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inequality problem

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inequality problem [#permalink] New post 09 Jun 2009, 19:40
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Hey guys was wondering if anyone could explain a good way to do this problem:


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

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


Answer: D.
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Re: inequality problem [#permalink] New post 10 Jun 2009, 09:47
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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.

The answer is D.
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Re: inequality problem [#permalink] New post 10 Jun 2009, 13:35
completely agree with nookway.
Re: inequality problem   [#permalink] 10 Jun 2009, 13:35
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