A and B play Football, Cricket and Hockey. B and C play Hockey and Badminton.…
2020
A and B play Football, Cricket and Hockey. B and C play Hockey and Badminton. C and D play Badminton and Tennis. D and A play Football, Cricket and Tennis. Find out the correct answer among the following:
(A) C does not play Cricket
(B) B and D both play Tennis
(C) A plays Football, Cricket and Badminton
(D) A, B and D play Football and Cricket
(E) Except B all play Tennis
Choose the most appropriate answer from the options given below:
- A.
(A), (B) and (E) only
- B.
(A), (D) and (E) only
- C.
(A), (B) and (C) only
- D.
(C), (D) and (E) only
Attempted by 1 students.
Show answer & explanation
Correct answer: B
Concept
This is a set-membership deduction. Each clue states the sports that a PAIR of people plays together, which means BOTH named people play every sport listed in that clue. To find everything one person plays, collect (take the union of) the sports from every clue that names that person. A conclusion is true only if it holds against the complete sport-set built this way for each person.
Application
Read each clue as 'both of these people play all of these sports', then gather each person's sports across all the clues they appear in:
A appears with B (Football, Cricket, Hockey) and with D (Football, Cricket, Tennis) -> A plays Football, Cricket, Hockey, Tennis.
B appears with A (Football, Cricket, Hockey) and with C (Hockey, Badminton) -> B plays Football, Cricket, Hockey, Badminton.
C appears with B (Hockey, Badminton) and with D (Badminton, Tennis) -> C plays Hockey, Badminton, Tennis.
D appears with C (Badminton, Tennis) and with A (Football, Cricket, Tennis) -> D plays Football, Cricket, Tennis, Badminton.
The completed table of who plays what:
Person | Sports played |
|---|---|
A | Football, Cricket, Hockey, Tennis |
B | Football, Cricket, Hockey, Badminton |
C | Hockey, Badminton, Tennis |
D | Football, Cricket, Tennis, Badminton |
Cross-check each statement
(A) C does not play Cricket -- TRUE. C's sports are Hockey, Badminton, Tennis, so Cricket is absent.
(B) B and D both play Tennis -- FALSE. D plays Tennis, but B's sports are Football, Cricket, Hockey, Badminton, with no Tennis.
(C) A plays Football, Cricket and Badminton -- FALSE. A plays Football and Cricket but not Badminton (A's set is Football, Cricket, Hockey, Tennis).
(D) A, B and D play Football and Cricket -- TRUE. Each of A, B and D has both Football and Cricket in their set.
(E) Except B all play Tennis -- TRUE. A, C and D each play Tennis, and B does not.
Result
The statements that hold are (A), (D) and (E). So the correct choice is the combination (A), (D) and (E) only.