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If mv < pv < 0, is v > 0? [#permalink]
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03 Sep 2008, 11:44
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If mv < pv < 0, is v > 0? (1) m < p (2) m < 0 OPEN DISCUSSION OF THIS QUESTION IS HERE: ifmvpv0isv134718.html
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Last edited by Bunuel on 10 Jan 2014, 03:08, edited 1 time in total.
Renamed the topic, edited the question and added the OA.



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Re: Quant  DS from Gmatprep  inequality.. [#permalink]
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03 Sep 2008, 12:09
Answer is B.
In case 2,
As we know mv < pv <0
so mv < 0. so v > 0 as m < 0 ( option 2). It is more than enough to say that v > 0.
So B alone is sufficient.
In case 1, m < p now if v is vs then both m and p has to be +ve.
and if v is +ve then both m and p has to ve.
So we can't tell whether v is +ve or ve.
so A is not sufficient.



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Re: Quant  DS from Gmatprep  inequality.. [#permalink]
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03 Sep 2008, 12:18
onesome68 wrote: DS question from Gmatprep  please provide explanation with answers:
if mv < pv < 0, is v > 0? (1) m < p (2) m < 0
I believe it is D. Case 1) m < p mv < pv < 0 mv  pv < pv  pv < pv ...subtract pv v(mp) < 0 < pv Since m < p OR (m  p) < 0 Therefore, v must be positive. SUFF Case 2) m < 0 Since mv < 0 (given), v must be positive. SUFF



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Re: Quant  DS from Gmatprep  inequality.. [#permalink]
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03 Sep 2008, 12:32
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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



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Re: Quant  DS from Gmatprep  inequality.. [#permalink]
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03 Sep 2008, 12:32
devilmirror wrote: onesome68 wrote: DS question from Gmatprep  please provide explanation with answers:
if mv < pv < 0, is v > 0? (1) m < p (2) m < 0
I believe it is D. Case 1) m < p mv < pv < 0 mv  pv < pv  pv < pv ...subtract pv v(mp) < 0 < pv Since m < p OR (m  p) < 0 Therefore, v must be positive. SUFF Case 2) m < 0 Since mv < 0 (given), v must be positive. SUFF Hey devilmirror, Agree with you. It should be D.. Little Tricky one. if mv < pv < 0, 1) m<p suffcient. mvpv<0 > v(mp)<0 given m<p > mp<0 and v+ve 2 ) suffcient. D
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Re: Quant  DS from Gmatprep  inequality.. [#permalink]
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03 Sep 2008, 14:14
OA is D only .. Thanks to all for the explanation..



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Re: Quant  DS from Gmatprep  inequality.. [#permalink]
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03 Sep 2008, 18:21
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 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(mp) < 0 and we know that m < p. So V has to be +ve.



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Re: Quant  DS from Gmatprep  inequality.. [#permalink]
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03 Sep 2008, 19:29
onesome68 wrote: 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(pm) > 0. So whatever is the sign for (pm), it should be the same as that of v so that their product remains positive: (1) m < p, therefore pm > 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. Answer is D.



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Re: Quant  DS from Gmatprep  inequality.. [#permalink]
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26 Feb 2011, 13:34
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!
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Re: if mv < pv < 0, is v > 0? (1) m < p (2) m < 0 [#permalink]
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09 Jan 2014, 20:22
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Re: If mv < pv < 0, is v > 0? [#permalink]
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10 Jan 2014, 03:09




Re: If mv < pv < 0, is v > 0?
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10 Jan 2014, 03:09







