If the number 321a9246b is divisible by 72, then find the value of (a2 - b2).
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 9.
72 = 8 × 9
Divisibility rule of 8: the last three digits must be divisible by 8
⇒ 46b ÷ 8
⇒ b = 4
Divisibility rule of 9: the sum of the digits must be divisible by 9
⇒ 3 + 2 + 1 + a + 9 + 2 + 4 + 6 + 4 = 31 + a
⇒ a = 5
⇒ (a2 - b2) = 52 - 42 = 25 - 16 = 9