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Re: Is |2x−y|<10? (1) 2x−y<10 (2) y−2x<10
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20 Nov 2016, 10:40

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Top Contributor

1

Bunuel wrote:

Is |2x−y|<10?

(1) 2x−y<10

(2) y−2x<10

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?

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

Re: Is |2x−y|<10? (1) 2x−y<10 (2) y−2x<10
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20 Nov 2016, 13:01

Statement 1 and 2 are individually insufficient (obvious if you work out a few numbers), therefore A, B and D are out.

If the two statements are considered together, then definitely |2x−y|<10.

Therefore the answer is C.
_________________

Uh uh. I know what you're thinking. "Is the answer A, B, C, D or E?" Well to tell you the truth in all this excitement I kinda lost track myself. But you've gotta ask yourself one question: "Do I feel lucky?" Well, do ya, punk?

Re: Is |2x−y|<10? (1) 2x−y<10 (2) y−2x<10
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23 Apr 2017, 02:27

GMATPrepNow wrote:

Bunuel wrote:

Is |2x−y|<10?

(1) 2x−y<10

(2) y−2x<10

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

After combining the 2 statements, can you add them? The result will be 0<20 (number and its opposite will always yield zero). But does 0<20 have any meaning? could it help me answer the Target question?

Re: Is |2x−y|<10? (1) 2x−y<10 (2) y−2x<10
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23 Apr 2017, 04:52

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[quote="Mo2men" Dear Brent,

After combining the 2 statements, can you add them? The result will be 0<20 (number and its opposite will always yield zero). But does 0<20 have any meaning? could it help me answer the Target question?[/quote]

Unfortunately, that won't help us, since a number and its opposite will always add to zero.