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Is V>0?

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Source: — Data Sufficiency |

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by [email protected] » Fri Mar 11, 2016 10:34 am
Hi binaras,

There's a discussion of this DS question here:

https://www.beatthegmat.com/inequality-t272612.html

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Rich
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by binaras » Fri Mar 11, 2016 10:22 pm
Hi Rich

Many thanks
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by Brent@GMATPrepNow » Sat Mar 12, 2016 8:50 am
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

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Brent
Brent Hanneson - Creator of GMATPrepNow.com
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