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Is m > n? [#permalink]
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18 Jun 2015, 02:42
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Re: Is m > n? [#permalink]
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18 Jun 2015, 07:34
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(1) n /m < 1It'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 > 0No 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.Answer
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Re: Is m > n? [#permalink]
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18 Jun 2015, 07:57
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 SUFFICIENTStatement 2: n > 0No information about m Hence, NOT SUFFICIENTCombining the Two statementsn > 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 SUFFICIENTAnswer: option
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Re: Is m > n? [#permalink]
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18 Jun 2015, 18:51
Say I've decided that A, B are out, each is not sufficient. Combining, \(\frac{n}{m} < 1 means \frac{m}{n}> 1\) So, \(\frac{(mn)}{n} >0\) If it's given that n > 0 (Combining B) (mn)> 0. So, m > n So I implied Am I missing anything?
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Is m > n? [#permalink]
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Updated on: 19 Jun 2015, 00:07
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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19 Jun 2015, 00:06
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, \(\frac{(mn)}{n} >0\) If it's given that n > 0 (Combining B) (mn)> 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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