question 6 of FDP question bank

[SRobin1068]

The data sufficiency question is:

Is mp greater than m?
(1) m > p > 0

(2) p is less than 1

I rephrased this question to: Is p > 1. I arrived at this rephrasing by dividing both sides of the original equation by m. Therefore, I chose B as the answer to this question, but the answer is C. Can someone please explain why?

Thanks,
Nina

[Guest]

Is mp > m does not imply p > 1. You do not know whether m is +ve or -ve. If m is -ve, when you divide both sides, the inequality is reversed and p < 1.

[GMAT_scares_me]

The data sufficiency question is:

Is mp greater than m?
(1) m > p > 0

(2) p is less than 1

I rephrased this question to: Is p > 1. I arrived at this rephrasing by dividing both sides of the original equation by m. Therefore, I chose B as the answer to this question, but the answer is C. Can someone please explain why?

Thanks,
Nina

You will have to do more work for this.

we have to determine : Is mp > m ?

1. m > p > 0
Choose values.
If m=2 p = 1 -> mp = 2 so here mp IS NOT more than m
If m=3 p = 2-> mp = 6 so here mp IS more than m
NOT SUFF

2. p < 1

if m=3 p=1/3 -> mp =1 so here mp IS NOT more than m
if m=1/2 p=1/3 -> mp = 1/6 here mp is NOT MORE than m
If m=-3 p = 1/3 -> mp = -1 here mp IS MORE than m
NOT SUFF

1 and 2 together

if m=3 p=1/3 -> mp =1 so here mp IS NOT more than m
if m=1/2 p=1/3 -> mp = 1/6 here mp is NOT MORE than m
if m=1/4 p=1/8 -> mp = 1/24 ........
[ so on] each choise of m and p based on 1&2 will give "mp IS NOT more than m"

Sufficient.

[StaceyKoprince]

Nice job, GMAT Scares Me (love your name!)

As the guest mentioned upthread, mp > m cannot simply translate into p>1 because when we multiply or divide an inequality by a negative number, we have to switch the sign. In this case, I don't know whether m is positive or negative, so if I'm going to approach the question this way, I have to create TWO formulas and follow them both through the problem:
If m is positive, then p>1
If m is negative, then p<1

That's annoying, but you can do it. A better way, given that the math is not too complex here, is to try numbers, as GMAT Scares Me did.

[pmenon]

is it ok to approach this question as such: i rearranged the stem to go from mp>m to mp-m>0 --> m(p-1) > 0 . So the only way this holds true is if m is positive and p>1, or m is negative and p is less than 1

from statement 1 , we know that m and p are positive, but not if p>1 ... so not sufficient.

from statement 2, we know that p is less than 1, but nothing about m...insufficient.

together, we know that 0<p<1, and m>0 ... with this we can clearly say that the answer is NO, so C is sufficient.

[rfernandez]

pmenon,

That's an excellent solution... nice work. It's always nice to try it with a purely algebraic approach!

Rey