BTGModeratorVI wrote: ↑Sun Jul 19, 2020 1:40 pm
Is |2x−y| < 10?
(1) 2x − y < 10
(2) y − 2x <10
Answer:
C
Source: Economist GMAT
Target question: Is |2x−y|<10?
This is a good candidate for
Rephrasing the Target Question
We can take the inequality |2x−y|<10 and rewrite is as -10 < 2x−y < 10
REPHRASED target question: Is -10 < 2x−y < 10?
Aside: Here’s a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100
Statement 1: 2x−y<10
So, it's possible that 2x−y = 9 or 2x−y = 8 or 2x−y = 0 or 2x−y = -11 etc
Now consider these two conflicting cases:
case a: If 2x−y = 9, then it IS the case that
-10 < 2x−y < 10
case b: If 2x−y = -11, then it is NOT the case that
-10 < 2x−y < 10
Since we cannot answer the
REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: y−2x<10
We want to know about 2x-y, so let's multiply both sides of the given inequality by -1
When we do that, we get: 2x-y > -10
Or we can write it as -10 < 2x-y
So, it's possible that 2x−y = -9 or 2x−y = -8 or 2x−y = 0 or 2x−y = 11 etc
Now consider these two conflicting cases:
case a: If 2x−y = -9, then it IS the case that
-10 < 2x−y < 10
case b: If 2x−y = 11, then it is NOT the case that
-10 < 2x−y < 10
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 2x−y < 10
Statement 2 tells us that -10 < 2x-y
When we COMBINE THEM, we get:
-10 < 2x−y < 10
Perfect! That's the REPHRASED target question that we were trying to answer!
Since we can answer the
REPHRASED target question with certainty, the combined statements are SUFFICIENT
Answer: C
