Source: Beat The GMAT Practice Questions If x + y = 3, and x^2 + y^2 = 5 then x^4 + y^4 = (A) 11 (B) 13 (C) 17 (D) 19 (E) 22

x^2 + y^2 = (x+y)^2 - 2xy 5 = 9 - 2xy => xy = 2 x^4 + y^4 = (x^2+y^2)^2 - 2(xy)^2 = 25 - 2(2)^2 = 25 - 8 = 17 Therefore the answer would be "C".

Yep - the correct answer is C. Here's my solution as well: x+y=3 means that (x+y)^2=9 We get x^2 + 2xy + y^2 = 9 Since we’re given that x^2 + y^2 = 5, then 2xy=4 which means that xy=2 If x^2 + y^2 = 5, then (x^2 + y^2)^2 = 25 We get x^4 + 2x^2y^2 + y^4 = 25 We already know that xy=2, so 2x^2y^2 = 8 So we get x^4 + 8 + y^4 = 25, which means that x^4 + y^4 = 17

Mr2Bits wrote:C : 17 X =2 Y = 1 Ha ha ha, that is too funny. I meant create a question that students couldn't plug in a few numbers to see which ones fit and it turns out that (2,1) works. Back to the drawing board for me I should have made it something like: x + y = 5, and x^2 + y^2 = 7 Nice catch!

Brent Hanneson wrote:Mr2Bits wrote:C : 17 X =2 Y = 1 Ha ha ha, that is too funny. I meant create a question that students couldn't plug in a few numbers to see which ones fit and it turns out that (2,1) works. Back to the drawing board for me I should have made it something like: x + y = 5, and x^2 + y^2 = 7 Nice catch! Yea, I saw it immediately and had to double take it to make sure I wasn't wrong. I have come to the conclusion that when taking the GMAT the obvious answer is most likely incorrect and there is some trick or piece that I'm missing