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

Mean, Median & Mode

Medium

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

10.5

9.5

✅ Correct Option: 2

Let the maximum value

=M

\newline

Let the minimum value

=m

\newline

Let the median value

= d

In a way, we've gotten the 3 numbers

(a, b, c)

\text{Mean} = \dfrac{M + m + d}{3} \quad \rightarrow (1)

From the first condition:

\Rightarrow

Max

(a, b, c) \ +

Min

(a, b, c) = 15

\Rightarrow M + m = 15 \quad \rightarrow (2)

From the second condition:

\Rightarrow

Median

(a, b, c) \ -

Mean

(a, b, c) = 2

\Rightarrow d - \text{Mean} = 2 \quad \rightarrow (3)

Putting

(1)

into

(3)

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

Putting

(2)

in the above:

\Rightarrow d - \left(\dfrac{15 + d}{3}\right) = 2

\Rightarrow 3d - 15 - d = 6

\Rightarrow 2d - 15 = 6

\Rightarrow d = \dfrac{21}{2} = 10.5

Therefore, the median of

a

b

, and

c

10.5