Data Sufficiency

If m and n are integer, is m>n?
1). m/n>1
2). (m-n)/n>(m-n)/m

oa E

1) m/n > 1

Both +ve - m>n
Both -ve - m<n

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

(m/n) + (n/m) > 2

say m =2 and n=1 (or) m=1 and n=2

Cant say if m>n

Together,

Again insufficient as both may -ve or +ve.. (say m=-2,n=-1) E

If m and n are integer, is m>n?
1). m/n>1
2). (m-n)/n>(m-n)/m


Whatever Anurag said is correct but there is one doubt that I am having...

Statement 1:

m/n > 1 solving this inequality...


m/n - 1 > 0

After this step, we get (m - n) > 0,

when this inequality is formed, it is certain that m>n


Statement 2:

1/n > 1/m This is the interpretation that we can form based on what is given to us...

from the above inequality we can ascertain that m > n...



So according to me the answer comes down to D...

Also please suggest that in inequalities when to use the inequalities basics or when to put values and check the answers....


Please help needed...

[email protected] wrote:If m and n are integer, is m>n?
1). m/n>1
2). (m-n)/n>(m-n)/m


Whatever Anurag said is correct but there is one doubt that I am having...

Statement 1:

m/n > 1 solving this inequality...


m/n - 1 > 0

After this step, we get (m - n) > 0,

when this inequality is formed, it is certain that m>n

you are making mistake, m/n - 1 > 0 translates into both i) m-n>0 and n>0 OR ii) m-n<0 and n<0. Thus, in one case you have m>n with n>0, yet another case brings m<n with n<0

[email protected] wrote: Statement 2:

1/n > 1/m This is the interpretation that we can form based on what is given to us...

from the above inequality we can ascertain that m > n...



So according to me the answer comes down to D...

@Amit, st(2) (m-n)/n>(m-n)/m translates into (m-n)/n - (m-n)/m > 0 and further to (m-n)*(1/n - 1/m) > 0 Agree?

It's not as you put 1/n > 1/m BUT it's rightly made 1/n > 1/m and m>n OR 1/n < 1/m and m<n. From there n<m and m>n (flipping the sign of inequality with reciprocal) and n>m and m<n.

You don't need to use plug-in value for all types of DS questions! This is only required for Yes/No questions. All others may be solved faster by using theory. Here is the post from different forum with relevant example of plugging values for DS question by MGMAT expert, Ron Purewal https://www.manhattangmat.com/forums/if- ... t5879.html

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


But Pemdas in the statements whatever is given is supposed to be true...

We are given m/n > 1 and so that is what it means is (m-n) > 0...

There is not modulus sign and so how can you say that (m-n) < 0 is also a possibility...

We have to take what is given to us, so it is given (m-n) > 0 so that is what we got...

Please explain if i am wrong..

pemdas wrote: you are making mistake, m/n - 1 > 0 translates into both i) m-n>0 and n>0 OR ii) m-n<0 and n<0. Thus, in one case you have m>n with n>0, yet another case brings m<n with n<0

@Amit, if you will ever improve your math wiz is because you want to ANALYZE stuff. By reading what has been posted (copied/pasted here) you could understand your doubt.

Anyways, let's start over. My understanding you conclude that statement(2) is Not Sufficient and have doubt about statement(1).

If all else fails, show by example
statement(1) m/n>1
Consider two numbers, -100, -1 along with m=-100, n=-1. The inequality -100/(-1)>1 holds true. Also consider two numbers, 100, 1 along with m=100, n=1. The second inequality 100/1>1 also holds true.

You have m<n from case 1) and m>n from case 2) and CANNOT exactly answer the question asked. Thus, statement(1) is Not Sufficient.

Now reread the quote above and ANALYZE - you could resolve doubt with a click.

pemdas wrote: you are making mistake, m/n - 1 > 0 translates into both i) m-n>0 and n>0 OR ii) m-n<0 and n<0. Thus, in one case you have m>n with n>0, yet another case brings m<n with n<0

m/n - 1 > 0 is equivalent to (m-n)/n > 0. Two cases: i)(m-n)>0 and n>0 OR ii) (m-n)<0 and n<0

[email protected] wrote:If m and n are integer, is m>n?
1). m/n>1
2). (m-n)/n>(m-n)/m


Whatever Anurag said is correct but there is one doubt that I am having...

Statement 1:

m/n > 1 solving this inequality...


m/n - 1 > 0

After this step, we get (m - n) > 0,

when this inequality is formed, it is certain that m>n


Statement 2:

1/n > 1/m This is the interpretation that we can form based on what is given to us...

from the above inequality we can ascertain that m > n...



So according to me the answer comes down to D...

Also please suggest that in inequalities when to use the inequalities basics or when to put values and check the answers....


Please help needed...

Amit-
the mistake with your solution is that you are canceling VARIABLES from both side of the inequalities

Lets take the follwing example
-2 > -3
We cant just cancel out -1 from both sides and say 2 > 3
This would be wrong
Whenever a negative sign is involved, the inequality sign is reversed.

-2 > -3
2 < 3

in this ques,
m/n > 1
(m-n)/n > 0
if n is postive,
(m-n) > 0, and hence, m > n

if n is negative,
(m-n) < 0, hence, n > m

but you dont knw whether n is positive or negative.


DO not to shift variables across the inequality sign, as you wouldn't know how it would affect the inequality sign.

I hope this is clear enough Amit