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Bunuel
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yashii9
Good explanation.
However I dont understand how can u solve this as algebra?
point 2 only says that R <> -S but it does not talk abt the value of either r or s.....it can be fraction, positive or zero
unless the values of r and s are specified how do we find value of Q?

Hence E.

I might be thinking a bit too much but its better to get this clarified here than screwing up in the exam. :)

yes, It can be fraction, positive or zero.. but whatever it is, one thing we know is that R <> -S which means R+S <> =0. Which means for (Q-1)(R+S) to be equal to 0, Q has to be 1.
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We have a winner!



Winner:

Vips0000

Official Explanation:

Answer is C

Statement 1 at first appears to be sufficient, as one can factor out the common \(q\) to get: \(q(r + s) = r + s\). This would suggest that \(q\) equals one. But you must ask about statement 2, “why are you here?”. Statement 2 is clearly not sufficient, but it sheds a bit of light on something you may not have considered with statement 1. If \(r\) were to equal \(-{s}\), then \(r + s\) would be 0. And in that case, our revised equation for statement 1, \(q(r + s) = r + s\), is true for any value of \(q\). So statement 2 is critical - it shows us that statement 1 is not sufficient alone, but that along with statement 2 we can rest assured that \(q\) is 1. The correct answer is C.
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Winner:

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YAY!!! :twisted:
Thanks.. Hopefully I'd be able to prepare much better with this package!! ;)
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thevenus
why not (A)?
(i)q(r+s)=(r+s)
q=? ...(doesn't matter what r or s is , we have to find the q ;not to check whether is positive negative or zero);the value cant be found out insufficient so (A) is
sufficient
(ii) lacks info-insufficient

Exactly, even i dont understand why everybody is trying to solve for r & s, when its clear from the 1st equation that q(r+s) = r+s => q =1.

And answer would be A. But i'm worried,looking at other answers!!!
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shekbhi
thevenus
why not (A)?
(i)q(r+s)=(r+s)
q=? ...(doesn't matter what r or s is , we have to find the q ;not to check whether is positive negative or zero);the value cant be found out insufficient so (A) is
sufficient
(ii) lacks info-insufficient

Exactly, even i dont understand why everybody is trying to solve for r & s, when its clear from the 1st equation that q(r+s) = r+s => q =1.

And answer would be A. But i'm worried,looking at other answers!!!

What is the value of integer \(q\)?

(1) \(qr + qs = r + s\) --> \(q(r+s)=r+s\) --> \(q(r+s)-(r+s)=0\) --> \((r+s)(q-1)=0\) --> EITHER \(r+s=0\) (\(r=-s\)) OR \(q-1=0\) (\(q=1\)). Notice that if \(r+s=0\), then \(q\) can take ANY value, not necessarily 1. Not sufficient.

(2) \(r\neq{-s}\). Clearly insufficient.

(1)+(2) Since from (2) \(r\neq{-s}\), then from (1) it must be true that \(q=1\). Sufficient.

Answer: C.

Hope it's clear.
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