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Is k^2 + k - 2 > 0?

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Is k^2 + k - 2 > 0?

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Is k^2 + k - 2 > 0?

(1) k is an integer greater than zero.
(2) k divided by 2 is an integer.

The OA is C .

Why is C? I don't know how to use both statements together to get a solution.

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Vincen wrote:
Is k^2 + k - 2 > 0?

(1) k is an integer greater than zero.
(2) k divided by 2 is an integer.

The OA is C .

Why is C? I don't know how to use both statements together to get a solution.
Statement 1: k > 0
Pick easy numbers. Case 1: k = 1. $$ k^2 + k -2$$ becomes $$1^2 + 1 - 2 = 0$$. So the expression is not greater than 0, and we have a NO.

Case 2: k = 2; $$ k^2 + k -2$$ becomes $$2^2 + 2 - 2 = 4$$ The expression is greater than 0, and we have a YES. Statement 1 alone is not sufficient.

Statement 2: We can reuse Case 2. If k = 2; $$ k^2 + k -2$$ becomes $$2^2 + 2 - 2 = 4$$ The expression is greater than 0, and we have a YES.
Case 3: k = -2. $$ k^2 + k -2$$ becomes $$(-2)^2 - 2 - 2 = 0$$. 0 is not greater than 0, we have a NO. Not sufficient.

Together. We know that k is a positive integer divisible by 2, so k = 2, 4, 6, et. No matter what we pick $$k^2 + k - 2$$ will be positive, and the answer will always be YES. The statements together are sufficient and the answer is C

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Vincen wrote:
Is k² + k - 2 positive?

(1) k is an integer greater than zero.
(2) k divided by 2 is an integer.
Target question: Is k² + k - 2 > 0?
This is a good candidate for rephrasing the target question.
What needs to happen in order for k² + k - 2 to be positive?
Factor to get: k² + k - 2 = (k + 2)(k - 1)
For (k + 2)(k - 1) to be positive, we need one of two scenarios:

Scenario A: (k + 2) and (k - 1) are both POSITIVE
For this to occur, k must be greater than 1

Scenario B: (k + 2) and (k - 1) are both NEGATIVE
For this to occur, k must be less than -2

In other words, for k² + k - 2 to be positive, it must be the case that EITHER k is greater than 1 OR k is less than -2
REPHRASED target question: Is it true that EITHER k is greater than 1, OR k is less than -2?

Aside: Here’s a video with tips on rephrasing the target question: http://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1100
Once we've rephrased the target question, we can head to the two statements....

Statement 1: k is an integer greater than zero.
There are several values of k that satisfy statement 1. Here are two:
Case a: k = 2, in which case the answer to the REPHRASED target question is YES
Case b: k = 1, in which case the answer to the REPHRASED target question is NO
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: k divided by 2 is an integer
There are several values of k that satisfy statement 2. Here are two:
Case a: k = 2, in which case the answer to the REPHRASED target question is YES
Case b: k = 0, in which case the answer to the REPHRASED target question is NO
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that k is positive
Statement 2 tells us that k divided by 2 is an integer.
In other words, k/2 must be a positive integer
Some possible values of k: 2, 4, 6, 8, . . .
In all of these cases, the answer to the REPHRASED target question is YES
Since we can answer the REPHRASED target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent

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k² + k - 2 > 0 becomes

(k + 2) * (k - 1) > 0

That'll be greater than 0 if either:

(i) the smaller of the two terms, k - 1, is positive
(ii) the larger of the two terms, k + 2, is negative

So our question can be rephrased as "Is either k > 1 or -2 > k?" and from there the statements are a snap! Smile

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