If 21y5 is a multiple of 9, where y is a digit, what is the value of y?

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asked Dec 27, 2017 in Mathematics by Golu (37,045 points) 19 174 629

If 21y5 is a multiple of 9, where y is a digit, what is the value of y?

1 Answer

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answered Dec 27, 2017 by Ankit Agarwal (28,847 points) 7 34 107

Since 21y5 is a multiple of 9.
Therefore according to the divisibility rule of 9, the sum of all the digits should be a multiple of 9.
Therefore, 2+1+y+5=9
=> 8+y = 9

=> y=1
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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