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

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If mv < pv < 0, is v > 0? [#permalink]

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03 Sep 2008, 10:44
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If mv < pv < 0, is v > 0?

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-mv-pv-0-is-v-134718.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 10 Jan 2014, 02:08, 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, 11:09

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, 11:18
onesome68 wrote:

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(m-p) < 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, 11:32
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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, 11:32
devilmirror wrote:
onesome68 wrote:

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(m-p) < 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.
mv-pv<0 --> v(m-p)<0
given m<p --> m-p<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, 13:14
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, 17:21
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(m-p) < 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, 18:29
onesome68 wrote:

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.

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Re: Quant - DS from Gmatprep - inequality.. [#permalink]

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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!
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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, 19:22
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Re: If mv < pv < 0, is v > 0? [#permalink]

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10 Jan 2014, 02:09
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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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-mv-pv-0-is-v-134718.html
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Re: If mv < pv < 0, is v > 0?   [#permalink] 10 Jan 2014, 02:09
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