There exists positive integers x,y such that both the expressions (3x+2y) and (4x-3y) are exactly divisibe by ?

Options a) 11 b) 7 c) 23 d) 17

solution
Let us eliminate y from a combination of the two

3(3x+2y) + 2( 4x -3y) = 17x

as sum of combination is divisible by 17 so ans is (d) 17 provided one of them is divisible by 17

this can be shown if we have x and y such that 3x+ 2y is divisible by 17

x= 3 , y = 4 satisfies it so (d) is solution