下面是两道
Mathematics > Standard Multiple Choice
Read the following SAT test question and then click on a button to select your answer.
At Central High School, the math club has members and the chess club hasmembers. If a total of students belong to only one of the two clubs, how many students belong to both clubs?
Answer Choices
(A)
(B)
(C)
(D)
(E)
The correct answer is C
Explanation
Let stand for the number of students who belong to both clubs. The members of the math club can be broken down into two groups: those who are in both clubs (there are students in this category) and those who are in the math club only (there are students in this category).
The members of the chess club can also be broken down into two groups: students who are in both clubs and students who are in the chess club only.
Since a total of students belong to only one of the two clubs, you know that . Solving this equation gives , so students belong to both clubs
Ten cars containing a total ofpeople passed through a checkpoint. If none of these cars contained more thanpeople, what is the greatest possible number of these cars that could have contained exactlypeople?
Answer Choices
(A) One
(B) Two
(C) Three
(D) Four
(E) Five
The correct answer is D
Explanation
It could not be true that each of the ten cars contained exactlypeople, as this would give a total of only. If nine of the cars contained exactlypeople, the remaining car could have no more thanpeople, for a total of only. Continuing in the same way, a pattern develops. If eight of the cars contained exactlypeople, the remaining two cars could have no more thanpeople each, for a total of only. If seven of the cars contained exactlypeople, the total number of people could be only. From the pattern, you can see that if four of the cars contained exactlypeople, and the remaining six cars contained the maximum ofpeople, the total number would be, as given in the question. Therefore, at most four of the ten cars could have contained exactly people.
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