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Manhattan Question Set # 6

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by richachampion » Sun Oct 09, 2016 5:58 pm
Is mp greater than m?

(1) m > p > 0

(2) p is less than 1

OA: C
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by [email protected] » Sun Oct 09, 2016 8:04 pm
Hi richachamption,

To start, this should be in the DS Forum. That having been said, this prompt can be solved by TESTing VALUES and using Number Properties. The key is to recognize that the variables are not necessarily positive integers.

We're asked if MP > M. This is a YES/NO question.

1) M > P > 0

IF... M = 4, P = 2, then the answer to the question is YES.
IF... M = 4, P = 1/2, then the answer to the question is NO.
Fact 1 is INSUFFICIENT

2) P is LESS than 1

This Fact tells us NOTHING about the value of M.
IF... M = 4, P = 1/2, then the answer to the question is NO.
IF... M = -4, P = 1/2, then the answer to the question is YES.
Fact 2 is INSUFFICIENT

Combined, we know that...
P is LESS than 1
M > P > 0

Since P = positive fraction, then M = larger positive and the answer to the question is ALWAYS NO (since multiplying a positive number by a positive fraction will ALWAYS lead to a product that is smaller than the first number).
Combined, SUFFICIENT

Final Answer: C

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by fiza gupta » Fri Oct 14, 2016 9:34 am
GIven: mp>m
mp-m>0
m(p-1)>0
can be true if:
(i)m>0 and p>1 or (ii)m<0 and p<1

1) m>p>0
m>0 but p>1 or 0<p<1(p>0)
didn't satisfy neither i nor ii
NOT SUFFICIENT

2) p<1
but m?
NOT SUFFICIENT

combining
p>0 and p<1 => 0<p<1
(mp<m because m>p and 0<p<1, multiplication of positive number with positive fraction leads to small number)
SUFFICIENT

SO C
Fiza Gupta
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by GMATinsight » Fri Oct 14, 2016 11:18 pm
richachampion wrote:Is mp greater than m?

(1) m > p > 0

(2) p is less than 1

OA: C
Question :Is mp greater than m?

Question :Is mp - m > 0?
Question :Is m(p - 1) > 0?

Statement 1: m > p > 0
Now we know that m and p are positive but whether p-1 is greater than 0 or not is still unknown hence
NOT SUFFICIENT

Statement 2: p < 1
Now we know that p-1 is Negative but whether m is greater than 0 or not is still unknown hence
NOT SUFFICIENT

Combining the two statements
Now we know that p-1 is Negative and m is positive hence
m(p-1) will be less than zero for sure
SUFFICIENT

Answer: Option C
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