1
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Question

# If the three digit number 20x is divisible by 9, find the smallest possible value of x.

A
3
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B
5
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C
6
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D
7
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Solution

## The correct option is D 7For a number to be divisible by 9, the sum of its digits should be divisible by 9. Hence for 20x to be divisible by 9, the value of 2 + 0 + x should be divisible by 9. Then, 2 + x should be divisible by 9. The smallest multiple of 9 which is greater than 2 is 9 itself. ⇒ x = 7 Therefore the smallest value of x for which the number 20x is divisible by 9 is 7. Verification: As we obtained the value of x as 7, the number is 207. Sum of its digits = 2 + 0 + 7 = 9. 9 is divisible by 9. Therefore, 207 is divisible by 9. (2079=23)

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