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= > now if we mutiply both sides by a +ve number, then the inequality sign remains same and if we multiply both sides witha -ve number, the inequality sign changes. as the sign remains same, after multiplying by V (mv < pv ) , so V >0

(2) m < 0

if v is -ve mv >0 and if v is +ve mv <0 ; as mv < 0 , v >0

= > now if we mutiply both sides by a +ve number, then the inequality sign remains same and if we multiply both sides witha -ve number, the inequality sign changes. as the sign remains same, after multiplying by V (mv < pv ) , so V >0

(2) m < 0

if v is -ve mv >0 and if v is +ve mv <0 ; as mv < 0 , v >0

Excellent point about the inequality and sign change you brought up.

Even if we take part of the original inequality mv < pv we still have v(m-p) < 0 and we know that m < p. So V has to be +ve.

DS question from Gmatprep - please provide explanation with answers:

if mv < pv < 0, is v > 0? (1) m < p (2) m < 0

First of all, since mv < pv, we know that pv - mv > 0, therefore v(p-m) > 0. So whatever is the sign for (p-m), it should be the same as that of v so that their product remains positive:

(1) m < p, therefore p-m > 0, so if this is positive, then v is positive. Suff.

(2) m is negative, since the product of mv from the question is negative, v must be positive.

Re: Quant - DS from Gmatprep - inequality.. [#permalink]
26 Feb 2011, 12:34

ssandeepan wrote:

IMO D.

if mv < pv < 0, is v > 0? (1) m < p

= > now if we mutiply both sides by a +ve number, then the inequality sign remains same and if we multiply both sides witha -ve number, the inequality sign changes. as the sign remains same, after multiplying by V (mv < pv ) , so V >0

(2) m < 0

if v is -ve mv >0 and if v is +ve mv <0 ; as mv < 0 , v >0

There are various ways to solve this questions. I took the longer route of picking values for variables which helped me avoid mistake I would usually make in 'visualizing' inequalities. Although you could reach the same conclusion by solving the inequalities by subtracting a term (and thus avoiding the flipping of inequality sign required when multiplying/dividing with a -ve variable), the solution you provides is just excellent. A simple observation of the original question and the first statement already saves a ton of calculations and mistakes. Valuable point! Kudos! _________________

-DK --------------------------------------------------------- If you like what you read then give a Kudos! Diagnostic Test: 620 The past is a guidepost, not a hitching post. ---------------------------------------------------------

Re: if mv < pv < 0, is v > 0? (1) m < p (2) m < 0 [#permalink]
09 Jan 2014, 19:22

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If mv < pv < 0, is v > 0? [#permalink]
10 Jan 2014, 02:09

Expert's post

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.

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