Data Sufficiency

from MGMAT question Bank:

Is mp greater than m?

(1) m > p > 0

(2) p is less than 1


SO, mp>m. my question is Why cant I divide by m to get P>1?


Thanks

That's because, m can be either positive or negative.
btw...IMO A.

Stmt 1 -

Since both m and p are postive, mp > m for all values of m and p.

Sufficient

Stmt 2 -
P<1

also m can be either postive or negative,

Let m = -1 and p = -2
mp = 2, m = -1 => mp > m

But for m = 2 and p = -2
mp = -4 and m = 2 => mp < m

Insufficient

m = 50, p = .5

The answer is (C)

Answer is E IMO

You can never know if mp is greater than m

From statement 1 you know that both are positive.

But if m = 0.2 and p = 0.1 mp = 0.02 < m

However if m = 10 and p = 2 mp = 20 > m

From statement 2 if p is less than 1, it could be positive or negative. So can m. So the product could be positive or negative.

Both 1 and 2 are insufficient on their own

Combined, we know that both are positive and p is in the set (0,1)

However we can still come to no conclusive result.

For example if m = 0.2 and p 0.1 mp is less than p

However if m = 10 and p = 0.5, mp is more than p

Therefore E

it's asking: MP > M

C combined: M>P>0, P<1

if P = 0.5, M>0.5, so 0.5*0.6<0.6
if P = 0.1, M>0.1, so 0.1*0.6<0.6

answer is always NO, so sufficient.

I agree with capnx. Answer is C.

capnx wrote:it's asking: MP > M

C combined: M>P>0, P<1

if P = 0.5, M>0.5, so 0.5*0.6<0.6
if P = 0.1, M>0.1, so 0.1*0.6<0.6

answer is always NO, so sufficient.

IMO A what's the OA?

fruti_yum wrote:

capnx wrote:it's asking: MP > M

C combined: M>P>0, P<1

if P = 0.5, M>0.5, so 0.5*0.6<0.6
if P = 0.1, M>0.1, so 0.1*0.6<0.6

answer is always NO, so sufficient.

IMO A what's the OA?

After dwelling on it.. Changed my answer.. I'll go with C.. Didn't consider the possibility that P > 1

sme0928 wrote:from MGMAT question Bank:

Is mp greater than m?

(1) m > p > 0

(2) p is less than 1


SO, mp>m. my question is Why cant I divide by m to get P>1?


Thanks

We don't know that mp > m... that's the question that we're trying to answer.

If your question is "why can't I rewrite the question as 'Is p>1?'", then the answer is as pradeepsarathy noted - we have no clue whether m is positive, negative or 0.

If m is positive, then the question does become Is p > 1. If m is 0, then the question is undefined. If m is negative, then the question becomes Is p < 1.

Whenever you see inequalities in DS, the first thing you should ask is "do I have to worry about dividing or multiplying by a negative?" Further, when you pick numbers on inequality questions, always consider the impact of picking negatives.

Let's start at the beginning:

Is mp > m?

If we want to rewrite this safely, we subtract m from both sides, to get:

is mp - m > 0

and then factor out m:

is m(p-1) > 0

Now we ask ourselves, when is a product of two terms greater than 0? We answer ourselves: when both terms have the same sign.

So, to get a yes answer, either:

m>0 and p-1>0 (i.e. p>1)

OR

m<0 and p-1<0 (i.e. p<1)

Now let's look at the statements:

(1) m > p > 0

We know that m>0, but do we know if p>1? No! So, (p-1) could be positive or negative: insufficient.

(2) p is less than 1

No info about m: insufficient.

Now we eliminate A, B and D. Since we still have two choices left, we have to try combining the statements.

From (1) we know that m is positive.

From (1) and (2) together, we know that p is a positive fraction. If p is a positive fraction, then (p-1) will always be negative.

If m is positive and p-1 is negative, the question changes from:

Is m(p-1) > 0

to:

is (+)*(-) > 0?

To which the answer is "DEFINITELY NOT": sufficient, choose (C).

Note: there are many alternative and, likely, quicker ways to attack this problem, especially picking numbers.

When we get to combination, we could also just reason it out. Once we realize that m is positive and p is a positive fraction, we can think:

"what happens to a positive number when we multiply it by a positive fraction? It gets SMALLER. So, when we multiply positive number m by positive fraction p, we're always going to get a product LESS than m, which means that mp will NEVER be greater than m... sufficient".