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Veritas Prep 10 Year Anniversary Promo Question #5

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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. _________________

(1) qr + qs = r + s <=> q (r+s) = (r+s) <=> r + s = 0 or q = 1 Can't determine q -> not sufficient (2) r is different to -s => r+s <> 0 . No information about q -> not sufficient

The answer is: ( C) Solution: What is the value of integer ?

We have: (1) qr+qs = r+s Then q(r+s) = r+s => (q-1)(r+s)=0 => q=1 or r=-s. So it’s not Sufficient Together with (2) r≠-s, we have q=1.So the answer is C

Ans is C. stmt 1) qr + qs = r + s => q(r+s) = (r+s) => q=1 if (r+s) not equal to 0 OR q does not have unique value if (r+s)=0 stmt 2) r not equal to -s => (r+s) not equal to 0 Hence, to find unique value of q stmt 1) & 2) both necessary

most of the people prefer to divide both sides by (r + S) and hence conclude that q = 1. As per my understanding, GMAT does not prefer that way because it eliminates one solution. (if one does as this, one will miss (r + s) = 0 as answer)

As per my understanding, q(r + s) = r + s q(r + s) - (r + s) = 0 (r + s)(q - 1) = 0

either (r + s) = 0 or (q - 1) = 0. if (r + s) = 0 then q can have any value. statement 1 insufficient.

Statement 2: r is not equal to -s does not provide any information about value of q statement 2 is insufficient.

statement 1 and 2: from statement 1, we know that either (r + s) = 0 or (q - 1) = 0 but from statement 2, we know that r NE -s, so (r + s) NE 0

substitute this in statemet 1. we will get (q - 1) = 0

Ans : C R+c should not be 0 in the 1st equation to get a value for Q This is confirmed by 2nd statement. " R+c not= 0" We need both statements together so ans is C

C. - (2) is not sufficient since irrelevant. BD out - (1) q (r+s) = r + s (q-1)(r+s)= 0 => Either (q-1) = 0 or (r+s) = 0. Not sufficient in case of (r+s) = 0. A out - Both (1)&(2), from (2) we have r+s <>0, combine with (1) we have q = 1: sufficient

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 _________________

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1) qr + qs = r + s thus, q (r+s) = (r+s). Now you can't divide since r+s=0. If r+s is not 0, then q=1. Hence insufficient 2) r+s is not = 0. no information about q.

Both combined - we can say that q = 1. Thus, answer is C

Last edited by prep on 19 Sep 2012, 19:51, edited 1 time in total.

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

A will only be the answer if statement (1) is sufficient to provide one exact answer to the question, what is the value of q? _________________

Let the value of r and s be anything q will always be equal to 1.

Not correct approach. what if R=S=0 then? Q(R+S) = 1*(R+S) => Q=1 ? as well as Q(R+S)=10*(R+S) =>Q=10 ? and it can be shown to be true for any other number... So first you can not claim Q=1 this way. Second, the conclusion u reached Q(R+S) =(R+S) => Q=1 this is arrived when you've divided both sides by (R+S). Which can not be done if R+S = 0, as it will be illegal operation to divide by 0. Unless you are certain about r+s <>0, you can not reach to conclusion. _________________

Let the value of r and s be anything q will always be equal to 1.

Not correct approach. what if R=S=0 then? Q(R+S) = 1*(R+S) => Q=1 ? as well as Q(R+S)=10*(R+S) =>Q=10 ? and it can be shown to be true for any other number... So first you can not claim Q=1 this way. Second, the conclusion u reached Q(R+S) =(R+S) => Q=1 this is arrived when you've divided both sides by (R+S). Which can not be done if R+S = 0, as it will be illegal operation to divide by 0. Unless you are certain about r+s <>0, you can not reach to conclusion.

Dear vips - if r or s is 0... the equation will be 0 on both side..and u can not get the value of q.

if either r or s is 0 u still get q=1 isnt it?

Also if we are to consider this as an unanswerable case - then even point 2 wont help. r not equal to -s...could well mean r =s =0 again no answer and then reach the conclusion to be E.

Ans:C Statement1:given qr+qs=r+s =>q(r+s)=r+s =>q=1 only when r not equal to -s If r=-s,then q is undefined Hence Statement1 is insufficient Statement2:given r not equal to -s No information about q Hence Statement2 is insufficient

By combining both statements 1 and 2 q=1 when r not equal to -s Hence C is the correct answer

Last edited by sdpp143 on 19 Sep 2012, 23:24, edited 1 time in total.

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