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 Post subject: GMAT Number TheoryPosted: Tue Aug 02, 2011 2:57 pm

Joined: Sun May 30, 2010 3:15 am
Posts: 424
If x and s are both positive integers, is the product of x and s even?
(1) (x + 3) is a prime number.
(2) (s + 1) is a prime number.

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.

(A) If at least one of x or s is even, the product xs will be even. This is because:
ODD × EVEN = EVEN and EVEN × EVEN = EVEN.

Statement (1) tells us that x + 3 is a prime number. Since x is at least 1 (from the question stem), the prime number (x + 3) must be at least 4. 4 is not prime, but all prime numbers greater than 4 are odd, so:
x + 3 = ODD
x = ODD - 3
An ODD number minus another ODD number is always EVEN. x = EVEN.

Since x is even, the product xs will be even and Statement (1) is sufficient.

Statement (2) allows for the possibility that the prime number is 2, where s = 1, which is an ODD. The prime number could also be 3, where s = 2, which is EVEN. The product xs can be odd or even, so Statement (2) is insufficient.

Since Statement (1) is sufficient, and Statement (2) is insufficient, the correct answer is choice (A).
----------
How is x at least 1?

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 Post subject: Re: math (t.2, qt.12): Number theory, ODD/EVENPosted: Tue Aug 02, 2011 3:06 pm

Joined: Sun May 30, 2010 2:23 am
Posts: 498
questioner wrote:
How is x at least 1?
x is at least 1 because x is an integer and x is positive. The smallest possible positive integer is 1.

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