If the 8-digit number 7y9745x2 is divisible by 72, then the value of (2x − y) for the greatest value of x is:
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Correct answer: D
Explanation
The correct answer is option 4 i.e. 16.
72 = 8 × 9
Divisibility rule of 8: the last three digits must be divisible by 8
⇒ 5x2 ÷ 8
⇒ x = 9
Divisibility rule of 9: the sum of the digits must be divisible by 9
⇒ 7 + y + 9 + 7 + 4 + 5 + 9 + 2 = 43 + y
⇒ y = 2
⇒ (2x − y) = 2 × 9 - 2 = 18 - 2 = 16