Question

If the number 2819X64 is completely divisible by 11, then the smallest whole number in place of X will be:

1. 4
2. 3
3. 5
4. 7

Answer 1

Correct Answer - Option 3 : 5

Given:

2819X64 is completely divisible by 11

Concept used:

If any number is divisible by 11, then the difference of the sum of its alternate digits is always divisible by 11.

ABCDEFG be a number divisible by 11

So, [(A + C + E + G) – (B + D + F)] is always divisible by 11.

Calculation:

2819X64 is completely divisible by 11

(2 + 1 + X + 4) – (8 + 9 + 6) is also divisible by 11

⇒ (2 + 1 + X + 4) – (8 + 9 + 6)

⇒ 7 + X – 23

⇒ X – 16

If we put X = 5, then the value of X – 16 will be divisible by 11

So, X = 5

∴ The smallest value of X is 5.