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

Quantitative Aptitude – Algebra – Inequalities

Question

CAT 2017 - Forenoon slot - Quantitative Aptitude - Algebra - Inequalities - The number of solutions (x, y, z)
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
Quantitative Aptitude - Algebra - Inequalities - The number of solutions (x, y, z)
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

CAT 2017 Questions from Quantitative Aptitude – Algebra

Quantitative Aptitude – Algebra – Inequalities – Ques: For how many integers n, will the inequality (n – 5) (n – 10) – 3(n – 2) ≤ 0 be satisfied?
Quantitative Aptitude – Algebra – Functions
Quantitative Aptitude – Algebra – Logarithms
Quantitative Aptitude – Algebra – Quadratic Equations
Quantitative Aptitude – Algebra – Maxima Minima
Quantitative Aptitude – Algebra – Polynomials
Quantitative Aptitude – Algebra – Simple Equations

Other posts related to Quantitative Aptitude – Algebra

Problems on Ages with complete solutions, answers, and tricks to solve
How to Solve Number of Integral Solutions Questions for CAT 2017
Quadratic Equations
Basic Functions and Modifications of Graphs
An introduction to functions (Algebra) for CAT 2017 exam
Functions from Algebra – Basic concepts and application for Quantitative Aptitude in CAT Exam
​​

Online Coaching Course for CAT Exam Preparation

a) 750+ Videos covering entire CAT syllabus
b) 2 Live Classes (online) every week for doubt clarification
c) Study Material & PDFs for practice and understanding
d) 10 Mock Tests in the latest pattern
e) Previous Year Questions solved on video

Know More about Online CAT Course

Quantitative Aptitude – Algebra – Inequalities – The number of solutions (x, y, z)
5 (100%) 52 votes