It is currently 13 Dec 2017, 12:56

# Decision(s) Day!:

CHAT Rooms | Ross R1 | Kellogg R1 | Darden R1 | Tepper R1

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Intern
Joined: 01 Jun 2008
Posts: 11

Kudos [?]: 14 [1], given: 0

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

### Show Tags

03 Sep 2008, 10:44
1
KUDOS
3
This post was
BOOKMARKED
00:00

Difficulty:

75% (hard)

Question Stats:

50% (01:11) correct 50% (01:20) wrong based on 111 sessions

### HideShow timer Statistics

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.

Kudos [?]: 14 [1], given: 0

Intern
Joined: 02 Sep 2008
Posts: 45

Kudos [?]: [0], given: 0

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

### Show Tags

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.

Kudos [?]: [0], given: 0

Senior Manager
Joined: 04 Jan 2006
Posts: 276

Kudos [?]: 44 [0], given: 0

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

### Show Tags

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

Kudos [?]: 44 [0], given: 0

Manager
Joined: 09 Jul 2007
Posts: 244

Kudos [?]: 281 [3], given: 0

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

### Show Tags

03 Sep 2008, 11:32
3
KUDOS
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

Kudos [?]: 281 [3], given: 0

SVP
Joined: 07 Nov 2007
Posts: 1790

Kudos [?]: 1102 [0], given: 5

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

### Show Tags

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
_________________

Smiling wins more friends than frowning

Kudos [?]: 1102 [0], given: 5

Intern
Joined: 01 Jun 2008
Posts: 11

Kudos [?]: 14 [0], given: 0

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

### Show Tags

03 Sep 2008, 13:14
OA is D only ..
Thanks to all for the explanation..

Kudos [?]: 14 [0], given: 0

VP
Joined: 05 Jul 2008
Posts: 1402

Kudos [?]: 452 [0], given: 1

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

### Show Tags

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.

Kudos [?]: 452 [0], given: 1

SVP
Joined: 21 Jul 2006
Posts: 1509

Kudos [?]: 1071 [0], given: 1

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

### Show Tags

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.

Kudos [?]: 1071 [0], given: 1

Intern
Joined: 23 Jun 2010
Posts: 35

Kudos [?]: 29 [0], given: 5

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

### Show Tags

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.
---------------------------------------------------------

Kudos [?]: 29 [0], given: 5

Non-Human User
Joined: 09 Sep 2013
Posts: 14869

Kudos [?]: 287 [0], given: 0

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

### Show Tags

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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 287 [0], given: 0

Math Expert
Joined: 02 Sep 2009
Posts: 42583

Kudos [?]: 135534 [0], given: 12697

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

### Show Tags

10 Jan 2014, 02:09
Expert's post
2
This post was
BOOKMARKED
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
_________________

Kudos [?]: 135534 [0], given: 12697

Re: If mv < pv < 0, is v > 0?   [#permalink] 10 Jan 2014, 02:09
Display posts from previous: Sort by