Number of Integer Solutions with Inequality Constraint

CAT 2006 Slot 1 · Quantitative Ability · Easy · Quantitative Aptitude

This is an easy Quantitative Ability question from the CAT 2006 Slot 1 paper. It tests Quantitative Aptitude. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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The number of solutions of the equation $2x + y = 40$ where both $x$ and $y$ are positive integers and $x \le y$ is:

A.
7
B.
13
C.
14
D.
18
E.
20

Answer

Explanation

$y = 40 - 2x$ . Since $x, y$ are positive integers, $x \ge 1$ and $40 - 2x \ge 1 \implies x \le 19$ . We also require $x \le y \implies x \le 40 - 2x \implies 3x \le 40 \implies x \le 13.33$ . So $x$ can take integer values from 1 to 13 inclusive. Total solutions $= 13$ .

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Number of Integer Solutions with Inequality Constraint

Explanation

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