# Aptitude - Numbers

### Exercise :: Numbers - General Questions

101.

The sum of even numbers between 1 and 31 is:

 A. 6 B. 28 C. 240 D. 512

Explanation:

Let Sn = (2 + 4 + 6 + ... + 30). This is an A.P. in which a = 2, d = 2 and l = 30

Let the number of terms be n. Then,

a + (n - 1)d = 30 2 + (n - 1) x 2 = 30 n = 15. Sn = n (a + l) = 15 x (2 + 30) = (15 x 16) = 240. 2 2

102.

If the number 91876 * 2 is completely divisible by 8, then the smallest whole number in place of * will be:

 A. 1 B. 2 C. 3 D. 4 E. None of these

Explanation:

Then number 6x2 must be divisible by 8. x = 3, as 632 is divisible 8.

103.

2056 x 987 = ?

 A. 1936372 B. 2029272 C. 1896172 D. 1926172 E. None of these

Explanation:

 2056 x 987 = 2056 x (1000 - 13) = 2056 x 1000 - 2056 x 13 = 2056000 - 26728 = 2029272.

104.

On multiplying a number by 7, the product is a number each of whose digits is 3. The smallest such number is:

 A. 47619 B. 47719 C. 48619 D. 47649

Explanation:

By hit and trial, we find that

47619 x 7 = 333333.

105.

 If 60% of 3 of a number is 36, then the number is: 5

 A. 80 B. 100 C. 75 D. 90

Explanation:

Let the number be x. Then

 60% of 3 of x = 36 5 60 x 3 x x = 36 100 5 x = 36 x 25 = 100 9 Required number = 100

106.

If x and y are the two digits of the number 653xy such that this number is divisible by 80, then x + y = ?

 A. 2 or 6 B. 4 C. 4 or 8 D. 8 E. None of these

Explanation:

80 = 2 x 5 x 8

Since 653xy is divisible by 2 and 5 both, so y = 0.

Now, 653x is divisible by 8, so 13x should be divisible by 8.

This happens when x = 6. x + y = (6 + 0) = 6.

107.

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

 A. 3 B. 6 C. 7 D. 8

Explanation:

Let the two consecutive odd integers be (2n + 1) and (2n + 3). Then,

(2n + 3)2 - (2n + 1)2 = (2n + 3 + 2n + 1) (2n + 3 - 2n - 1)

= (4n + 4) x 2

= 8(n + 1), which is divisible by 8.

108.

What is the unit digit in (4137)754?

 A. 1 B. 3 C. 7 D. 9

Explanation:

Unit digit in (4137)754 = Unit digit in {[(4137)4]188 x (4137)2}

=Unit digit in { 292915317923361 x 17114769 }

= (1 x 9) = 9

109.

587 x 999 = ?

 A. 586413 B. 587523 C. 614823 D. 615173

Explanation:

 587 x 999 = 587 x (1000 - 1) = 587 x 1000 - 587 x 1 = 587000 - 587 = 586413.

110.

A number was divided successively in order by 4, 5 and 6. The remainders were respectively 2, 3 and 4. The number is:

 A. 214 B. 476 C. 954 D. 1908

Explanation:

``` 4 | x            z = 6 x 1 + 4  = 10
-----------
5 | y -2         y = 5 x z + 3  = 5 x 10 + 3  = 53
-----------
6 | z - 3        x = 4 x y + 2  = 4 x 53 + 2  = 214
-----------
| 1 - 4

Hence, required number = 214.
```