Cross multiplying and inequalities

[matthew.a.roseman]

Hello,

Let's say you have a DS question as follows: [(M+X)/(N+X)] > (M/N)?

If I know that M and N are both positive can I cross multiply this equation OR do I also need to know that (M+X) and (N+X) are also positive in order to do so. Basically, I'm looking to get a better understanding of when I can simplify inequalities and when I cannot given the constraints of dividing/multiplying by negative numbers. Thanks!

[vyom.bharadwaj]

[(M+X)/(N+X)] > (M/N)-This is one of the property of the inequalities.

The question in DS could be framed like:-
The value of x is given as option A
The value of M and N is given as option B.
Here you need to know only the value of m and n and the question could be solved.
The equation is independant of the value of x.

Also for negative values simply change the sign (i.e. > will be changed to <) and solve.

Hope I have clarified your doubts.

[jerly_vivek]

our inequality is:
(m+x)/(n+x)>m/n
We only need to know m and n, sign of x is irrelevant. lets see how.

Multiply both side of inequality with n. since n is positive, we do not need to change the inequality.
n(m+x)/(n+x)>m

similarly, multiplying both side by 1/m
n(m+x)/m(n+x)>1
n(m+x)>m(n+x).

[Ben Ku]

Hello,

Let's say you have a DS question as follows: [(M+X)/(N+X)] > (M/N)?

If I know that M and N are both positive can I cross multiply this equation OR do I also need to know that (M+X) and (N+X) are also positive in order to do so. Basically, I'm looking to get a better understanding of when I can simplify inequalities and when I cannot given the constraints of dividing/multiplying by negative numbers. Thanks!

Cross multiplying is basically multiplying both sides by the denominators. So in order to cross multiply across an inequality, you need to know that both N and N + X are positive, since those are the denominators.