Inequality

[josh80]

If mv < pv < 0, is v > 0?

1) m < p

2) m < 0

[Brent@GMATPrepNow]

If mv < pv < 0, is v > 0?

1) m < p
2) m < 0

Nice question. What's the source?

Target question: Is v > 0

Given: mv < pv < 0

Statement 1: m < p

IMPORTANT: Notice what happens if we take mv < pv and divide both sides by v.
The resulting inequality will depend on whether v is positive or negative. So, let's consider two cases:
case a: v is NEGATIVE.
When we take mv < pv and divide both sides by v, we get m > p
We changed the direction of the inequality sign since we divided by a NEGATIVE value.

case b: v is POSITIVE.
When we take mv < pv and divide both sides by v, we get m < p
The direction of the inequality sign stayed the same since we divided by a POSITIVE value.

Statement 1 tells us that m < p, which means we can rule out case a.
So, we conclude that v is POSITIVE
In other words, v > 0
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: m < 0
We're told that mv < pv < 0, which means that mv < 0
In other words, the product mv is NEGATIVE
Statement 2 tell us that m is NEGATIVE
In order for the product mv to be NEGATIVE, v must be positive
In other words, v > 0
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent

[Patrick_GMATFix]

This is QID 1241 in the GMATFix Solutions Engine. Follow the link for a more thorough discussion.

In short, because mv and pv have the same sign (they're both < 0), we know that m and p must have the same sign as well.

Statement 1 m < p
mv < pv can be reduced to m < p by dividing both sides by v. Since the inequality sign in the result "<" did not flip direction, we can safely conclude that v is positive. (if v were negative, dividing mv<pv by v would yield m>p)

(1) is Sufficient

Statement 2 m < 0
We know from the stem that mv<0. Since m is negative, v must be positive (if v were also negative, then mv would be greater than 0).

(2) is Sufficient

Answer: D