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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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20 Jun 2012, 02:53
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If mv < pv < 0, is v > 0?

(1) m < p
(2) m < 0
[Reveal] Spoiler: OA

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

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20 Jun 2012, 02:55
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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.

Hope it's clear.
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Re: If mv < pv < 0, is v > 0? [#permalink]

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20 Jun 2012, 04:00
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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
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Re: If mv < pv < 0, is v > 0? [#permalink]

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

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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!

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

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30 Jan 2014, 01:20
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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?
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Re: If mv < pv < 0, is v > 0? [#permalink]

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30 Jan 2014, 01:31
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!!

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

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11 Oct 2014, 07:27
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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)

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

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22 Oct 2015, 06:09
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If mv < pv < 0, is v > 0? [#permalink]

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29 Dec 2015, 16:19
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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.
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Re: If mv < pv < 0, is v > 0? [#permalink]

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23 Nov 2016, 03:22
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spc11 wrote:
if mv < pv <0, is v > 0?

1. m<p
2. m<0

I couldn't find this in the question bank. Apologies if its a repeat question.

Please refer to the discussion above.

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

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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

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

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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!

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

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13 Feb 2017, 18:47
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.
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Re: If mv < pv < 0, is v > 0?   [#permalink] 13 Feb 2017, 18:47
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