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

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by Blocked Brain » Sat Jul 11, 2009 4:35 am
Question from GMAT Test Prep:
If mv<pv<0, is v>0?
(1) m<p
(2) m<0

Answer: Each statement alone is sufficient.

How should I think through this problem? Thanks.
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by Robinmrtha » Sat Jul 11, 2009 4:47 am
the question is asking whether v is positive or negative...
given
mv<pv<0
when v is positive...then
m<p<0
i.e. both m and p are negative but p is greater than m
and if v is negative...then
m>p>0

Statement 1.
We know that m<p
therefore v should be positive...
sufficient

Statement 2.
m<0
for m to be less than 0, the v should always be positive...
sufficient

Hence the answer is D...
Hope this helps....
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by gmat740 » Sat Jul 11, 2009 9:19 am
II :
mv<0
since m=-ve
so v =+ve

I:

m<p

now multiply both sides by v
mv<pv

since the sign of inequality does not change,so we can say v =+ve

Hope this helps
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by gmat_for_life » Mon Apr 18, 2016 10:38 am
Hello Experts,

Could you please verify if my approach to this question is correct?

we have mv<pv<0 and the question is whether v>0?

We can rewrite the above inequalities as
v(m-p)<0----(1)
mv<0-------(2) and
pv<0----------(3)

from equation 2, we have either m<0 and v>0 or m>0 and v<0
from equation 3, we have either p<0 and v>0 or p>0 and v<0

therefore, for v to be greater than 0, m<0 and p<0. From equation 1, we can state that m-p<0 for v>0. So the question can be rephrased as 'is m<p'?

Statement 1: Sufficient
Statement 2: from equation 2, we know that when m<0, v>0. Hence sufficient.

Thanks,
Amit
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by Brent@GMATPrepNow » Mon Apr 18, 2016 10:54 am
Hi Amit,

Your solution is great. Here's a longer version that explains every step:
If mv < pv < 0, is v > 0?

1) m < p
2) m < 0
Nice question.

Target question: Is v > 0

Given: mv < pv < 0

Statement 1: m < p

IMPORTANT: Notice what happens if we take mv < pv and divide both sides by v.
The resulting inequality will depend on whether v is NEGATIVE or POSITIVE. So, let's consider two cases:
case a: v is NEGATIVE.
When we take mv < pv and divide both sides by v, we get m > p
We changed the direction of the inequality sign since we divided by a NEGATIVE value.

case b: v is POSITIVE.
When we take mv < pv and divide both sides by v, we get m < p
The direction of the inequality sign stayed the same since we divided by a POSITIVE value.

Statement 1 tells us that m < p, which means we can rule out case a.
So, we conclude that v is POSITIVE
In other words, v > 0
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: m < 0
We're told that mv < pv < 0, which means that mv < 0
In other words, the product mv is NEGATIVE
Statement 2 tell us that m is NEGATIVE
In order for the product mv to be NEGATIVE, v must be positive
In other words, v > 0
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by DavidG@VeritasPrep » Mon Apr 18, 2016 10:56 am
gmat_for_life wrote:Hello Experts,

Could you please verify if my approach to this question is correct?

we have mv<pv<0 and the question is whether v>0?

We can rewrite the above inequalities as
v(m-p)<0----(1)
mv<0-------(2) and
pv<0----------(3)

from equation 2, we have either m<0 and v>0 or m>0 and v<0
from equation 3, we have either p<0 and v>0 or p>0 and v<0

therefore, for v to be greater than 0, m<0 and p<0. From equation 1, we can state that m-p<0 for v>0. So the question can be rephrased as 'is m<p'?

Statement 1: Sufficient
Statement 2: from equation 2, we know that when m<0, v>0. Hence sufficient.

Thanks,
Amit
The approach is a little bit lengthier than it needs to be, but sure, the mathematical reasoning is valid.
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by gmat_for_life » Mon Apr 18, 2016 11:09 am
Thanks a lot David and Brent!

Your solutions and explanations are always helpful :)

I have one more doubt not related to this question but something that has been troubling me since a long time.Could you guys please help me out with this?

if x^2=36, what is x?
I have read numerous posts which state that the answer is |6|, which should yield only '6' as the answer. However the correct answer is either 6 or -6. This logic seems baffling to me! :(

Regards,
Amit
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by DavidG@VeritasPrep » Mon Apr 18, 2016 11:19 am
gmat_for_life wrote:Thanks a lot David and Brent!

Your solutions and explanations are always helpful :)

I have one more doubt not related to this question but something that has been troubling me since a long time.Could you guys please help me out with this?

if x^2=36, what is x?
I have read numerous posts which state that the answer is |6|, which should yield only '6' as the answer. However the correct answer is either 6 or -6. This logic seems baffling to me! :(

Regards,
Amit
if x^2=36, we could say that |x| = 6, meaning that x is 6 units from 0 on the number line. (And x is either -6 or 6.) However, it would not be accurate to simply claim that the answer is |6|, because, as you noted, |6| is just 6.
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