Question

If a seven-digit number 7x634y2 is divisible by 88, then for the largest value of y, what is the difference of the values of x and y?

• A. 8
• B. 4
• C. 2
• D. 6

Answer 1

Answer:

C. 2

Solution: Concept: The divisibility rule of 8 states that for a number to be divisible by 8, its last three-digit should be perfectly divisible by 8. The divisibility rule of 11 states that for a number to be divisible by 11, the difference between the sum of odd and even digits should be completely divisible by 11. Calculations: Using Divisibility rule of 8, we get- ∴ 4y2 is completely divisible by 8 if y is 7(largest value of y). (∴ y = 7) Similarly using divisibility rule of 11, we get- ⇒ (7 + 6 + 4 + 2) - (x + 3 + 7) = 19 - 10 - x = 9 - x ⇒ The number is perfectly divisible if x = 9 (∴ x = 9) ∴ Value of x - y = 9 - 7 = 2 The value of x - y is 2.