If a seven-digit number 7x634y2 is divisible by 88, then for the largest value of y, what is the difference between the values of x and y?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 2.
88 = 8 × 11
Divisibility rule of 8: the last three digits must be divisible by 8
⇒ 4y2 ÷ 8
⇒ y = 7
Divisibility rule of 11: if the difference between the sum of its digits at odd places and the sum of its digits at even places is either 0 or divisible by 11
⇒ (7 + 6 + 4 + 2) - (x + 3 + 7)
⇒ 19 - x - 10 = 0
⇒ 9 - x = 0
⇒ x = 9
Difference = 9 - 7 = 2