mn? (1) m/n1 (2) (m-n)/n(m-n)/m (integer) 24!

Question

m>n?

 (1) m/n>1

 (2) (m-n)/n>(m-n)/m


(integer) 24! has how many 0s?

vshaunak@gmail.com · Answer

My answer is 'E'.

Statement1: m/n>1
m and n both should be either positive or negative.
for +ve, m>n for -ve m<n> m-n/m
solving this m/n + n/m > 2
plug in numbers m =10, n =5 this is true. That means m >n
m = -10, n =-5 this is also true. That means m <n>n
m = -10, n =-5 satisfy stmt1 and stmt2. It means m < n

Hence INSUFF

neeraj kaushal · Answer

Answer is B

As statement 1 is not sufficient because m/n can be greater than 1 even when m=-4 and n=-2 where m<n and m=4 and n=2 where m>2 .

Stement 2 is sufficient as we solve inequalities we can cross off m-n from both sides of inequality and left with 1/n>1/m which leads to m>n 

So B is the answer

vshaunak@gmail.com · Answer

Unless we know whether m-n is +ve, we can't cross m-n from both sides without changing the sign of inequality.

kirakira · Answer

(2) Certainly you can cross off (m-n) but not sure about the sign of the inequality. If (m-n) > 0 => 1/n > 1/m If (m-n) <0> 1/n < 1/m Hence, (E)

jainvik7 · Answer

E for me.

Option 1 -- Not sufficient (as the explanations above)

Option 2 -- 
A better approach for evaluating the second option would be -->

 (m-n)/n>(m-n)/m 
or, m^2 - mn > mn - n^2
or, m^2 + n^2 - 2mn > 0
or, (m - n )^2 > 0

Put some positive and negative values for both m and n. Not sufficient. 

Any suggestions/comments on this please.

sidbidus · Answer

I'll go with E

Statement 1 : Insufficient
------------------------------

Let m = 3 and
 n = 2

Here 3/2 > 1 and m>n

Let m = -3 and
 n = -2

Here -3/-2 > 1 but n>m

so insufficient

Statement 2: Insufficient
-----------------------------

(m-n)/n>(m-n)/m

We cannnot cancel (m-n) on both sides coz we don't know the sign of m-n.

This gives

m/n + n/m > 2

Let m = 4 and
 n = 2

Here 5/2 > 2 and m>n

Let m = -4 and
 n = -2

Here also 5/2 > 2 but m<n.....so insufficient.

Taking them together also doen't help

So  E  it should be.

24! = 24 *...*20*.....*15*.....*10*......*5*......1

basically we are looking for the multiples of 5....coz 10=5*2
we get 4 multiples of 5 and we have more that 4 multiples of 2 here.

so 24!=x *10*10*10*10

 So we wil have '4' 0s

F75 · Answer

Answer E because we do not know whether m and n are positive.

Amit05 · Answer

Answer is E though I too initially concluded B cancelling (m-n ) from both sides of inequality. 

Can someone give the reasoning on why can't we cancel (m-n) from b.s of inequality ?

KillerSquirrel · Answer

see my explanation in: https://www.gmatclub.com/phpbb/viewtopic.php?t=45472

Jamesk486 · Answer

My answer is 'E'.

Statement1: m/n>1 
m and n both should be either positive or negative.
for +ve, m>n for -ve m m-n/m
solving this m/n + n/m > 2
plug in numbers m =10, n =5 this is true. That means m >n 
m = -10, n =-5 this is also true. That means m n 
m = -10, n =-5 satisfy stmt1 and stmt2. It means m n for -ve m m-n/m
solving this m/n + n/m > 2 

is this from statement one? i don't really understand what you did..

m>n? (1) m/n>1 (2) (m-n)/n>(m-n)/m (integer) 24!

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