hitmoss wrote:If x is an integer, is x³ even?

(1) 2x + 2 is even.
(2) 3x + 1 is even.

Target question: Is x³ even?
If x is an integer, there are two possible cases:
case a: x is EVEN, in which case x³ = (EVEN)(EVEN)(EVEN) = EVEN
case b: x is ODD, in which case x³ = (ODD)(ODD)(ODD) = ODD

So, x³ is even ONLY WHEN x is even. So, we can REPHRASE our target question....
REPHRASED target question: Is x even?

Aside: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

Statement 1: 2x + 2 is even
If we factor this expression, we get 2(x + 1)
Since we can rewrite 2x + 2 as the product of 2 and some integer, (x+1), we can see that 2x + 2 IS ALWAYS EVEN for any integer value of x
In other words, x can be either even or odd
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 3x + 1 is even
If 3x + 1 is even, then we can conclude that 3x is ODD.
If 3x is odd, then x must be odd [if x were even, then 3x would be even]
So, we can be certain that x is NOT even
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent

Hi hitmoss,

This DS question can be solved by using Number Properties and/or TESTing VALUES.

We're told that X is an INTEGER. We're asked if X^3 is EVEN. This is a YES/NO question.

Fact 1: 2X + 2 is EVEN

IF....
X = 1
2(1) + 2 = 4
1^3 = 1 and the answer to the question is NO

IF....
X = 2
2(2) + 2 = 6
2^3 = 8 and the answer to the question is YES
Fact 1 is INSUFFICIENT

Fact 2: 3X + 1 is EVEN

IF....
X = 1
3(1) + 1 = 4
1^3 = 1 and the answer to the question is NO

IF...
X = 2
3(2) + 1 = 7 which is NOT even. This means that X CANNOT be 2. If you recognize the Number Property here, you'll realize that X CANNOT be EVEN. Since we know that X is an INTEGER, since it cannot be even, it MUST be ODD....

(Odd)^3 = Odd
eg
1^3 = 1
3^3 = 27
5^3 = 125
Etc.
The answer to the question is ALWAYS NO.
Fact 2 is SUFFICIENT

Final Answer: B

GMAT assassins aren't born, they're made,
Rich