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

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If 0 < a < b, is c < 0? 1.cb < ca 2.|c| > 1 [#permalink] New post   12 Nov 2015, 09:10
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If 0 < a < b, is c < 0?
1.cb < ca
2.|c| > 1

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A
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BrentGMATPrepNow
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Re: If 0 < a < b, is c < 0? 1.cb < ca 2.|c| > 1 [#permalink] New post   12 Nov 2015, 09:35
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GMATinsight wrote:
If 0 < a < b, is c < 0?

1) cb < ca
2) |c| > 1


Slightly different solution:

Target question: Is c < 0?

Given: 0 < a < b

Statement 1: cb < ca
Subtract ca from both sides to get: cb - ca < 0
Factor: c(b - a) < 0
IMPORTANT: if a < b, we can be certain that (b - a) is POSITIVE.
So, we can divide both sides of the inequality by (b - a) to get: c < 0
PERFECT!
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 statement 2. 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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Re: If 0 < a < b, is c < 0? 1.cb < ca 2.|c| > 1 [#permalink] New post   12 Nov 2015, 09:29
GMATinsight wrote:
If 0 < a < b, is c < 0?
1.cb < ca
2.|c| > 1

https://www.GMATinsight.com


GIven , b>a , is c<0?

Per statement 1, cb<ca --> cb-ca<0---> c(b-a) < 0 only possible for c<0 as b>a --> b-a>0. Sufficient.

Per statement 2, |c| >1 ---> c<-1 or c>1, making this statement not sufficient.

A is thus the correct answer.
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Re: If 0 < a < b, is c < 0? 1.cb < ca 2.|c| > 1 [#permalink] New post   28 Oct 2018, 12:36
1) cb<ca
only possible if c is < 0, because a<b is given
so to make a>b, both a and b must be multiplied by any no which is smaller than 0
ex- 3<7
so when we multiply any negative no to both the sides and sign changes.
-6>-14
hence A is sufficient.
2)|c|> 1 given two conditions
c>1 and c<-1
not suff

Ans - (A)
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Re: If 0 < a < b, is c < 0? 1.cb < ca 2.|c| > 1 [#permalink] New post   06 Dec 2020, 07:17
GMATinsight wrote:
If 0 < a < b, is c < 0?
1.cb < ca
2.|c| > 1

https://www.GMATinsight.com


(1) \(cb - ca < 0\)
\(c(b-a) < 0\)
\(c < 0\) or \(b < a\)

Since we're told in the question that a < b, we can conclude c < 0. SUFFICIENT.

(2) \(|c| > 1 \)

\(c > 1\) or \(c < -1\)

INSUFFICIENT.

Answer is A.
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Re: If 0 < a < b, is c < 0? 1.cb < ca 2.|c| > 1 [#permalink] New post   20 Dec 2020, 09:10
But if we assume the values of a & b as 1/4 and 1/2 and then take C = 2 as statement 1, we get contradicting answers thus A shouldn't be sufficient. What am I missing here?
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Re: If 0 < a < b, is c < 0? 1.cb < ca 2.|c| > 1 [#permalink] New post   28 Sep 2023, 08:10
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Re: If 0 < a < b, is c < 0? 1.cb < ca 2.|c| > 1 [#permalink]
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