Question

If x and y are integers then the equation $5x+19y=64$ has:

• A. no solution for x < 300 and y < 0
• B. no solution for x > 250 and y > - 100
• C. a solution for 250 < x < 300
• D. a solution for -59 < y < -56

Answer 1

The correct option is C a solution for 250 < x < 300

We see that if y = 1, we get an integer solution for x = 9, now if y changes (increases or decreases) by 5, x will change (decrease or increase) by 19.

Looking at options, if x = 256 we get y = - 64.

Using these values we see option 1, 2 and 4 are eliminated and also that there exists a solution for $250<x<300.$