IPMAT Indore 2025 · Quantitative Ability · Question 38

Step 1 — name the three regions of the Venn diagram. Since they are in AP, write them as

n\left( A-B \right)=a-d, n\left( A\cap B \right)=a, n\left( B-A \right)=a+d

Step 2 — the three regions make up the union.

n\left( A\cup B \right)=\left( a-d \right)+a+\left( a+d \right)=3a=18 \Rightarrow a=6

The d cancels, so we never need its value.

Step 3 — build n\left( A \right) and n\left( B \right). Each set is “its own part” plus “the overlap”:

n\left( A \right)=\left( a-d \right)+a, n\left( B \right)=\left( a+d \right)+a

Step 4 — add them.

n\left( A \right)+n\left( B \right)=\left( a-d \right)+\left( a+d \right)+2a=4a=4\times 6=24

Alternative one-liner: n\left( A \right)+n\left( B \right)=n\left( A\cup B \right)+n\left( A\cap B \right)=18+6=24.

Answer: Option 1 — 24