CAT 2020 Quant Question [Slot 2] with Solution 16

Question

The number of pairs of integers (x , y) satisfying $x \ge y \ge - 20$ and $2x + 5y = 99$ is

Option: 17
Solution:

$2x + 5y = 99$

When $y = - 19,x = 97;$ since $x \ge y$; 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 $a = - 19,d = 2,tn = 13$

${t_n} = a + (n - 1)d$

$- 19 + (n - 1)(2) = 13$

$(n - 1)2 = 32 \Rightarrow n = 17$

Hence number of pairs integers is 17

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