If triangle represents Men, rectangle represents Businessman and circle represents Millionaire, then which number represents Men that are both Businessman and Millionaire ?
10
The number is 10 — option 3.
Translate the question into set language. The three shapes stand for three sets :
| Shape | Set |
|---|---|
| Triangle | Men |
| Rectangle | Businessmen |
| Circle | Millionaires |
“Men who are both businessman and millionaire” means a person belonging to all three sets at once. In a Venn diagram that is the single region where all three shapes overlap — the intersection \(T\cap R\cap C\).
Read the region off the figure. The only number lying inside the triangle, the rectangle and the circle together is 10.
| Number | Region | Meaning |
|---|---|---|
| 13 | Triangle only | Men who are neither businessmen nor millionaires |
| 7 | Circle only | Millionaires who are neither men nor businessmen |
| 3 | Circle and triangle | Men who are millionaires but not businessmen |
| 12 | Rectangle and triangle | Men who are businessmen but not millionaires |
| 8 | Circle and rectangle | Businessmen who are millionaires but not men |
| 10 | All three | Men who are both businessmen and millionaires |
Why the distractors are placed as they are. Options 1 and 4 — 12 and 3 — are the two double overlaps that each include the triangle. A candidate who reads the question as “men who are businessmen” picks 12, and one who reads it as “men who are millionaires” picks 3. Option 2, 13, is the triangle alone. Only by insisting on the word both does one arrive at the triple overlap.
The general rule for such questions : count how many conditions the question imposes, and look for the region enclosed by exactly that many shapes. Three conditions here, so three shapes must overlap.
Hence, the answer is 10.
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