M03-25

Question

Are the positive numbers  p ,  q , and  r  equal?

(1)  p = q 
 
(2)  q^2 = r^2

Bunuel · Accepted Answer

Official Solution:

Are the positive numbers  p ,  q , and  r  equal? 
 
(1)  p = q . 
 
This is not sufficient, as there is no information about  r .
 
(2)  q^2 = r^2 . 
 
Given that  q  and  r  are positive numbers, we can conclude that  q = r . However, this is still not sufficient as there is no information about  p .
 
(1)+(2) Since  p = q  and  q = r , it follows that  p = q = r . Sufficient.

Answer: C

bgpower · Answer

Hi Bunuel,

Thanks for this question.

I agree with the solution provided. Concerning the old debate whether 0^2=1 or 0^2=0, could it be assumed that for the purposes of the GMAT 0^2=0. With regards to this question this could change the answer substantially, as if not, it could mean that in (2) p and q can b both 0 and 1, and so the sanswer would be (E).

Thank you!

Bunuel · Answer

There is no debate whatsoever:

0^(positive) = 0, for example, 0^2 = 0.

(anything but 0)^0 = 1, for example, 3^0 = 1.

0^0 is undefined and not tested on the GMAT.

For the question at hand none of the variables can be 0, because we are told that p, q, and r are  positive  numbers, while 0 is neither positive nor negative.

Hope it helps.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

M03-25

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