GMAT Number Theory (Data Sufficiency)

questioner · **Joined:** Tue Apr 13, 2010 8:48 am **Posts:** 448

If ab = c where a and b are prime numbers and c is a positive integer, what is the value of b?
(1) c is even.
(2) a is odd.

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) If ab = c, then a and b are prime factors of c, because a and b are prime numbers.
Let's start with Statement (1). If c is even, and c is the product of a and b, then we know that either a or b is even, or that they're both even. Since the only even prime number is 2, either a, b, or both must be 2. Since a could be 2, and b could be any other prime number, Statement (1) is insufficient.

Statement (2) tells us that a is odd. This tells us nothing about b, so b could still be any prime number. Therefore, Statement (2) is also insufficient.

When we combine Statements (1) and (2), we can conclude that, if c is even, and a is odd, then b must be 2. This is sufficient to answer the question. Since the statements combined provide enough information to answer the question, the correct answer is choice (C).For more help with this subject, please see: Properties of Integers-------------

Is it not possible that the value of b could be either 2 or -2 making the correct answer E?

Gennadiy · **Joined:** Fri Apr 09, 2010 2:11 pm **Posts:** 426

Original statement tells us that b is a prime number. Therefore it is a positive integer. So it can not be -2.

GMAT Number Theory (Data Sufficiency)

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