Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 20 Jul 2019, 10:59

### 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

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 16 Feb 2012
Posts: 170
Concentration: Finance, Economics
If mv < pv < 0, is v > 0?  [#permalink]

### Show Tags

20 Jun 2012, 02:53
15
83
00:00

Difficulty:

65% (hard)

Question Stats:

53% (01:30) correct 47% (01:31) wrong based on 1371 sessions

### HideShow timer Statistics

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

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

_________________
Kudos if you like the post!

Failing to plan is planning to fail.
Math Expert
Joined: 02 Sep 2009
Posts: 56304
Re: If mv < pv < 0, is v > 0?  [#permalink]

### Show Tags

20 Jun 2012, 02:55
72
57
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.

Hope it's clear.
_________________
Intern
Joined: 09 Jan 2014
Posts: 15
GMAT Date: 05-28-2015
GPA: 3.48
Re: If mv < pv < 0, is v > 0?  [#permalink]

### Show Tags

11 Oct 2014, 07:27
9
3
Stiv wrote:
If mv < pv < 0, is v > 0?

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

Statement 1 : Since m<p
(m-p)<0
We also know that mv<pv ie (m-p)v<0
Since (m-p)<0 therefore v>0
SUFFICIENT

Statement 2: Given m<0
Since mv<0
therefore v > 0
SUFFICIENT

Hence (D)
##### General Discussion
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9446
Location: Pune, India
Re: If mv < pv < 0, is v > 0?  [#permalink]

### Show Tags

20 Jun 2012, 04:00
17
8
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.

Check this post for a very similar question:
if-zy-xy-0-is-x-z-x-z-101210.html#p1098097
_________________
Karishma
Veritas Prep GMAT Instructor

Director
Joined: 29 Nov 2012
Posts: 731
Re: If mv < pv < 0, is v > 0?  [#permalink]

### Show Tags

05 Mar 2013, 07:09
I made a mistake of ignoring the info in the stiumulus and picked B instead silly error great explanation Bunuel And Karishma
Intern
Status: Aiming for 750+
Joined: 16 Oct 2013
Posts: 21
GMAT Date: 05-05-2014
Re: If mv < pv < 0, is v > 0?  [#permalink]

### Show Tags

30 Jan 2014, 00:53
I am sorry but I somehow still dont understand. I chose B, which I know is incorrect.

Well, let me tell you why I do not understand the Stmt. 1 is sufficient.

Given: mv<pv<0. It is given that MV and PV ARE -ve. This means, When V is -ve, M,P are +ve and vice versa.

I tabulated as below:

m v p mv pv
+ - + - -
- + - - -

Now, statement 1 says m < p. It does not say if they are negative or positive.

So, it is possible that:

3 < 5 (m=3 and p=5) and this means V is -ve

OR

-3 < -1 (m=-3 and p=-1) and this means V is +ve

Different answers so stmt 1 should be insufficient. What I am missing?

Thank you!
Math Expert
Joined: 02 Sep 2009
Posts: 56304
Re: If mv < pv < 0, is v > 0?  [#permalink]

### Show Tags

30 Jan 2014, 01:20
3
flower07 wrote:
I am sorry but I somehow still dont understand. I chose B, which I know is incorrect.

Well, let me tell you why I do not understand the Stmt. 1 is sufficient.

Given: mv<pv<0. It is given that MV and PV ARE -ve. This means, When V is -ve, M,P are +ve and vice versa.

I tabulated as below:

m v p mv pv
+ - + - -
- + - - -

Now, statement 1 says m < p. It does not say if they are negative or positive.

So, it is possible that:

3 < 5 (m=3 and p=5) and this means V is -ve

OR

-3 < -1 (m=-3 and p=-1) and this means V is +ve

Different answers so stmt 1 should be insufficient. What I am missing?

Thank you!

Ask yourself: if m=3 and p=5 and v is negative, say -1, does mv < pv< 0 hold true?
_________________
Intern
Status: Aiming for 750+
Joined: 16 Oct 2013
Posts: 21
GMAT Date: 05-05-2014
Re: If mv < pv < 0, is v > 0?  [#permalink]

### Show Tags

30 Jan 2014, 01:31
1
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

Thank you!!
Senior Manager
Joined: 10 Mar 2013
Posts: 487
Location: Germany
Concentration: Finance, Entrepreneurship
Schools: WHU MBA"20 (A)
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
If mv < pv < 0, is v > 0?  [#permalink]

### Show Tags

29 Dec 2015, 16:19
1
Stiv wrote:
If mv < pv < 0, is v > 0?

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

(1) means both m and p are negative, so in order $$mv$$ and $$pv$$ to be < 0, $$v$$ must be greater than zero. (If it's -ve mv will > 0)
(2) same is in (1) m<0 means $$m$$ is -ve, and in order mv to be negative v must be greater than zero.
_________________
When you’re up, your friends know who you are. When you’re down, you know who your friends are.

800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50
GMAT PREP 670
MGMAT CAT 630
KAPLAN CAT 660
Intern
Joined: 22 Jul 2016
Posts: 21
Re: If mv < pv < 0, is v > 0?  [#permalink]

### Show Tags

06 Jan 2017, 11:38
Given : $$mv<pv<0$$ --------(a)

Statement 1) m < p
I tried plugging numbers :
m=-3, p=-2
to satisfy (a) consider different values of v :
v is positive : v=5 , (-3)(5) < (-2)(5) < 0 = -15 < -10 < 0 ----- satisfy (a)
v is negative : v=-5 , (-3)(-5) < (-2)(-5) < 0 = 15 < 10 < 0 ----- does not satisfy (a)
Hence, v must be positive

Statement 2) m < 0
from (a) , we can see that mv < 0
hence to satisfy mv < 0 when m < 0 , we need a positive value of v [(-ve)*(+ve)=(-ve)]
Therefore v must be positive

Ans: D
Intern
Joined: 11 Jan 2015
Posts: 33
If mv < pv < 0, is v > 0?  [#permalink]

### Show Tags

11 Jan 2017, 14:58
Could someone (@Bunuel) please check this alternative approach?

Rephrase stem to $$mv-pv<0$$ --> $$v(m-p)<0$$

Stm 1: $$m<p$$ --> $$m-p<0$$, so $$v$$ has to be positive for the above inequality to hold true. Sufficient.

Stm 2: Now this is where i screwed it up since i focused on my rephrased inequality and completely ignored the given one. Is there a way to draw the right conclusion from this inequality $$v(m-p)<0$$ in combination with the constraint $$m<0$$ of stm 2?

Otherwise i have to adjust my approach for those kind of questions since i tought rephrasing the question stem would in most cases help to evaluate both statements. Probably in this case it made things more complicated...

Thank you!
Director
Joined: 26 Oct 2016
Posts: 626
Location: United States
Schools: HBS '19
GMAT 1: 770 Q51 V44
GPA: 4
WE: Education (Education)
Re: If mv < pv < 0, is v > 0?  [#permalink]

### Show Tags

13 Feb 2017, 18:47
2
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

Hence D.
_________________
Thanks & Regards,
Anaira Mitch
Manager
Joined: 11 Sep 2013
Posts: 139
Concentration: Finance, Finance
Re: If mv < pv < 0, is v > 0?  [#permalink]

### Show Tags

25 Dec 2017, 07:48
1. m<p, if m and p are positive then v must be -ve,
for example 2(-2)<3(-2) = -4<-6 ==== Not possible. So, m and p have to be -ve and v is +ve.
Suff
2. m is -ve so v must be +ve. Suff

Ans D
Non-Human User
Joined: 09 Sep 2013
Posts: 11719
Re: If mv < pv < 0, is v > 0?  [#permalink]

### Show Tags

28 Dec 2018, 06:50
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.
_________________
Re: If mv < pv < 0, is v > 0?   [#permalink] 28 Dec 2018, 06:50
Display posts from previous: Sort by