Question

If $4x-17y=1$ & $x,y\le 500.$ find how many positive integer solutions are possible ?

• A. $29$
• B. $28$
• C. $27$
• D. Can not be determined

Answer 1

The correct option is A $29$

$4x-17y=1$
$x=\frac{1+17y}{4}$
$x$ is an integer when $y=3,7,11,15,...115$
Thus, number of values of $y$ form an AP.

Maximum value of $y$ can be $115$ else $x$ will be greater than $500$
Hence, using the $n$th term formula of an AP,
$115=3+(n-1)\left(4\right)$
$112=4n-4$
$4n=116$
$n=\frac{116}{4}$ = $29$
Hence, there can be $29$ possible values.