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
