srcc25anu wrote:st2: r=s
if r = s = 1, 1/r + 1/s = 2 (not 4) but if r = s = 1/2, them 1/r + 1/s = 4
hence insufficient

and when you put r = s in the original equation it solves r = s = 1/2 but that does not mean r = s are actually 1/2 each. r and s could assume many other values and the only restriction is that either r or s is not 0.

Brent@GMATPrepNow wrote:

zazoz wrote:if rs isn't 0, is (1/r)+(1/s)=4

1)r+s=4rs
2)r=s

Target question: Is 1/r + 1/s = 4?

This one is a great candidate for rephrasing the target question
Let's add 1/r + 1/s to create one rational expression.
Find common denominator: s/rs + r/rs
Add numerators: (s+r)/rs
So, 1/r + 1/s = (s+r)/rs

So, rather than ask "Does 1/r + 1/s = 4?" we can ask "Does (s+r)/rs = 4?"

Even better, we can cross multiply the equation to get: "Does s+r = 4sr?"

Statement 1: r + s = 4rs
This is exactly what one of our rephrased target questions asks.
So, statement 1 is SUFFICIENT

Statement 2: r = s
Knowing that r=s does not help us determine whether s+r = 4sr
So, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

Brent@GMATPrepNow wrote:

zazoz wrote:if rs isn't 0, is (1/r)+(1/s)=4

1)r+s=4rs
2)r=s

Thank you Brent; I would like to show how I solve this an how I reach to sufficient!! I know its incorrect. I know that if I consider r=s=3 it will show me that's insufficient.

Statement 2: I said to myself "Plug r=s into the question" then I reached to r=1/2 so s=1/2. After that, I, once again put r=s=1/2 into the question and reach to yes, it is sufficient. I said to myself that this method gives me just one answer nothing more. At first place can I plug r=s into the question or it is a wrong way because we want to improve that is the equation equals 4 or not? I think maybe I am not allowed to plug statement into the equation? Sorry for asking again

Sure, it's okay that you plugged r=s into the target question. HOWEVER, it's important to note that when you do this, you are essentially assuming that the answer to the target question is YES, even though your job is to the answer to the target question with certainty.

So, when you assumed that the answer to the target question is YES, you reached the conclusion that r = s = 1/2. This part is not necessarily true. It's POSSIBLE that, given statement 2, r = s = 1/2, in which case the answer to the target question is YES.

However, being told that r = s, does not mean that r = s = 1/2.
It could also be the case that r = s = 3, in which case the answer to the target question is NO.

Once we have two conflicting answers to the target question, we can conclude that statement 2 is not sufficient.

Cheers,
Brent