149 is a 3-digit positive integer, product of… | GMAT Sprint

Free Practice Question

PS · Problem Solving

705-805

Combinations

149 is a 3-digit positive integer, product of whose digits is 1x4x9 = 36. How many 3-digit positive integers exist whose product of digits is 36?

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Explanation

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Official Explanation

Official

The factor pairs of 36:

36*1

18*2

12*3

9*4

and

6*6

Focusing on the first three as they have double digit values:

36*1: The 36*1 can be broken down to a product of three digits while keeping 1, in the following ways:

9*4*1

6*6*1

9*4*1

can be arranged in

3! = 6

different ways.

6*6*1

can be arranged in

\frac{3!}{2!1!} = 3

ways.

18*2: The 18*2 can be broken down to a product of three digits while keeping 2 in the following ways:

9*2*2

6*3*2

.…

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What this question tests

What it tests

Whether you can count arrangements and selections correctly — permutations vs. combinations.

Common trap

Overcounting: treating a selection as ordered when order does not matter, or forgetting to divide by duplicates.