If 0

Question

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

(1) cb < ca

(2) a – b > c

BrentGMATPrepNow · Answer

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 RELATED VIDEO https://www.youtube.com/watch?v=Od98BOicIq4

GMATinsight · Answer

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

JeffTargetTestPrep · Answer

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

GMATGuruNY · Answer

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.

D .

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If 0 < a < b, is c < 0? (1) cb < ca (2) a – b > c

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