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Question

Choose the digit(s) that can fill in the blank of a four-digit number 531 to make it divisible by 9.

A
0
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B
1
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C
6
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D
9
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Solution

The correct option is D 9
Let the digit to be filled is x.
x+5+3+1=x+9

For the number x531 to be divisible by 9,9+x should be multiple of 9.

x+9=9×n

For n=1,
9+x=9×1
x=0

For n=2,
9+x=9×2
x=9

However, for x=0,x531, i.e., 0531 is a three digit number.

The possible digit that can fill in the blank is 9.

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