CAT Quantitative Aptitude Questions | CAT Algebra - Linear Equations; Quadratic Equations

The question is about finding the median of three numbers. Details about three numbers are given and we need to find out the median. Framing and solving equations is an integral part of Linear Equations and Quadratic Equations. Get as much practice as you can in these two topics because the benefits of being good at framing equations will be useful in other concepts.

Question 8: Consider three numbers a, b and c. Max (a,b,c) + Min (a,b,c) = 13. Median (a,b,c) - Mean (a,b,c) = 2. Find the median of a, b, and c.?

1. 11.5
2. 9
3. 9.5
4. 12

Explanatory Answer

Method of solving this CAT Question from CAT Algebra - Linear Equations: This is a simple one! Knowing the concepts would help!

The numbers can be arranged in ascending order thus:
Min < Median < Max

According to the question,
Min + Max = 13
Median - \\frac{Min + Med + Max}{3}\\) = Median - \\frac{12 + Med}{3}\\) = 2.

Solving, we get Median = 9.5

The question is "Consider three numbers a, b and c. Max (a,b,c) + Min (a,b,c) = 13. Median (a,b,c) - Mean (a,b,c) = 2. Find the median of a, b, and c.?"

Hence the answer is "9.5"

Choice C is the correct answer.