If an 11-digit number 765y88436x6 is divisible by 72, and x assumes the largest value, then what is the value of (x − y)?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 8.
72 = 8 × 9
Divisibility rule of 8: the last three digits must be divisible by 8
⇒ 6x6 ÷ 8
⇒ x = 9
Divisibility rule of 9: the sum of the digits must be divisible by 9
⇒ 7 + 6 + 5 + y + 8 + 8 + 4 + 3 + 6 + 9 + 6 = 62 + y
⇒ y = 1
⇒ (x − y) = 9 - 1 = 8