CAT 2017 Slot 1 — QA Question 25
Fundamental Principles of P&CEasy
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
Answer & solution
- A
101
99
- C
87
- D
105
Solution
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.
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The number of solutions is 1 + 2 + … + 12 + 11 + 10 = 78 + 21 = 99.
Hence, option (b).