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If m > 0, is m/n > m?

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Bunuel
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If m > 0, is m/n > m? [#permalink] New post   01 Nov 2015, 09:21
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If m > 0, is m/n > m?

(1) 0.5 < n < 0.75
(2) m > 0.5

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Re: If m > 0, is m/n > m? [#permalink] New post   01 Nov 2015, 11:05
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Basically question asks if 1/n>1
Statement 1: tells that n lies between 0.5 and 0.75 thus 1/n >1.
SUFFICIENT

Statement 2: provides no information on n.
If n =2 then 1/n >n is true
If n =-2 then 1/n >n is false
INSUFFICIENT

OME: A
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Re: If m > 0, is m/n > m? [#permalink] New post   01 Nov 2015, 12:32
m/n > m
=> m/n - m > 0
=>(m- mn)/n > 0
=>m(1-n)/n > 0
and m > 0

1. 0.5< n < 0.75

1- n will be positive

Sufficient

2. m > .5
Not sufficient

Answer A
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Re: If m > 0, is m/n > m? [#permalink] New post   01 Nov 2015, 12:35
Bunuel wrote:
If m > 0, is m/n > m?
(1) 0.5 < n < 0.75
(2) m > 0.5
Kudos for a correct solution.

Given m > 0. So, the value of m can be any value greater than zero e.g. 0.25, 0.50, 1.25, 4 etc.

Now questions asks whether \(\frac{m}{n}\) > m? i.e. \(\frac{1}{n}\) > 1?

Statement 1 says 0.5 < n < 0.75. Here to be noted that any positive number, if divided by a decimal (d) such that 0 < d < 1 , then that positive number will be less than its quotient. For example, \(\frac{.2}{.6}\) = .33, \(\frac{5}{.60}\) = 8.33 , \(\frac{.7}{.7}\) = 1 etc. So \(\frac{m}{n}\) will be less than m. Sufficient.

Statement 2 says m > 0.5. however there is no mention of n. So dual answer is possible. NOT Sufficient.

So Option (A) wins.
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Re: If m > 0, is m/n > m? [#permalink] New post   01 Nov 2015, 12:47
for m/n to be greater than m, n must be a decimal between 0 and 1, regardless of the value of M, since any number divided by a fraction is greater than itself.
statement 1 tells us exactly what we need. n is a decimal, and is not negative. this is sufficient.
statement 2 gives us a value of m. if n = 2 then m/n is not greater than m, but if n =0.5, then m/n is greater than m. not sufficient. answer A.
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Re: If m > 0, is m/n > m? [#permalink] New post   01 Nov 2015, 13:04
m > 0, that is m is positive.

Note : If a number is +ve then it can be multiplied or divide by itself on both side of inequality.

Question "is m/n > m" becomes "is 1/n > 1" when we divide by m on both sides.

1) 0.5 < n < 0.75

so lets say n is 0.6 i.e. 6/10, then 1/n would be 10/6 which is greater than 1. Sufficient.

2) m > 0.5, as we need value of n here. information about m does not help. Insufficient.

Hence, "A" is the right answer.
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Re: If m > 0, is m/n > m? [#permalink] New post   01 Nov 2015, 23:06
Hi,

Going by the premise; m > 0 => m = 0.1, 0.2, 0.3, 1.2, 1.4 etc

Now using Statement 1: 0.5 < n < 0.75

Case 1: m = 0.1 n = 0.6; m/n = 0.1/0.6 = 0.16666 and m = 0.1 So m/n > m
Case 2: m = 1.2 n = 0.7; m/n = 1.7 So m/n > m

Sufficient

Statement 2: We have no idea about n
Insufficient

Hence Option A
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Re: If m > 0, is m/n > m? [#permalink] New post   24 Apr 2023, 09:44
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Re: If m > 0, is m/n > m? [#permalink]
24 Apr 2023, 09:44
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