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

[BTGModeratorVI]

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

Answer: A
Source: Veritas Prep

[Brent@GMATPrepNow]

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

Answer: A
Source: Veritas Prep

Target question: Is c < 0?

Given: 0 < a < b

Statement 1: cb < ca
Subtract ca from both sides to get: cb - ca < 0
Factor: c(b - a) < 0
IMPORTANT: if a < b, we can be certain that (b - a) is POSITIVE.
So, we can divide both sides of the inequality by (b - a) to get: c < 0
PERFECT!
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: |c| > 1
There are several values of c that satisfy statement 2. Here are two:
Case a: c = -2, in which case c < 0
Case b: c = 2, in which case c > 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent

[swerve]

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

Answer: A
Source: Veritas Prep

Here we go:

1) \(cb < ca\)
Only possible if \(c\) is less than \( 0\), because \(a < b\) is given, so to make \(a > b\), both \(a\) and \(b\) must be multiplied by any number which is less than \(0\)

For example \(-3<7\)
So when we multiply any negative number to both the sides and sign changes.
\(-6 > -14\)

Hence, A is sufficient. \(\Large{\color{green}\checkmark}\)

2) \(|c|> 1\) given two conditions

\(c > 1\) and \(c < -1\). Not Sufficient \(\Large{\color{red}\chi}\)

Therefore, A