# GMAT Quantitative Practice, Data Sufficiency

*Question 4*

If A, B and C each represents a distinct digit in the positive three-digit number ABC, what is the number?

(1) The product of the three digits is 20.

(2) A < B < C

- Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is NOT sufficient.
- Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is NOT sufficient.
- BOTH statements (1) and (2) TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
- Each statement ALONE is sufficient to answer the question.
- Statements (1) and (2) TOGETHER are NOT sufficient to answer the question.

## Explanatory Answer

Consider statement (1) alone. The positive single-digit factors of 20 are 1, 2, 4 and 5. In any order, two combinations of three digits satisfy statement (1):

4 ☓ 5 ☓ 1 = 20

5 ☓ 2 ☓ 2 = 20

Therefore, statement (1) alone does not suffice to answer the question. Statement (2) alone clearly does not suffice, as many three-digit numbers meet this condition: 123, 124, 125, and so forth. Now consider both statements together. Only one of the two number combinations satisfying statement (1) also satisfies statement (2):

1 < 4 < 5

Statements (1) and (2) together suffice to answer the question. The three-digit number is 145. The correct response is (C).