Discussion
A nine-digit number 565x9274y is divisible by number 88. Then, the value of (2x + 3y) is :
Answer: B
The value of \((2x + 3y)\) is 26.
A number divisible by 88 is divisible by both 8 and 11.
Divisibility by 8: the last three digits, 74y, must be divisible by 8. Only 744 = 8 × 93 works, so y = 4.
Divisibility by 11: in 5 6 5 x 9 2 7 4 4, the digits in odd places sum to 5 + 5 + 9 + 7 + 4 = 30 and those in even places to 6 + x + 2 + 4 = 12 + x. Their difference, 18 - x, must be a multiple of 11, so x = 7.
\[ 2x + 3y = 2(7) + 3(4) = 14 + 12 = 26 \]
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