Question

The number of pairs of integers $(x , y)$ satisfying $x≥y≥-20$ and $2x+5y=99$ is
[This Question was asked as TITA]

• A. 18
• B. 11
• C. 15
• D. 17

Answer 1

Answer: (D)

17

Answer 2

$2x+5y=99$
When, $y=-19,\ x=97$;since $x≥y;$ the maximum value of y is $13$and corresponding value of x is $17$.
We know that the solutions of y are in arithmetic progression with common difference $2$.
Here, $a=-19,\ d=2,\ t_n=13$
$t_n=a+(n-1)d$
$-19+(n-1)(2)=13$
$(n-1)2=32$
$⇒ n=17$
Hence number of pairs integers is $17$

So, the correct option is (D): $17$