A school has 200 students. All of the students are very special. Some of them always speak the truth, and the rest of them, never speak the truth. Among the subject areas of Maths, Science, and Social Studies, each student has one favourite. A survey was conducted; each student was asked three yes-or-no questions. The questions were: “Do you like Maths the most?” “Do you like Science the most?” “Do you like Social Studies the most?”
The results were as follows:
104 students said “Yes,” they like Maths the most.
86 students said “Yes,” they like Science the most.
60 students said “Yes,” they like Social Studies the most.
How many students speak the truth, and how many do not?
Answer
There are 150 students who speak the truth and 50 students who do not.
Students who speak the truth will answer “yes” to one favourite subject, whereas those not speaking the truth will answer “yes” to two subjects (but not to their real favourite). Since there are 250 answers (104 + 86 + 60), there are 50 extra “yes” answers, from the 50 students who do not speak the truth.
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