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If 0 < a < b, is c < 0? (1) cb < ca (2) a – b > c
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06 Jun 2017, 11:28
06 Jun 2017, 11:28
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Re: If 0 < a < b, is c < 0? (1) cb < ca (2) a – b > c
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06 Jun 2017, 13:37
06 Jun 2017, 13:37
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Bunuel wrote:
If 0 < a < b, is c < 0?
(1) cb < ca
(2) a – b > c
(1) cb < ca
(2) a – b > c
Target question: Is c < 0?
Given: 0 < a < b
If a < b, then we know that b - a > 0
In other words, b - a = some positive number
It also means that a - b = some negative number
Statement 1: cb < ca
Subtract ca from both sides to get: cb - ca < 0
Factor: c(b - a) < 0
So, c(some positive number) < 0
This means that c must be a negative number.
In other words, c < 0
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: a – b > c
So, some negative number > c
If c is less than some negative number, then c must be a negative number.
In other words, c < 0
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer:
ASIDE: For statement 1, once we get to c(some positive number) < 0, we can also just divide both sides by some positive number to get c < 0
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Re: If 0 < a < b, is c < 0? (1) cb < ca (2) a – b > c
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06 Jun 2017, 23:34
06 Jun 2017, 23:34
Expert Reply
Bunuel wrote:
If 0 < a < b, is c < 0?
(1) cb < ca
(2) a – b > c
(1) cb < ca
(2) a – b > c
Is c <0?
Statement 1: c(b-a)<0
But since b>a>0 so b-a will be positive
Hence c must be negative
Sufficient
Statement 2: a-b>c
a-b is negative as a<b
I.e. c<negative
Hence c is definitely negative
Sufficient
Answer Option D
