Is pq = 1?

(1) pqp = p

(2) qpq = q

Solving for the statements:

For 1 : p = 0 or pq=1

For 2: q=0 or pq = 1

Since pq =1 for both statement, isn't it sufficient? So p or q doesn't = 0, since pq=1. I chose C but the answer is E. Help please
. thx

Remember that pq = 1 is the question. We don't know whether it's actually true; it might be false. Only the two statements are given as true.

So, for statement 1, p could be 0, and then pqp = p would be 0 = 0 (regardless of what q is), and the answer to the question "is pq = 1?" is no.
Or, p could be 1 and q could be 1. Then pqp = p would be 1=1, and the answer to the question "is pq = 1?" is yes.

_________________
Stacey Koprince
Instructor
Director of Online Community
ManhattanGMAT

What is ans?

BR

Please make sure to read the complete post before replying. The original poster indicated that the answer is E.

_________________
Stacey Koprince
Instructor
Director of Online Community
ManhattanGMAT

Hi Stacey ,

I have a doubt with regard to this question.

When -- Both Statement 1) and Statement 2) are indicating that pq =1 , then why the answer to this question is E) and not C).

Please let me know your comments.

NEITHER statement says pq=1. they both say that pq=1 is ONE possibility but that something else can be true. note that p=q=0 is consistent with both statements as well..

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Tim Sanders
Manhattan GMAT Instructor

I too have the same doubt

From Stmt 1 => P = 0 or pq-1 = 0 which implies pq=1
From Stmt 2 => q= 0 or pq-1 = 0 which again implies pq = 1

From the 2 stmts together we know that pq=1 is the common comdition, therefore the answer is C.

COuld you please provide an alternate explanation so that we know why the correct answer is E

GMATFrenzy:

This is my understanding. As per question stem we need to figure out what is the product of numbers p & q. We need to realize that we are dealing with two variables and not a single variable (p*q). We have to ensure that for all possible values of p and q the statements should hold true.

As you have analyzed the possible solutions for statement 1 are

p= 0 or pq = 1

Possible solutions for statement 2 are
q = 0 or pq =1

So at this stage both answer options A, B & D are out. So we are left with C & E. To figure out we need to answer a simple question can we ensure pq = 1 for all different values of P & Q ? The answer is NO because if P= 0 and Q = 0 then both statement 1 and 2 are satisfied but the product pq is not equal to 1.

Hence you cannot definitely say that pq =1

On a side note once I read this question my automatic answer choice was also C :-). Once I started analyzing the question stem more thoroughly I figured out that the answer choice is E and not C. One thing is clear for me got to stay extra alert in situations like these as I think many of us would fall into the pitfall of C. Thanks a lot to the original poster for this quesation.

Thanks all !

let us know if you have any further questions on this one..

_________________
Tim Sanders
Manhattan GMAT Instructor