Is m n? (1) 3/7

Question

Is m > n?

(1) 3/7 < m < 5/7

(2) 2/7 < n < 4/7

amanvermagmat · Answer

The question is whether m > n or whether m-n > 0. Individually the statements are obviously not sufficient as each statement talks about just one entity out of m/n and not the other. So lets combine them. We are given the range of m as 3/7 < m < 5/7. And we are also given the range of n as 2/7 < n < 4/7. If we mutliply this range of n by -1, we will get: -2/7 > n > -4/7 (signs of inequality will flip because we are mutliplying by a negative number). OR -4/7 < n < -2/7. Now range of m and -n are both inequalities in the same direction, so we can add them. Adding the range of 'm' and '-n' we get: 3/7+(-4/7) < m+(-n) < 5/7+(-4/7) OR -1/7 < m-n < 1/7. So the required entity m-n could be negative or 0 or positive. We thus cant say whether m-n> 0 or m-n=0 or m-n <0. Not sufficient . Hence E answer .

Archit3110 · Answer

from 1: we can say 21<m<35 
From 2: 14<n<28

so combing 1 & 2 m can be equal to n at an y value 22 to 27 , so in sufficient.. IMO E

amanvermagmat · Answer

Hello

from (1), can you please check how you have concluded 21 < m < 35? 
To get 21 on the left, we will need to multiply the entire inequality by 49. That will give us: 21 < 49m < 35.

Similarly in (2), we need to multiply entire inequality by 49 to get 14 and 28. We will get: 14 < 49n < 28.

So then we can compare 49m and 49n with each other. Result will still be E, as you have concluded - but I thought I should point this out.

Archit3110 · Answer

Yes I missed including 49m and 49n.. answer would still be E..

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Is m > n? (1) 3/7 < m < 5/7 (2) 2/7 < n < 4/7

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