What is the smallest positive integer greater than 100 that is divisible by 9? — GMAT

What is the smallest positive integer greater than $100$ that is divisible by $9$ ?

Answer: 108

The smallest positive integer greater than

100

that is divisible by

9

108

An integer is divisible by 9 if it is an integer multiple of 9. Multiples of 9 around 100 are

9 \times 11 = 99

and

9 \times 12 = 108

. Since 99 is not greater than 100, the smallest integer meeting the condition is 108.

Divide 100 by 9 to locate the adjacent multiples of 9.

100 = 9 \times 11 + 1

This shows that

9 \times 11 = 99

is the largest multiple of 9 that is less than or equal to 100.

Determine the next multiple of 9 by adding 9 to 99 (or evaluating

9 \times 12

99 + 9 = 108

Since 99 is less than 100, the next consecutive multiple of 9 must be the smallest multiple strictly greater than 100.

Divisibility and Multiples of Integers

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