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If 0 < a < b, is c < 0?

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If 0 < a < b, is c < 0?

by gmattesttaker2 » Mon Jun 23, 2014 7:01 am
Hello,

Can you please tell me how to solve Statement 2:

If 0 < a < b, is c < 0?
1.cb < ca
2.|c| > 1

OA: A

1) Since b > a and given cb < ca => c[spoiler] < 0 - Sufficient.[/spoiler]

2) |c| > 1
=> c > +/- 1
=> c > 1 or c > -1
However, I was not sure how to prove from here that 2 is in-sufficient. Can you please assist?

Thanks a lot,
Sri
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Source: — Data Sufficiency |

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by [email protected] » Mon Jun 23, 2014 11:57 am
Hi Sri,

You made a minor math mistake when you dealt with Fact 2:

We're told that |C| > 1

This means that C can be positive (e.g. 2, 3, 4, 1.5) or negative (e.g. -2, -3, -4, -1.5). More specifically, it means that.....

C > 1
or
C < -1

Since the question is asking if C < 0? Then the answer is inconsistent...

If C = 2, then the answer is NO.
If C = -2, then the answer is YES.
Fact 2 is INSUFFICIENT.

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by GMATinsight » Mon Jun 23, 2014 9:14 pm
2) |c| > 1
=> c > +/- 1
=> c > 1 or c > -1
However, I was not sure how to prove from here that 2 is in-sufficient. Can you please assist?
This step was a mistake because
|c| > 1 means c>1 or c<-1

Therefore this statement is Insufficient.

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by Brent@GMATPrepNow » Tue Jun 24, 2014 8:43 pm
gmattesttaker2 wrote: If 0 < a < b, is c < 0?

1) cb < ca
2) |c| > 1
Here's another way to handle statement 1.

Target question: Is c < 0?

Given: 0 < a < b
IMPORTANT: if a < b, then b - a = some positive number

Statement 1: cb < ca
Subtract ca from both sides to get cb - ca < 0
Factor to get: c(b - a) < 0
Replace b - a to get: c(some positive number) < 0
This means that c must be negative.
In other words, c < 0
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: |c| > 1
There are several values of c that satisfy this condition. Here are two:
Case a: c = -2, in which case c < 0
Case b: c = 2, in which case c > 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

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