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Question
If 21y5 is a multiple of 9, where y is a digit, what is the value of y?
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Solution
If a number is a multiple of 9, then the sum of its digits will be divisible by 9.
Sum of digits of 21y5 = 2 + 1 + y + 5 = 8 + y
Hence, 8 + y should be a multiple of 9.
This is possible when 8 + y is any one of these numbers 0, 9, 18, 27, and so on …
However, since y is a single digit number, this sum can be 9 only. Therefore, y should be 1 only.
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