The number of solutions (x, y, z) to the equation x â€“ y â€“ z = 25, where x, y, and z are positive integers such that x â‰¤ 40, y â‰¤ 12, and z â‰¤ 12 is

A) 101

B) 99

C) 87

D) 105

Option (B)

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 â‰¤ x â‰¤ 40

The number of solutions is 1 + 2 + â€¦â€¦ + 12 + 11 + 10 = 78 + 21 = 99

Option (B)

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