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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