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by SG1492 » Sat Jul 12, 2014 10:55 pm
If a,b,and c are integers, is 2a - b + c greater than a - b - 2c?
(1) a is positive.
(2) c is positive.

OA:C
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Source: — Data Sufficiency |
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by GMATinsight » Sat Jul 12, 2014 10:56 pm
Question:

Is 2a - b + c > a - b - 2c?

Question Rephrased:

Is (2a - b + c) - (a - b - 2c) >0

Is a + 3c >0 ?

Statement 1) a>0 but If c is negative with high absolute value in comparison to a then answer to the question will be NO and if c is positive then answer will be YES

INCONSISTENT VALUES THEREFORE INSUFFICIENT


Statement 2) c>0 but If a is negative with Very high absolute value in comparison to 3c then answer to the question will be NO and if a is positive then answer will be YES

INCONSISTENT VALUES THEREFORE INSUFFICIENT

Combining the two statement a nd c are both positive therefore a+3c will be positive as well. Therefore SUFFICIENT.

ANSWER: [spoiler]OPTION "C"[/spoiler]
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by Brent@GMATPrepNow » Sun Jul 13, 2014 6:07 am
Drishti wrote:If a,b,and c are integers, is 2a - b + c greater than a - b - 2c?

(1) a is positive.
(2) c is positive.
Target question: Is 2a - b + c > a - b - 2c?
This is a great candidate for rephrasing the target question.

Aside: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

Take 2a - b + c > a - b - 2c
Add b to both sides to get: 2a + c > a - 2c
Add 2c to both sides to get: 2a + 3c > a
Subtract a from both sides to get: a + 3c > 0

REPHRASED target question: Is a + 3c > 0?

Statement 1: a is positive.
No information about c, so there's no way to determine whether a + 3c > 0

Alternatively, we can examine some conflicting cases that satisfy statement 1 (a is positive):
Case a: a = 1 and c = 1, in which case a + 3c > 0
Case b: a = 1 and c = -1, in which case a + 3c < 0
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: c is positive.
No information about c, so there's no way to determine whether a + 3c > 0

Alternatively, we can examine some conflicting cases that satisfy statement 2 (c is positive):
Case a: a = 1 and c = 1, in which case a + 3c > 0
Case b: a = -5 and c = 1, in which case a + 3c < 0
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 a is positive
Statement 2 tells us that c is positive
If a and c are both positive, then it MUST BE THE CASE that a + 3c > 0
Since we can answer the REPHRASED target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent

For even more information on rephrasing the target question, you can read this article I wrote for BTG: https://www.beatthegmat.com/mba/2014/06/ ... t-question
Brent Hanneson - Creator of GMATPrepNow.com
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