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

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CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
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If 0 < a < b, is c < 0? 1.cb < ca 2.|c| > 1  [#permalink]

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12 Nov 2015, 09:10
1
13
00:00

Difficulty:

15% (low)

Question Stats:

79% (01:16) correct 21% (01:33) wrong based on 407 sessions

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

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Re: If 0 < a < b, is c < 0? 1.cb < ca 2.|c| > 1  [#permalink]

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12 Nov 2015, 09:35
9
2
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

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Brent
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##### General Discussion
CEO
Joined: 20 Mar 2014
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Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
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WE: Engineering (Aerospace and Defense)
Re: If 0 < a < b, is c < 0? 1.cb < ca 2.|c| > 1  [#permalink]

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12 Nov 2015, 09:29
GMATinsight wrote:
If 0 < a < b, is c < 0?
1.cb < ca
2.|c| > 1

http://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.
Intern
Joined: 05 Jan 2017
Posts: 35
Re: If 0 < a < b, is c < 0? 1.cb < ca 2.|c| > 1  [#permalink]

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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] 28 Oct 2018, 12:36
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# If 0 < a < b, is c < 0? 1.cb < ca 2.|c| > 1

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