Please note that this is not an official GMAT question; it’s my attempt to create difficult (650+ level) GMAT-style questions for this forum.

I multiplied both p and q by their respective conjugates to come up with p= (sqrt(14) + sqrt(13)) q= (sqrt(14) - sqrt(13)) 3pq = 3(14-13) = 3 now we have: (sqrt(14) + sqrt(13))^2 + 3 + (sqrt(14) - sqrt(13)) 27 + 2sqrt(14x13) + 3 + 27 - 2sqrt(14x13) 27 + 3 + 27 57 Fixed my silly mistake

p^2 + 3pq +q^ = p^2 + 2pq + q^2 + pq = (p+q)^2 + pq substituting values give B as answer

sacx wrote:p^2 + 3pq +q^ = p^2 + 2pq + q^2 + pq = (p+q)^2 + pq substituting values give B as answer Nice, the answer is B. I posted this question to note that it is sometimes beneficial to know how to simplify rational expressions involving roots. In this question, I think it speeds up the process. See what you think.

Hi Brent, The question image isn't showing up for me. I tried it in Firefox and IE. Can someone help ? It may be an isolated case for me. :roll:

DeepakR wrote:Hi Brent, The question image isn't showing up for me. I tried it in Firefox and IE. Can someone help ? It may be an isolated case for me. :roll: Hey DeepakR, This is a jpeg, just like all of my other posts. I'm not sure what to suggest. Brent

Hi Brent, Now i am able to view the image and i get 57. Not sure what was the issue previously anyway Thanks. - Deepak

Brent Hanneson wrote: Nice, the answer is B. I posted this question to note that it is sometimes beneficial to know how to simplify rational expressions involving roots. In this question, I think it speeds up the process. See what you think. Thanks Bernt I get reminded about conjugates that i learnt in school... may be it helps me at the test