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The answer is A. 1) (r+s) / rs = 4 => (r/rs) + (s/rs) = 4 => (1/r) + (1/s) = 4 SUFFICIENT 2) plug in r=s=1/2, you get 4=4. But plug in r=s=1, you get 2=4. INSUFFICIENT.

For me the answer is A
r+s=4rs
dividing both sides by rs
r/rs+s/rs=4
1/r+1/s=4 (Sufficient)
r=s
Different values of r or s suggest that 1/r+1/s may or may not be =4 thus insufficient
so Answer is A

The answer is A. 1) (r+s) / rs = 4 => (r/rs) + (s/rs) = 4 => (1/r) + (1/s) = 4 SUFFICIENT 2) plug in r=s=1/2, you get 4=4. But plug in r=s=1, you get 2=4. INSUFFICIENT.

gar!! failed to see that...

why can't we just answer this question w/the info provided in the stem? did we really need additional info to figure that out? 1/r + 1/s = 4 => s/rs + r/rs = 4 => 1/r + 1/s = 4

Well we could certainly have done it that way Fig if the stem had told us that 1/r+1/s is indeed equal to 4. The stem is asking whether the expression is a true equation or not. And to validate the stem we are provided with two different sets of information which are statements A & B.
Actually this is how i had made D the correct option by putting r=s in the stem. But as u see, stem is not stated to be true, it is asked wherther it is true or not.
I hope this explains ur question.

sorry dude
u see when the boss is just around the corner, then such mistakes are bound to happen. Especially when ur boss is more like a blood hound, who only wnats ur blood instead of ur sweat.
And yes u did make it more difficult. It happens to me too. simple solution is in fornt of me, but i start making complex equations.

1) (r+s)/rs= 4rs/rs = 4, SUF
2) r=s, from the stem => 1/r, but since we do not know how much does r worth we also do not know how much 1/r worths, INSUF.

r+s=4 rs or (r+s)/rs=4 or (r/rs)+(s/rs)=4 or 1/r+1/s=4 . so sufficient .

statements 2 is clearly out . correct answer = A .

if this portion of the question " rs is not equal to 0 " is not given , then ? what would happen ?

Posted from my mobile device

If rs#0, is 1/r + 1/s = 4 ?

Question: is \(\frac{1}{r}+\frac{1}{s}=4\) --> is \(\frac{r+s}{rs}=4\) --> is \(r+s=4rs\)?

(1) \(r+s=4rs\), directly answers the question. Sufficient.

(2) \(r = s\), the question becomes: is \(\frac{1}{r}+\frac{1}{r}=4\) ? --> is \(r=\frac{1}{2}\)? but we dont' know whether \(r=\frac{1}{2}\). Not sufficient.

Answer: A.

As for your question: if rs#0 were not given, then r=s=0 would be possible and in this case 1/r + 1/s would be undefined.