Based on the given Venn diagram, which of the following statement(s) is/are…
2021
Based on the given Venn diagram, which of the following statement(s) is/are NOT correct?
Statements:
I. The number of balls which are not blue is 4.
II. The total number of cartoons is 23.
- A.
Only I
- B.
Only II
- C.
Both I and II
- D.
Neither I nor II
Attempted by 37 students.
Show answer & explanation
Correct answer: B
Concept
In an overlapping-shapes Venn diagram, each shape stands for one category, and a number belongs to a category only if it lies inside that shape. To count a category you add every number that falls inside its outline; to count items of one category that are excluded from another, you keep only the numbers that lie inside the first shape but outside the second.
Application: read each region
Here Ball = vertical rectangle, Cartoon = horizontal rectangle, Blue = triangle. Mapping each number to the shapes it lies inside:
Number | Inside which shapes |
|---|---|
4 (top) | Ball only |
3 (left) | Cartoon and Blue |
16 (centre) | Ball, Cartoon and Blue |
2 (right) | Cartoon only |
8 (bottom-left) | Blue only |
4 (bottom-centre) | Ball and Blue |
Evaluate each statement
Balls that are not blue: among the Ball numbers (top 4, centre 16, bottom 4), the centre 16 and the bottom 4 also lie inside the triangle, so only the top 4 lies inside Ball while outside Blue. Balls not blue = 4, so Statement I matches the diagram.
Total cartoons: add every number inside the horizontal rectangle, that is 3 + 16 + 2 = 21. The statement claims 23, but the diagram gives 21, so Statement II does not match the diagram.
The question asks which statement(s) are NOT correct. Statement I agrees with the diagram and Statement II does not, so exactly one statement fails: the cartoon-total statement.
Cross-check
As a check, the full Ball count is 4 + 16 + 4 = 24, of which 16 + 4 = 20 are also blue, leaving 24 - 20 = 4 balls that are not blue, confirming Statement I. The cartoon outline encloses 3, 16 and 2 only, summing to 21 and never reaching 23, confirming Statement II is the false one. Hence the option naming only the cartoon-total statement is the answer.