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

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

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20 Jun 2012, 02:55
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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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
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Re: If mv < pv < 0, is v > 0?  [#permalink]

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20 Jun 2012, 04:00
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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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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Posts: 59125
Re: If mv < pv < 0, is v > 0?  [#permalink]

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

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

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18 Oct 2014, 02:06
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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Posts: 59125
Re: If mv < pv< 0, is v > 0?  [#permalink]

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18 Oct 2014, 02:13
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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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. Answer D _________________ When you’re up, your friends know who you are. When you’re down, you know who your friends are. Share some Kudos, if my posts help you. Thank you ! 800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50 GMAT PREP 670 MGMAT CAT 630 KAPLAN CAT 660 Director Joined: 26 Oct 2016 Posts: 600 Location: United States Concentration: Marketing, International Business 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 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. _________________ Thanks & Regards, Anaira Mitch Director Joined: 24 Oct 2016 Posts: 563 GMAT 1: 670 Q46 V36 GMAT 2: 690 Q47 V38 Re: If mv < pv< 0, is v > 0? [#permalink] ### Show Tags 17 Aug 2019, 10:45 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. ANSWER: D _________________ If you found my post useful, KUDOS are much appreciated. Giving Kudos is a great way to thank and motivate contributors, without costing you anything. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8149 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If mv < pv< 0, is v > 0? [#permalink] ### Show Tags 17 Aug 2019, 12:27 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. Therefore, D is the answer. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Re: If mv < pv < 0, is v < 0 ? m < p m < 0 mv  [#permalink]

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21 Oct 2019, 01:25
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Re: If mv < pv < 0, is v < 0 ? m < p m < 0 mv   [#permalink] 21 Oct 2019, 01:25
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