BTGModeratorVI wrote: ↑

Tue May 12, 2020 2:12 pm

Is k^2 + k – 2 > 0?

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

Answer: C
Source: 800Score

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?

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