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If (a-b)/c<0, is a>b?

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If (a-b)/c<0, is a>b? [#permalink] New post 16 Mar 2013, 22:15
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Question Stats:

75% (01:49) correct 25% (01:17) wrong based on 32 sessions
If (a-b)/c<0, is a>b?

(1) c < 0
(2) a + b < 0
[Reveal] Spoiler: OA

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Last edited by Bunuel on 17 Mar 2013, 01:37, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Inequalities [#permalink] New post 16 Mar 2013, 22:20
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(a-b)/c <0

=> c(a-b)/c^2 < 0
=> ac -bc <0
=> ac<bc

Statement (1) : Tells the sign of (C) means sufficient.

Statement (2) : a+b < 0

=> a < -b

a b a<-b Is a>b?
+ + Not Poss N/A
- - Yes No
- + Yes No
+ - Yes No

Why the answer is not (D).

Please tell what I am missing above

Rgds,
TGC
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Re: If (a-b)/c<0, is a>b? [#permalink] New post 17 Mar 2013, 01:46
Before cross multiplying or multiplying numerator and denominator by c you should keep in mind that c should not be equal to 0
So which statement proves c won't be 0
(1) c < 0
This statement implies that c is not equal to 0
(2) a + b < 0
You aren't sure whether c would be 0 or not.
Hence, the answer should be A

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Re: If (a-b)/c<0, is a>b? [#permalink] New post 17 Mar 2013, 01:53
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Re: If (a-b)/c<0, is a>b? [#permalink] New post 17 Mar 2013, 07:14
Bunuel wrote:
If (a-b)/c<0, is a>b?

(1) c < 0. Multiply (a-b)/c<0 by negative c and flip the sign a-b>0 --> a>b. Sufficient.

(2) a + b < 0. The sum of two numbers is less than zero. Can we tell which of them is greater? (Can we tell whether a>b or a<b?) No, consider a=1, b=-2 and c=-1 AND a=-2, b=1 and c=1. Not sufficient.

Answer: A.



What is wrong in the solution that I gave?

Rgds,
TGC
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Re: Inequalities [#permalink] New post 17 Mar 2013, 07:54
targetgmatchotu wrote:
(a-b)/c <0

=> c(a-b)/c^2 < 0
=> ac -bc <0
=> ac<bc

Statement (1) : Tells the sign of (C) means sufficient.

Statement (2) : a+b < 0

=> a < -b

a b a<-b Is a>b?
+ + Not Poss N/A
- - Yes No
- + Yes No
+ - Yes No

Why the answer is not (D).

Please tell what I am missing above

Rgds,
TGC


Consider one of the cases in your approach above: if both a and b are negative, it's possible that a>b as well as a<b. For example, a=-1, b=-2, and c=-1 AND a=-2, b=-1, and c=1.

Hope it helps.
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Senior Manager
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Joined: 03 Aug 2012
Posts: 323
Concentration: General Management, General Management
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Kudos [?]: 18 [0], given: 69

Re: Inequalities [#permalink] New post 17 Mar 2013, 09:10
Bunuel wrote:
targetgmatchotu wrote:
(a-b)/c <0

=> c(a-b)/c^2 < 0
=> ac -bc <0
=> ac<bc

Statement (1) : Tells the sign of (C) means sufficient.

Statement (2) : a+b < 0

=> a < -b

a b a<-b Is a>b?
+ + Not Poss N/A
- - Yes No
- + Yes No
+ - Yes No

Why the answer is not (D).

Please tell what I am missing above

Rgds,
TGC


Consider one of the cases in your approach above: if both a and b are negative, it's possible that a>b as well as a<b. For example, a=-1, b=-2, and c=-1 AND a=-2, b=-1, and c=1.

Hope it helps.


Why to take c variable in picture .

Given that a<-b
I think appropriate would be
a = -1
b = -2 (here a>b still holding a<-b)

a = -2
b = -1 (here a <b still holding a<-b)

Hence,wrong
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Re: Inequalities [#permalink] New post 17 Mar 2013, 09:38
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targetgmatchotu wrote:
Bunuel wrote:
targetgmatchotu wrote:
(a-b)/c <0

=> c(a-b)/c^2 < 0
=> ac -bc <0
=> ac<bc

Statement (1) : Tells the sign of (C) means sufficient.

Statement (2) : a+b < 0

=> a < -b

a b a<-b Is a>b?
+ + Not Poss N/A
- - Yes No
- + Yes No
+ - Yes No

Why the answer is not (D).

Please tell what I am missing above

Rgds,
TGC


Consider one of the cases in your approach above: if both a and b are negative, it's possible that a>b as well as a<b. For example, a=-1, b=-2, and c=-1 AND a=-2, b=-1, and c=1.

Hope it helps.


Why to take c variable in picture .

Given that a<-b
I think appropriate would be
a = -1
b = -2 (here a>b still holding a<-b)

a = -2
b = -1 (here a <b still holding a<-b)

Hence,wrong


Hi TGC
good to see you back on the forums..........people gather courage from life's storms.

I think the process you suggested is correct and has got no flaws in it....its concise...i do not find any use of third variable here.

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Re: Inequalities   [#permalink] 17 Mar 2013, 09:38
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