If a 10-digit number 46789x531y is divisible by 72, then the value of (2x + 5y), for the largest value of x is:
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Correct answer: B
Explanation
The Correct Answer is option 2 i.e. 28.
Divisibility rule:
If a number is divisible by 72 it must be divisible by 8 and 9
Divisibility by 8:
The last 3 digits must be divisible by 8
Eight-digit no.: 46789x531y is divisible by 72
The last 3 digits 31y must be divisible by 8:
Hence, y = 2
Now it will be divisible by 9 also:
Sum of digits = 4 + 6 + 7 + 8 + 9 + x + 5 + 3 + 1 + 2 = 45 + x
The largest value of x so that it is divisible by 9 = 9
Hence,
⇒ (2x + 5y) = 2 × 9 + 5 × 2 = 28