Question

X2-5y2=1232 find the possible values of x and y

Answer 1

Given that:- x^6 = y^2 + 127

x can have a value of 1....................n, however x>2 because:

If x = 1, x^6 = 1 and y = sqrt(1-127). y is an irrational number. Not possible.

If x = 2, x^6 = 64 and y = sqrt(64-127). y is an irrational number. Not possible.

If x = 3, x^6 = 729 and y = sqrt(729-127) = sqrt(602). Now y is a fraction. Not possible.

If x = 4, x^6 = 64x64 and y = sqrt{(64x64) -127} = .......?

Now its not possible to do any calculation beyond this point in 2-5 minuets. Until and unless there is a quick approach, I would say this not a gmat-type question. I would love to see if anybody has a quick approach.