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MathNet 2013 Question 55

Math Olympiad Vault · MathNet 2013

Question 55

On the island of Knights(who always tell the truth) and Knaves(who always lie), the 2013 residents are asked three questions: “Do you support team A?”, “Do you support team B?”, “Do you support team C?”. Everyone answers all three questions and supports exactly one team. There are 3000 “Yes” answers in total. How many residents are Knights?
(A)987
(B)1023
(C)1026
(D)2013
(E)The information is insufficient.