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.

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

RELATED VIDEO FROM OUR COURSE

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(1) We don't know about c, it could be 0, negative, or positive. Insufficient.

(2) 3a>3b ⇒a>b, as 3 is positive, Sufficient.

The answer is B
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Is a > b ?

(1) ca > cb
ca - cb > 0
c(a - b) >0

1. c and (a - b) > 0 then YES a > b where a and b are both positive
2. c and (a - b) > 0 then NO a > b where a must be smaller than b

(2) 3a > 3b
a > b
Sufficient.
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