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Re: If mv < pv < 0, is v > 0? [#permalink]
20 Jun 2012, 01:55

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

Given: \(mv<pv<0\) --> two cases:

If \(v>0\) then when dividing by \(v\) we would have: \(m<p<0\); If \(v<0\) then when dividing by \(v\) we would have: \(m>p>0\) (flip the sign when dividing by negative value).

(1) m < p --> we have the first case, so \(v>0\). Sufficient. (2) m < 0 --> we have the first case, so \(v>0\). Sufficient.

Re: If mv < pv < 0, is v > 0? [#permalink]
20 Jun 2012, 03:00

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Stiv wrote:

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

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

You can solve such questions easily by re-stating '< 0' as 'negative' and '> 0' as 'positive'.

mv < pv < 0 implies both 'pv' and 'mv' are negative and mv is more negative i.e. has greater absolute value as compared to pv. Since v will be equal in both, m will have a greater absolute value as compared to p.

When will mv and pv both be negative? In 2 cases: Case 1: When v is positive and m and p are both negative. Case 2: When v is negative and m and p are both positive.

So how will we know whether v is positive? If we know that at least one of m and p is negative, then v must be positive. If at least one of m and p is positive, then v must be negative.

Now that we understand the question and the implications of the given data, we go on to the statements.

Stmnt 1: m < p m has greater absolute value as compared to p but it is still smaller than p. This means m must be negative. If m is negative, p must be negative too which implies that v must be positive. Sufficient.

Stmnt 2: m < 0 Very straight forward. m and p both must be negative and v must be positive. Sufficient.

Re: If mv < pv < 0, is v > 0? [#permalink]
30 Jan 2014, 00:31

Bunuel wrote:

Ask yourself: if m=3 and p=5 and v is negative, say -1, does mv < pv< 0 hold true?

Aha!! I get it now. So, when m=3, p=5 and v is -ve, mv (-3) becomes > pv (-5) making the given condition void.

So, Stmt 1 is sufficient. Great learning for the day. (This makes me wanna repeat to myself - When you pick numbers, quickly plug in to see if they are correct)

I also figured this just now:

mv < pv < 0 (mv-pv) <0 v(m-p)<0

If v is +ve, m<p (This is what the Statement 1 is saying too) If v is -ve, m>p

Re: If mv < pv < 0, is v > 0? [#permalink]
22 Oct 2015, 05:09

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