Proportion mv<pv is true for m<p when v is positive only, given this answers our question with statement(1) Sufficient and we answer yes. Statement(2) m<0 means v>0 and is Sufficient.
d

topic of question is inequality

Spartacus2000 wrote:If mv < pv < 0, is v > 0?

(1) m < p
(2) m < 0

Spartacus2000 wrote:If mv < pv < 0, is v > 0?

(1) m < p
(2) m < 0

Statement 1: m < p for above inequality ( mv < pv < 0) to hold m & p must have same sign.

case 1: m<p m>0 & p>0

so in this case for mv < pv < 0 to be true v<0

m < p when multiplied by v (v<0) the inequality will become mv > pv => v cannot be <0

case 2: m <0 & p<0 => v > 0

mv < pv < 0 is true

=> v can only be >0 = Statement 1 is sufficient

Statement 2:

m < 0

we know mv <0 => if m< 0 v must be >0 ..hence Statement 2 is sufficient


Answer is D

v(m-p) < 0 meaning v<0 or m-p <0

a m<p meaning m-p < 0 means v>0 sufficient.

b m<0 check for p + and - values.

p+ (m-p) < 0 means v> 0
p- pv< 0 means v>0.
sufficient.

thus D it is.

Topic would be torture / irrelevant to grad school.


mv < pv < 0, is v > 0

My first bit of advice is to be super careful with DS. They seem to be built on tricking people. Doesn't hurt to do a little bit of extra checking when working on these.

1) m<p
I used values to check different scenarios. For example:
m = -3, p = -2, v=4
-12 < -8 < 0
When I made v negative and assigned new values to m and p to satisfy m<p, it messed everything up.
(Sufficient)

2) m<0
we know that m is negative, and that mv<0, so v must be positive. (sufficient)

Answer: D

We are given mv < pv < 0.

If v > 0, then m < p < 0, or m < p, p < 0, AND m < 0.

The contrapositive must hold true: if v <= 0, then m >= p, p >= 0, and m >= 0.

Thus you can immediately rephrase the question stem as follows:

Is either m < p, p < 0, or m < 0?

Statement 1) check, sufficient.
Statement 2) check, sufficient.

D