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

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

Grade:12

2 Answers

Harshit Singh
askIITians Faculty 5870 Points
2 months ago
Dear Student

Suppose 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.
That is, 2+1+y+5 = 8+y
Therefore, 8+y is a factor 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, the value of y should be 1 only i.e. 8+y = 8+1 = 9.

Thanks
Ram Kushwah
108 Points
one month ago
The Given number is
21y5
If this number is divisible by 9 then as per the divisibility rule
the sum of digits will be divisible by 9
Here sum of digits:
=2+1+y+5
=8+y
8+y can be 9,18 etc
But y =0 ,1,3,4,5,6,7,8,9
If y=1 then 8+y=8+1=9
Thus y= 1 correct solution  
Please aprove

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