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Is X^3 even?

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Junior | Next Rank: 30 Posts
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by hitmoss » Mon Apr 27, 2015 6:32 am
If x is an integer, is x3 even?

(1) 2x + 2 is even.

(2) 3x + 1 is even.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.

OA is: B
Hitmoss:)

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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Mon Apr 27, 2015 8:27 am
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
Brent Hanneson - Creator of GMATPrepNow.com
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by [email protected] » Mon Apr 27, 2015 10:25 am
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

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Rich
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