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Math Expert V
Joined: 02 Sep 2009
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Is m > n?  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 60% (01:19) correct 40% (00:59) wrong based on 137 sessions

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Is m > n?

(1) n /m < 1
(2) n > 0

Kudos for a correct solution.

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Re: Is m > n?  [#permalink]

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2
(1) n /m < 1
It's important to remember that as we don't know if m is positive or negative, we can't multiply by it in an inequality.
e.g. is you multiply, then n < m, but if n = 2, m = -2, then we get 2 < -2, which is incorrect, when you multiply by a negative the sign should be flipped, but we don't know if we should flip it if we don't have any info on the sign of denominator m.
So, let's plug values: n = 1, m =2, then m>n. (1/2 = 0,5 < 1)
But, if we plug n=1, m = -2, then n>m. (1/-2 = -0,5 <1)
Not sufficient.

(2) n > 0
No info on m. Not sufficient.

(1) & (2) Together
The second statement does not help to resolve the problem we encountered in Statement 1. Not sufficient.

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Re: Is m > n?  [#permalink]

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Bunuel wrote:
Is m > n?

(1) n /m < 1
(2) n > 0

Kudos for a correct solution.

Question : Is m > n?

Statement 1: n/m < 1

@n=-1, m could be 1 i.e. m > n
@n=1, m could be -1 i.e. m < n

Hence, NOT SUFFICIENT

Statement 2: n > 0

No information about m
Hence, NOT SUFFICIENT

Combining the Two statements
n > 0 and n/m < 1

@n=1, m could be -1 i.e. m < n
@n=1, m could be 2 i.e. m > n

Hence, NOT SUFFICIENT

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Re: Is m > n?  [#permalink]

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Say I've decided that A, B are out, each is not sufficient.

Combining,
$$\frac{n}{m} < 1 means \frac{m}{n}> 1$$
So,
$$\frac{(m-n)}{n} >0$$

If it's given that n > 0 (Combining B)
(m-n)> 0. So, m > n

So I implied

Am I missing anything?
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Is m > n?  [#permalink]

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Bunuel wrote:
Is m > n?

(1) n /m < 1
(2) n > 0

Kudos for a correct solution.

1: if m > 0, n < m. If m < 0, n > m. So insufficient.
2: Insufficient, tells nothing about m.

Together: insufficient. m can still be negative or positive. For example, n = 4, m = 8, m > n. But if n = 4, m = -8, n/m < 1 and n > m. Answer is E.

aardvark wrote:
$$\frac{n}{m} < 1 means \frac{m}{n}> 1$$

That assumes that m and n have the same sign (since you are multiplying both sides by m/n). If they have opposite signs (so m/n < 0), you have to change the inequality.

Originally posted by bluesquare on 19 Jun 2015, 00:05.
Last edited by bluesquare on 19 Jun 2015, 00:07, edited 1 time in total.
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Re: Is m > n?  [#permalink]

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aardvark wrote:
Say I've decided that A, B are out, each is not sufficient.

Combining,
$$\frac{n}{m} < 1 means \frac{m}{n}> 1$$
So,
$$\frac{(m-n)}{n} >0$$

If it's given that n > 0 (Combining B)
(m-n)> 0. So, m > n

So I implied

Am I missing anything?

You can't take reciprocal if you don't know the sign. If m = 2 and n = 1, then $$\frac{1}{2}<1$$, and $$\frac{2}{1}> 1$$, but if m=-2 and n = 1, then $$\frac{1}{-2} < 1$$, and $$\frac{-2}{1} < 1$$.
Sign changes only if both are either negative or positive.
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Math Expert V
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Re: Is m > n?  [#permalink]

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Bunuel wrote:
Is m > n?

(1) n /m < 1
(2) n > 0

Kudos for a correct solution.

MANHATTAN GMAT OFFICIAL SOLUTION:

(1) INSUFFICIENT. It is tempting to cross multiply to get n < m. However, we don't know whether m is positive, so we don't know whether to flip the sign.

(2) INSUFFICIENT. This statement tells us nothing about m.

(1) & (2) INSUFFICIENT. The fact that n is positive does not tell us whether m is positive. For example, it is possible than n = 2 and m = –1. It is also possible that n = 2 and m = 3. Either of these scenarios would fit Statements (1) and (2) but yield different answers to the question.

The correct answer is E.
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Re: Is m > n?  [#permalink]

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_________________ Re: Is m > n?   [#permalink] 25 Mar 2018, 01:41
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