Question

How many integer values of x and y are there such that 4x+7y=3, while |x| < 500 and |y| < 500 ?

• A. 144
• B. 141
• C. 143
• D. 142

Answer 1

The correct option is C 143

Here 4x+7y=3,
$x=\frac{(3-7y)}{4}$
when y=0, x=non integer
y=1, x=-1
y=2,3,4 x=non integer
y=5, x=-8
so between 0 and -500, x forms an AP -1,-8......,-498 with common difference d= -7
An=A+(n-1)d
n=72 terms
and between 0 and 500, x forms AP 6,13....,496 with d=7
n=71 terms
in total 72+71=143 terms.