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
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Is X^3 even?
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Target question: Is x³ even?hitmoss wrote:If x is an integer, is x³ even?
(1) 2x + 2 is even.
(2) 3x + 1 is 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
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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
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
