Question

What is the sum of all possible values of y if x is a positive integer, xy > 0, and 6x+2y=25?
(A) 5 (B) 7 (C) 8 (D) 15 (E) 20

Answer 1

The given equation is → 6 x + 2 y =25, also x y> 0

Also, it is given that x is a positive integer.

1. x=1 , then putting the value of x in 6 x + 2 y =25, we get 6×1 + 2 y=25,

   → 2 y= 25-6,→ 2 y=19→y =19/2

2. x=2, then putting  the value of x in 6 x + 2 y =25, we get 6×2 + 2 y=25,

→12+ 2 y= 25→ 2 y=25-12→ 2 y =13→ y=13/2

3. Take x=3,then putting  the value of x in 6 x + 2 y =25, we get 6×3 + 2 y=25,→ 18 + 2 y =25→ 2 y =25-18→2 y =7 → y=7/2

4.Take x=3,then putting  the value of x in 6 x + 2 y =25, we get 6×4 + 2 y=25,→ 24 + 2 y =25→ 2 y =25-24→2 y =1 → y=1/2

Four values of y when x is a positive integer and x y> 0 are , 19/2,13/2,7/2,1/2.

Sum of all values of y=19/2+13/2+ 7/2+1/2=19+13+7+1 /2=40/2=20

So (E) 20 is the correct answer.