Question

If the seven-digit number 161x208 is divisible by 11 and the four-digit number 953y is divisible by 9, then, what is the value of (x + y)?
1. 7
2. 8
3. 12
4. 10

Answer 1

Correct Answer - Option 1 : 7

GIVEN:

The seven-digit number 161x208 is divisible by 11 and the four-digit number 953y is divisible by 9

CONCEPT:

Divisibility rule for 11 = Find the sum of the digits in the even places and the sum of the digits in the odd places. If the difference between the two sums is 0 or a multiple of 11, then the given number would be divisible by 11.

Divisibility law of 9 = A number divisible by 9 if the sum of its digit is divisible by 9.

CALCULATION:

(i) The seven-digit number 161x208 is divisible by 11.

⇒ (1 + 1 + 2 + 8) – (6 + x + 0)

⇒ 12 – (6 + x)

⇒ (6 – x)

If we put x = 6, then the difference become zero.

⇒ x = 6

(ii) The four digit number 953y is divisible by 9.

⇒ 9 + 5 + 3 + y

⇒ 17 + y

If we put y = 1, the number become 18 which is divisible by 9.

⇒ y = 1

According to question –

(x + y) = (6 + 1) = 7

∴ The value of (x + y) is 7.