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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

  1. Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is NOT sufficient.
  2. Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is NOT sufficient.
  3. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
  4. Each statement ALONE is sufficient to answer the question.
  5. 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).