IPMAT Indore 2024 · Quantitative Ability · Question 14

The structure of this set. The eight companies form a strictly increasing chain of age blocks: every employee of A is younger than every employee of B, who are all younger than every employee of C, and so on. So if you lined up all 245 employees by age, they would come out company by company, in order A, B, C, D, E, F, G, H — with no interleaving anywhere.

Total headcount.

32+28+43+39+35+29+23+16=245

The median rule you need throughout. For n values in sorted order:

n odd: the median is the \frac{n+1}{2}-th value.

n even: the median is the average of the \frac{n}{2}-th and \left( \frac{n}{2}+1 \right)-th values.

Step 1 — find the median position. There are 245 employees — an odd number — so the median is the

\frac{245+1}{2}=123\text{rd}

value in the sorted list.

Step 2 — use the chain to locate the 123rd person. Because the companies form a strictly increasing chain, the sorted list is simply A, then B, then C, and so on. Build the cumulative count:

Position 123 falls inside company D.

Step 3 — which employee of D is it?

123-103=20

so it is D’s 20th employee by age.

Step 4 — recognise that this is D’s own median. D has 39 employees — odd — so D’s median is its

\frac{39+1}{2}=20\text{th}

employee, which the table gives as 45.

The overall median is D’s median, exactly.

Answer: 45

Shortcut. Cumulate, then land. 245 employees \Rightarrow the 123rd value. Running totals 32,60,103,142 show 123 sits in D, at D’s 123-103=20th place — and 20 is precisely D’s median position since D has 39 (odd) employees.

So the answer is just D’s tabulated median, 45 — no construction of individual ages is needed. Whenever the overall median position coincides with a company’s own median position, the table hands you the answer directly.