m and n are both integers. Is mn?

Question

m and n are both integers. Is m>n?

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

NitishJain · Answer

E.

Statement1: m/n >1

it is possible if both are +ve or both are -ve

let's say m=6, n =2. m/n >1. so is m>n. YES
let's say m=-6, n =-2. m/n >1. so is m>n. NO

NOT SUFFICIENT

Statement 2: (m-n)/n < (m-n)/m. or m/n - 1 < 1- n/m. or m/n + n/m < 2

Here also combination of +ve and -ve values for m,n fails to uniquely suggest m>n NOT SUFFICIENT

Combining both:

m/n> 1
m/n + n/m < 2

=> n/m < 1

Here also the combination of +ve and -ve values for m,n fails to uniquely suggest m>n NOT SUFFICIENT

happyapple123 · Answer

NitishJain

I think B is sufficient?

B is sufficient if you plug in m=2 and n=1. Thus m>n. Can't find any examples to prove m<n.

NitishJain · Answer

Hello  happyapple123

try m = -2 and n = -1,here n >m

Bunuel · Answer

For (2) to get a NO answer, try m < 0 and n > 0.

Bunuel · Answer

Those values do not satisfy (m-n)/n < (m-n)/m.

NitishJain · Answer

Correct sir. thanks.

happyapple123 · Answer

Bunuel

Thanks. Does it mean the answer is C not E then?

Bunuel · Answer

The question is flawed. m/n > 1 and (m-n)/n < (m-n)/m cannot simultaneously be true. Is the question really from egmat?

Lipun · Answer

Statement 1: m/n>1 implies both m and n are either positive or negative. Case1: m,n>0 => m>n Case2: m,n<0 => m -0.4-2.5 < 0 Case2: m>n, m=5, n =-2 => -2.5-0.4 < 0 Not sufficient. S1 and S2 together: From S1 we know m,n>0 => m>n----(1) and m,n<0 => m0 => m-n>0. Cancelling the numerator on both sides we obtain 1/n<1/m => m m-n<0. The negative signs will cancel out in numerator and denominator and we obtain LHS > RHS. This also fails. S1 contradicts S2. Even for option E, we need S1 and S2 complementing each other but resulting in more than 1 solution in which case we can't determine the exact solution. Not sure, where I'm going wrong.

Kinshook · Answer

Given:m and n are both integers. Asked: Is m>n? (1) m/n > 1 m/n - 1 > 0 (m-n)/n>0 If n>0; m>n But if n<0; m=0 mn < 0 NOT SUFFICIENT (1) + (2) (1) m/n > 1 m/n - 1 > 0 (m-n)/n>0 (2) (m-n)/n < (m-n)/m (m-n)/n - (m-n)/m < 0 (m-n)(1/n- 1/m) < 0 (m-n)(m-n)/mn < 0 1/mn < 0; mn<0; Since (m-n)^2>=0 If n<0; m>0; m>n But if n>0; m<0; m

satya2029 · Answer

Excatly.
From 1 
m/n>1
and From 2
mn<0

satya2029 · Answer

From 1 
m/n>1
From 2
mn<0
How it is possible that Both are simultaneously true?

m and n are both integers. Is m>n?

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