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

1) m < p
2) m < 0

Nice question.

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 NEGATIVE or POSITIVE. 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

j_shreyans wrote:Hi ,

Given: mv<pv<0

Target Question : v>0 ?

statement 1 - m<p

lets try the numbers

m=-2 and p=-1

then v should be positive.

if m=1 and p=2

then v should be negative

so this statement is not sufficient.

The part above in red is not correct.

If m=1, p=2 and v is negative (e.g., v = -1), then the GIVEN CONDITIONS (mv < pv < 0) are not met.
When we plug in the values of m, p and v, we get: (1)(-1) < (2)(-1) < 0
This simplifies to -1 < -2 < 0, which is incorrect.

Cheers,
Brent