Question

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

• A. 29
• B. 28
• C. 27
• D. Cannot be determoned

Answer 1

The correct option is A 29

Given:$4x-17y=1$

$x,y\le 500$

$4x-17y=1$

$4x=1+17y$

$x=\frac{1+17y}{4}$

for $x\le 500$ and $y\le 50$

'2' will integral only when $(1+17y)$ will be completely divisible by 4 and y should take only odd values

'y' satisfies the values 3, 7, 11, 15........

for every odds, one is satisfying our condition. So we need to find the half of total no of odds between our range 1 to 2235 (for $x<500)$

The total number of odd=$58$

Half of the total number of odd=$\frac{58}{2}$=$29$