On Apr 27, 9:14 pm, monkeyboy <fsen...@lynx.neu.edu> wrote: > I recently started doing a Mathematics GRE exam just for fun. I've > been cruising through the calculus questions, but have hit an algebra > problem that stumped me. Unfortunately detailed solutions are not > provided, only the correct answer, could some one point me in the > right direction... > > Question: > Let x and y be positive integers such that 3x + 7y is divisible by 11. > Which of the following must also be divisible by 11? > > Solution: > 4x - 9y > > Thanks
Sheesh, everybody is making heavy weather of this question. The complete solution to 3x + 7y = 0 (mod 11) is given by x = 4t, y = 3t (mod 11), for an arbitrary integer t. Thus, 4x - 9y = 4(4t) - 9(3t) = -11t (mod 11), i.e. 4x - 9y = 0 (mod 11).