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 $=M$

Let the minimum value $=m$

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 $c$ is $10.5$ .

IPMAT Indore 2024

The following table shows the number of employees and their median age in eight companies located in a district.

Company	Number of employees	Median age
A	32	24
B	28	30
C	43	39
D	39	45
E	35	49
F	29	54
G	23	59
H	16	63

It is known that the age of all employees are integers. It is known that the age of every employee in A is strictly less than the age of every employee in B, the age of every employee in B is strictly less than the age of every employee in C, ..., the age of every employee in G is strictly less than the age of every employee in H.

The median age of employees across the eight companies is:

IPMAT Indore 2021

A class consists of 30 students. Each of them has registered for 5 courses. Each course instructor conducts an exam out of 200 marks. The average percentage marks of all 30 students across all courses they have registered for, is 80%. Two of them apply for revaluation in a course. If none of their marks reduce, and the average of all 30 students across all courses becomes 80.02%, the maximum possible increase in marks for either of the 2 students is

IPMAT Indore 2022

Let 50 distinct positive integers be chosen such that the highest among them is 100, and the average of the largest 25 integers among them exceeds the average of the remaining integers by 50. Then the maximum possible value of the sum of all the 50 integers is _________.

IPMAT Indore 2026

The possible values of $x$ in the set $\{1, 5, 13\}$ for which the mean of eight observations $5, 8, 3x + 2, 15, 27, 29, 36, 5x - 2$ equals their median are

IPMAT Indore 2019

The average of five distinct integers is 110 and the smallest number among them is 100. The maximum possible value of the largest integer is

IPMAT Indore 2024

The following table shows the number of employees and their median age in eight companies located in a district.

Company	Number of employees	Median age
A	32	24
B	28	30
C	43	39
D	39	45
E	35	49
F	29	54
G	23	59
H	16	63

In company F, the lowest possible sum of the ages of all employees is:

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

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IPMAT Indore Past Year Questions (Topic-Wise)

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