Post subject: GMAT Number Theory (Data Sufficiency)

Posted: Mon Apr 30, 2012 12:34 pm

Joined: Sun May 30, 2010 3:15 am Posts: 424

The sum of the digits of a three-digit number is 11. What is the product of the three digits? (1) The number is divisible by 5. (2) The hundreds digit is twice the tens digit.

A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. D. Either statement BY ITSELF is sufficient to answer the question. E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, meaning that further information would be needed to answer the question.

(C) Statement (1) alone is not sufficient because it tells us only that the number has a units digit of 0 or 5. If the number has a units digit of 0, the product of the digits will be 0 (since 0 times any number is 0), and if the number has a units digit of 5, the product of the digits might not be zero (depending on whether one of the other digits is 0).

For instance, the number 515 has digits that add to 11, yet the product of the digits is 25. Therefore, Statement (1) is insufficient.

Statement (2) is not sufficient by itself either. By choosing the tens digit starting from 1, we conclude the following. The number can be 218 or 425 or 632. The product of the digits is different in each case.

Combined, the two statements are sufficient. The only possibility is that the number is 425, and so the product of the digits is 40.

Since the statements are both insufficient individually but sufficient when combined, the correct answer is choice (C). ---------- This doesn't explain why the one's digit cannot be 0 when Statement 1 and 2 are combined.

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