Question
Four out of seven Chestnut High School Chess Academy students (A, B, C, D, E, F and G) are to be selected in a school chess team in such a way that if A is selected, then B cannot be in that team and if B is selected, then E cannot be in that team. If one of D and F is selected, then the other must be chosen. Which of the following statements must be true?
Answer: Option A
:
A
Option (A): If B is selected, then A and E cannot be selected. The other 3 must be from CDFG but D and F have to be together so the team will be B, D, F and any one of C or G. So D must be selected in the team, hence this Option is definitely TRUE.
Option(B): If A is selected B cannot be chosen. The other 3 members can be any 3 from C, D, E, F and G. This Option is not definitely TRUE.
Option (C): If B is selected, then A and E are ruled out. The other 3 can be chosen from C, D, F and G. Of this D and F must be chosen with the last member being either C or G. This Option is not definitely TRUE.
Option (D): C need not be chosen on every team. If we select DFEG, this is a valid team without C. Option(A)
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:
A
Option (A): If B is selected, then A and E cannot be selected. The other 3 must be from CDFG but D and F have to be together so the team will be B, D, F and any one of C or G. So D must be selected in the team, hence this Option is definitely TRUE.
Option(B): If A is selected B cannot be chosen. The other 3 members can be any 3 from C, D, E, F and G. This Option is not definitely TRUE.
Option (C): If B is selected, then A and E are ruled out. The other 3 can be chosen from C, D, F and G. Of this D and F must be chosen with the last member being either C or G. This Option is not definitely TRUE.
Option (D): C need not be chosen on every team. If we select DFEG, this is a valid team without C. Option(A)
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