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Is p/m>0? 1) p>m 2) pm>0.

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Math Revolution GMAT Instructor
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Is p/m>0? 1) p>m 2) pm>0. [#permalink]

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New post 02 Aug 2017, 00:56
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Is p/m>0?

1) p>m
2) pm>0.

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Re: Is p/m>0? 1) p>m 2) pm>0. [#permalink]

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New post 02 Aug 2017, 02:46
MathRevolution wrote:
Is p/m>0?

1) p>m
2) pm>0.


\(\frac{p}{m}>0\)..
it is possible ONLY when both p and m are of SAME sign

lets see the statements

1) p>m
if p = 2, m= 3.. yes
if p= -2, m=3...no
insuff

2) pm>0
here it tells us that both p and m are of SAMR sign..
hence suff

B
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Re: Is p/m>0? 1) p>m 2) pm>0. [#permalink]

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New post 02 Aug 2017, 02:58
MathRevolution wrote:
Is p/m>0?

1) p>m
2) pm>0.


\(\frac{p}{m}>0\)

Only when \(p\) and \(m\) both are positive or both are negative (ie; \(p\) and \(m\) both should have same sign), \(\frac{p}{m}\) will be greater than \(0\).

1) \(p>m\)

We cannot find the sign of \(p\) or \(m\). Hence I is Not Sufficient.

2) \(pm>0\)

\(pm\) is greater than \(0\), that is; \(p\) and \(m\) both are positive or both are negative (ie; \(p\) and \(m\) both have same sign).

Hence II is Sufficient.

Answer (B)...
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Is p/m>0? 1) p>m 2) pm>0. [#permalink]

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New post 02 Aug 2017, 04:48
MathRevolution wrote:
Is p/m>0?

1) p>m
2) pm>0.


Remember, if the product of any number of variables is > or < 0 then so will be the case for the product of the reciprocals of those variables.

In fact, to generalize any combination (either as direct products or products of the reciprocals) of a set of variables will yield the same parity wrt 0.

For example abcd/ef >0=> abcdef>0, ab/cdef>0, a/bcdef>0, abc/def>0, so on and so forth.

Statement 1: p or m could have all sorts of parities (both negatives, both positives, 1 neg + 1 pos, 1 pos + 1 neg). Not sufficient.
Statement 2: In light of our discussion above Sufficient
Expert Post
Math Revolution GMAT Instructor
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Re: Is p/m>0? 1) p>m 2) pm>0. [#permalink]

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New post 04 Aug 2017, 02:18
==> If you modify the original condition and the question, from is p/m>0?, you multiply \(m^2\) on both sides, you get (Squared number is always positive, so even if you multiply, the inequality sign doesn't change) \(p/m(m^2)>0(m^2)\)?, which becomes pm>0?.

The answer is B.
Answer: B
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Re: Is p/m>0? 1) p>m 2) pm>0.   [#permalink] 04 Aug 2017, 02:18
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