IPMAT Indore 2024 · Quantitative Ability · Question 30

Step 1 — note that the given regions are disjoint. Read the wording carefully: “4-wheeler but not a 2-wheeler” and “2-wheeler but not a 4-wheeler” are the two exclusive regions, and “neither” is outside both circles. These three never overlap, and together with “both” they account for everyone.

Step 2 — add up the four disjoint regions.

\underset{\text{only 4W}}{\underset{⏟}{250}}+\underset{\text{only 2W}}{\underset{⏟}{100}}+\underset{\text{neither}}{\underset{⏟}{100}}+\underset{\text{both}}{\underset{⏟}{x}}=500

Step 3 — solve.

450+x=500 \Rightarrow x=50

Answer: Option 3 — 50

Shortcut. Four boxes, one subtraction. A two-set Venn diagram has exactly four regions: only-A, only-B, both, neither. When the question hands you three of them, the fourth is just 500-\left( 250+100+100 \right)=50.

The only real trap is misreading “250 owned a 4-wheeler” as the total 4-wheeler count. It says “but not a 2-wheeler”, so it is already the exclusive region — no inclusion–exclusion formula is needed at all. Taking it as a total gives 100, which is option (d).