A number 6x54y is completely divisible by both 9 and 11, then find the

1.	A number 6x54y is completely divisible by both 9 and 11, then find the sum of ‘x’ and ‘y’ (y > x).1. 162. 123. 144. 10
Answer» Correct Answer - Option 2 : 12 GIVEN: A number 6x54y is completely divisible by both 9 and 11. CALCULATION: Divisibility by 9 : If the sum of the digits of a number is divisible by 9, then the number is divisible by 9. Sum of digits = 6 + x + 5 + 4 + y = (15 + x + y) Possible value of ‘x + y’ = 2 and 12 Divisibility by 11: If the difference between the sum of the odd-numbered digits and the sum of the even-numbered digits, counted from right to left, is divisible by 11, then the number is divisible by 11. (6 + 5 + y) – (x + 4) = (7 + y – x) Possible value of ‘y – x’ = 4 Since difference between ‘x’ and ‘y’ is 4 so, its sum cannot be 2. Hence, sum of ‘x’ and ‘y’ = 12

A number 6x54y is completely divisible by both 9 and 11, then find the sum of ‘x’ and ‘y’ (y > x).1. 162. 123. 144. 10

Answer» Correct Answer - Option 2 : 12

GIVEN:

A number 6x54y is completely divisible by both 9 and 11.

CALCULATION:

Divisibility by 9 : If the sum of the digits of a number is divisible by 9, then the number is divisible by 9.

Sum of digits = 6 + x + 5 + 4 + y = (15 + x + y)

Possible value of ‘x + y’ = 2 and 12

Divisibility by 11: If the difference between the sum of the odd-numbered digits and the sum of the even-numbered digits, counted from right to left, is divisible by 11, then the number is divisible by 11.

(6 + 5 + y) – (x + 4) = (7 + y – x)

Possible value of ‘y – x’ = 4

Since difference between ‘x’ and ‘y’ is 4 so, its sum cannot be 2.

Hence, sum of ‘x’ and ‘y’ = 12

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