3610000 + 16 + 15200. = 3625216.

90.

What is the unit digit in(795 - 358)?

 A. 0 B. 4 C. 6 D. 7

Explanation:

Unit digit in 795 = Unit digit in [(74)23 x 73]
= Unit digit in [(Unit digit in(2401))23 x (343)]
= Unit digit in (123 x 343)
= Unit digit in (343)
= 3

Unit digit in 358 = Unit digit in [(34)14 x 32]
= Unit digit in [Unit digit in (81)14 x 32]
= Unit digit in [(1)14 x 32]
= Unit digit in (1 x 9)
= Unit digit in (9)
= 9

Unit digit in (795 - 358) = Unit digit in (343 - 9) = Unit digit in (334) = 4.

So, Option B is the answer.