If the nine-digit number 43x1145y2 is divisible by 88, then what is the smallest value of (3x – 2y)?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e -7
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Concept |
Understanding |
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If a number is divisible by 88 it must be divisible by 8 and 11 Divisibility by 8: Last 3 digits must be divisible by 8. Divisibility by 11: [Sum of digits at odd positions] – [Sum of digits at even positions] = 0 or divisible by 11 |
43x1145y2 is divisible by 88 |
Last 3 digits 5y2 must be divisible by 8: Hence, y = 9 or 5 or 1 If divisible by 11: If y = 1 (4 + x + 1 + 5 + 2) – (3 + 1 + 4 + 1) = 0 ⇒ 12 + x – 9 = 0 ⇒ x = -2 (Not possible) If y = 5 (4 + x + 1 + 5 + 2) – (3 + 1 + 4 + 5) = 0 ⇒ 12 + x – 13 = 0 ⇒ x = 1 Hence, x = 1, y = 5 (3x – 2y) = 3 – 10 = -7 |