If r and s are each greater than 0, is (r + n)/(s + n) >

Answer should be C.
must have both conditions.

e.g
r=3, s=2, n=1

That's only true if your fraction has a positive numerator and denominator (which we know in this question) *and* if the overall value of the fraction is less than 1. If the value of the fraction is greater than 1, then adding the same positive value to the numerator and denominator will decrease the value of the fraction. For example, if you add 1 to the top and bottom of the fraction 2/3, the value increases to 3/4. If you add 1 to the top and bottom of the fraction 3/2, the value decreases to 4/3.

Should be C.

St 1. if r and s each equal to the same number say 2 it becomes insuff.
st 2. we don't know n's sign

Together Sufficient, hence C

Hi Experts i think the answer should be B
but OA as per grockit is C

here is my aproach:-
working on stem
doing cross multiplication we get an equation
rs + ns > rs + nr
simplifying we get
S>R
so our question becomes Is s > r
B gives the solution directly
am i missing something...

We cannot cross-multiply here since we don;t know the sign of s+n.

If r and s are each greater than 0, is (r + n)/(s + n) > r/s?

(1) n > 0. Since both n and s are positive, then we can safely cross-multiply and the question becomes: is \(rs+ns>rs+nr\)? --> is \(ns>nr\)? --> reduce by positive \(n\): is \(s>r\)? We don't know that. Not sufficient.

(2) r < s. Not sufficient.

(1)+(2) the question from (1) became: \(s>r\)? The second statement answers it. Sufficient.

Answer: C.

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If r and s are each greater than 0, is (r + n)/(s + n) > r/s?

(1) n > 0
(2) r < s

If we modify the question, we want to know whether (r+n)/(s+n)>r/s, so s(r+n)>r(s+n), sr+sn>rs+rn, and sn-rn>0, and ultimately we want to know whether (s-r)n>0.
There are 3 variables (r,s,n) and we are given 2 equations from the 2 conditions, making (E) our likely answer.
Looking at the conditions together, the answer to the question becomes 'yes' so this is sufficient, and the answer becomes (C).

For cases where we need 3 more equation, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.

Hi, MathRevolution

In text highlighted in Blue , I don't think without knowing about the sign of variable n we can cross multiply. could you please explain?

The stem says that "r and s are each greater than 0", thus both s + n and n are positive, which means that we can cross-multiply.

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.