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

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Question Stats: 54% (01:29) correct 46% (01:30) wrong based on 1490 sessions

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

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

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Math Expert V
Joined: 02 Sep 2009
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Re: If mv < pv < 0, is v > 0?  [#permalink]

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76
61
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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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
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Re: If mv < pv < 0, is v > 0?  [#permalink]

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18
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
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Re: If mv < pv < 0, is v > 0?  [#permalink]

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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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Joined: 02 Sep 2009
Posts: 59125
Re: If mv < pv < 0, is v > 0?  [#permalink]

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

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

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Bunuel wrote:
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.

I understood Bunuel's explanation for statement-1 but following values makes statement-1 insufficient. Please help me understand this:

(1) m<p

lets take v=1, m=-3, p=-2 it gives mv=-3, pv=-2 and hence does not violate mv<pv<0 as -3<-2<0, so v is +ve here
lets take v=-1, m=3, p=2 it gives mv=-3, pv=-2 and hence does not violate mv<pv<0 as -3<-2<0 but v is -ve here

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

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HKD1710 wrote:
Bunuel wrote:
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.

I understood Bunuel's explanation for statement-1 but following values makes statement-1 insufficient. Please help me understand this:

(1) m<p

lets take v=1, m=-3, p=-2 it gives mv=-3, pv=-2 and hence does not violate mv<pv<0 as -3<-2<0, so v is +ve here
lets take v=-1, m=3, p=2 it gives mv=-3, pv=-2 and hence does not violate mv<pv<0 as -3<-2<0 but v is -ve here

Thanks

m = 3 and p = 2 violate the first statement, which says that m < p.
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If mv < pv < 0, is v > 0?  [#permalink]

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

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3
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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GMAT 1: 670 Q46 V36 GMAT 2: 690 Q47 V38 Re: If mv < pv< 0, is v > 0?  [#permalink]

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enigma123 wrote:
If mv < pv< 0, is v > 0?

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

Main Topic

Inequalities

Rule:
Multiplying/dividing inequalities by
+ variable: Don't flip sign
- variable: Flip sign

Divide by v
If v = +, then m < p < 0
If v = -, then m > p > 0

1) Implies v = +. Sufficient.
2) Implies v = +. Sufficient.

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

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enigma123 wrote:
If mv < pv< 0, is v > 0?

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

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. Then we recheck the question. We should simplify conditions if necessary.

$$mv < pv$$
$$⇔ mv - pv < 0$$
$$⇔ v(m-p) < 0$$

Since the original condition is equivalent to $$v(m-p) < 0$$, the question is equivalent to $$m - p < 0$$ or $$m < p$$.
This is same as condition 1).
Thus condition 1) is sufficient.

Condition 2)
When we consider both condition 2), $$m < 0$$ and the original condition, $$mv < 0$$, we have $$v > 0$$.
Thus condition 2) is also sufficient.

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

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