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If 0 < a < b, is c < 0?

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Source: — Data Sufficiency |
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by GMATGuruNY » Mon Nov 04, 2019 4:10 am
ktrout2020 wrote:If 0 < a < b, is c < 0?

(1) cb < ca
(2) a - b > c

Source: Veritas
0 < a < b implies the following:
b-a = bigger - smaller = POSITIVE
a-b = smaller - bigger = NEGATIVE

Statement 1:
cb - ca < 0
c(b-a) < 0
Implication:
c and b-a have DIFFERENT SIGNS.
Since b-a is positive, c must be negative.
SUFFICIENT.

Statement 2:
c < a-b
c < negative
Thus, c must be negative.
SUFFICIENT.

The correct answer is D.
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by Brent@GMATPrepNow » Mon Nov 04, 2019 5:47 am
ktrout2020 wrote:If 0 < a < b, is c < 0?

(1) cb < ca
(2) a - b > c

Source: Veritas
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: D

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

Cheers,
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