Logical Venn Diagrams Questions and Answers

Answer: B

20 candidates offered A + B + C.

The permitted sets of three are A B C, A B D, A B F and C D E: A and B go together and A excludes E, and without A and B the only set that keeps F away from C and D is C D E. E appears only in C D E, so 70 candidates took C D E. F appears only in A B F, so 35 took A B F. C appears in A B C and C D E, so A B C has 90 − 70 = 20. D appears in A B D and C D E, so A B D has 85 − 70 = 15. Check: A = 20 + 15 + 35 = 70.

So the combination A B C was taken by 20 candidates. The figure 15 belongs to A B D, 35 to A B F, and 70 to C D E.

Answer: D

70 candidates combined C with D.

The permitted sets of three are A B C, A B D, A B F and C D E: A and B go together and A excludes E, and without A and B the only set that keeps F away from C and D is C D E. E appears only in C D E, so 70 candidates took C D E. F appears only in A B F, so 35 took A B F. C appears in A B C and C D E, so A B C has 90 − 70 = 20. D appears in A B D and C D E, so A B D has 85 − 70 = 15. Check: A = 20 + 15 + 35 = 70.

C and D occur together only in the set C D E, and 70 candidates took it. Nobody can take C and D with A and B in the same set, because three subjects only are allowed.

Answer: C

35 candidates offered B with F.

The permitted sets of three are A B C, A B D, A B F and C D E: A and B go together and A excludes E, and without A and B the only set that keeps F away from C and D is C D E. E appears only in C D E, so 70 candidates took C D E. F appears only in A B F, so 35 took A B F. C appears in A B C and C D E, so A B C has 90 − 70 = 20. D appears in A B D and C D E, so A B D has 85 − 70 = 15. Check: A = 20 + 15 + 35 = 70.

B and F occur together only in A B F, and F is taken by 35 candidates in all, all of them in A B F, so 35 offered B with F.

Answer: A

The number of artists who are players only is 14.

Artists are the points inside the square and players are the points inside the circle, so artists who are players are in both. 'Only' excludes the doctors, who are inside the triangle. Reading the regions: 8 lies in the square alone, 13 in the circle alone, 6 in the triangle alone, 5 in the circle and triangle, 3 in all three shapes (an artist who is both a player and a doctor), and 10 and 4 in the circle and square but outside the triangle.

\[ 10 + 4 = 14 \]

The distractors come from counting the wrong regions: 10 alone forgets the 4 region below the triangle, 4 alone forgets the 10 region, and 13 is the circle-only region, which holds players who are neither doctors nor artists.

Answer: C

The correct diagram is (C), two separate circles inside one large circle.

Engineers and accountants are both professionals, so each of their circles lies inside the circle for professionals. An engineer is not, as a class, an accountant, and the two groups are treated as separate, so their circles do not overlap.

(A) puts one group outside professionals altogether, (B) shows three unrelated classes, and (D) makes accountants a subset of engineers (or the reverse), which is not their relationship.

Answer: D

The correct figure is (D), two separate circles inside one large circle.

Tables and chairs are both kinds of furniture, so both their circles lie inside the furniture circle. A table is not a chair, so the two inner circles are separate.

(A) makes chairs a kind of table (or the reverse). (B) puts one class outside furniture altogether, and (C) shows a class only partly overlapping furniture, which would mean some tables or chairs are not furniture.

Answer: A

The word is Den.

A stable is the home of a horse, a burrow of a rabbit, and a nest of a bird: each is the dwelling place of an animal. A den is the home of a lion or other wild animal, so it belongs with them.

A slum and a city are human settlements, and a herd is a group of animals, not a place where they live.

Answer: B

The answer is 10.

Each region of the diagram is a combination of the four shapes. The question wants men (inside the rectangle) who are civil servants (inside the circle) but are not educated (outside the square) and not urban (outside the triangle).

Region 10 lies inside both the circle and the rectangle, and the square and the triangle do not reach it, so it is the one that fits. Region 6 is in the circle only, so it is not male; region 7 is in the rectangle only, so it is not a civil servant; region 4 is also in the square (educated), and region 5 is in the square and the triangle (educated and urban).

Of the other options, 4 is the region of educated male civil servants who are not urban, 9 is the region of educated men who are not civil servants, and 16 is not a region number in the diagram.