Quantitative Aptitude – Algebra – Inequalities – The number of solutions (x, y, z)

Quantitative Aptitude – Algebra – Inequalities

Question

The number of solutions (x, y, z) to the equation x – y – z = 25, where x, y, and z are positive integers such that x ≤ 40, y ≤ 12, and z ≤ 12 is

A) 101
B) 99
C) 87
D) 105

Answer

Option (B)

Solution

From CAT 2017 – Quantitative Aptitude – Algebra – Inequalities, we can see that,
x = 25 + y + z. The possible values of x, y, z and the corresponding number of values of y, z are tabulated below (x, y, z are positive integers).
We see that 27 ≤ x ≤ 40

The number of solutions is 1 + 2 + …… + 12 + 11 + 10 = 78 + 21 = 99
Option (B)

Download CAT 2017 Question Paper with answers and detailed solutions in PDF

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