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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We are given that 0 < a < b and we need to determine whether c is negative.

Statement One Alone:

cb < ca

Since we know that a and b are positive and that b is greater than a, we see that c must be negative. For example, if a = 2 and b = 3, in order for cb < ca, c could be -1, such that -3 < -2. Statement one alone is sufficient to answer the question.

Statement Two Alone:

a – b > c

Since a is less than b and they are both positive, (a - b) must be negative; thus, we have:

Negative number > c

Since c is less than some negative number, c is also negative. Statement two is sufficient to answer the question.

Answer: D
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