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Re: inequality problem [#permalink]
10 Jun 2009, 09:47

1

This post received KUDOS

Given:

mv<pv<0 ---- (1)

Asking

v<0?

Looking at (1) mv and pv are both less than zero. This means either m & p are positive and v is negative or m & p are negative and v is positive.

Lets look at statement 1.

It tells us m<p we also know that mv<pv from (1). The only way we can get m<p is by dividing both sides by v, however we do not change the inequality sign if the number or variable we are dividing by is positive. Hence if we divide both sides by v when v is positive we get m<p. Hence statement 1 is sufficient to tell us that v is not less than 0.

Lets look at statement 2. It tells us m<0 i.e. m is negative. If m is negative then p is also negative. And if m & p are negative than v has to be positive from (1) Hence v is not less than 0. Statement 2 is sufficient.