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Is a > b ?

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Manager
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Joined: 13 Aug 2010
Posts: 113
Is a > b ?  [#permalink]

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New post 21 Oct 2010, 01:13
2
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

69% (00:41) correct 31% (00:42) wrong based on 72 sessions

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Is a > b ?

(1) ca > cb
(2) 3a > 3b
Manager
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Joined: 15 Apr 2010
Posts: 127
Re: Is a > b ?  [#permalink]

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New post 21 Oct 2010, 01:25
1. ca > cb
We do not know the sign of variable c. It could be positive or negative.
If c is +ve then a > b
If c is -ve then a < b.

Not sufficient.

2. 3a > 3b
diving by 3 we get, a > b
Sufficient

Hence, B is the correct answer.
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Re: Is a > b ?  [#permalink]

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New post 31 Oct 2018, 05:56
Top Contributor
prab wrote:
Is a > b ?

(1) ca > cb
(2) 3a > 3b


Target question: Is a > b ?

Statement 1: ca > cb
The temptation here is to divide both sides by c to get a > b, but this approach has a major flaw, since we don't know whether c is POSITIVE or NEGATIVE
If c is NEGATIVE, then we must REVERSE the direction of the inequality after dividing by c (see the video below for more on this)

Alternatively, we can demonstrate this by examining some values of a, b and c that satisfy statement 1:
Case a: a = 1, b = 0 and c = 1. In this case, ca > cb becomes (1)(1) > (1)(0), which is true. Here, the answer to the target question is YES, it is the case that a > b
Case b: a = 0, b = 1 and c = -1. In this case, ca > cb becomes (-1)(0) > (-1)(1), which is true. Here, the answer to the target question is NO, it is NOT the case that a > b
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 3a > 3b
Since 3 is POSITIVE, we can safely divide both sides of the inequality by 3 to get: a > b
So, the answer to the target question is YES, it is the case that a > b
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

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Re: Is a > b ?   [#permalink] 31 Oct 2018, 05:56
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