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

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Blocked Brain: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Sat Jul 11, 2009 2:47 am

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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Source: Beat The GMAT — Problem Solving | Sat Jul 11, 2009 4:35 am

Robinmrtha: Senior | Next Rank: 100 Posts; Posts: 91; Joined: Wed Apr 01, 2009 9:53 pm; Thanked: 11 times

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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gmat740: MBA Student; Posts: 1194; Joined: Sat Aug 16, 2008 9:42 pmFollowed by: 17 members; Location: Paris, France; Thanked: 71 times; GMAT Score:710

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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gmat_for_life: Senior | Next Rank: 100 Posts; Posts: 75; Joined: Fri Jun 26, 2015 7:43 am

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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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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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DavidG@VeritasPrep: Legendary Member; Posts: 2663; Joined: Wed Jan 14, 2015 8:25 amFollowed by: 128 members; Location: Boston, MA; Thanked: 1153 times; GMAT Score:770

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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gmat_for_life: Senior | Next Rank: 100 Posts; Posts: 75; Joined: Fri Jun 26, 2015 7:43 am

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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DavidG@VeritasPrep: Legendary Member; Posts: 2663; Joined: Wed Jan 14, 2015 8:25 amFollowed by: 128 members; Location: Boston, MA; Thanked: 1153 times; GMAT Score:770

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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