IPMAT Indore 2025 (MCQ) - Suppose a, b and c are three real numbers such that Max (a, b, c) + Min (a, b, c) = 15, and Median (a, b, c) - Mean (a, b, c) = 2. Then the median of a, b and c is | PYQs + Solutions

IPMAT Indore 2025

Arithmetic

Averages

Medium

Suppose $a, b$ and $c$ are three real numbers such that $\text{Max} (a, b, c) + \text{Min} (a, b, c) = 15$ , and $\text{Median} (a, b, c) - \text{Mean} (a, b, c) = 2$ . Then the median of $a, b$ and $c$ is

10.5

9.5

✅ Correct Option: 2

Let's denote the maximum value as

M

, the minimum value as

m

, and the median value as

d

From the first condition:

\newline

\text{Max}(a,b,c) + \text{Min}(a,b,c) = 15

\newline

M + m = 15

The mean of three numbers is:

\text{Mean}(a,b,c) = \dfrac{M + m + d}{3}

From the second condition:

\newline

\text{Median}(a,b,c) - \text{Mean}(a,b,c) = 2

d - \dfrac{M + m + d}{3} = 2

Simplifying:

\dfrac{3d - (M + m + d)}{3} = 2

\dfrac{2d - (M + m)}{3} = 2

2d - (M + m) = 6

Substituting

M + m = 15

2d - 15 = 6

2d = 21

d = 10.5

Therefore, the median of

a

b

, and

c

10.5