每日一题

Mathematics>Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer.

Ten cars containing a total of 32 people passed through a checkpoint. If none of these cars contained more than 4 people, what is the greatest possible number of these cars that could have contained exactly 2 people?

(A) One
(B) Two
(C) Three
(D) Four
(E) Five

答案和解析

答案：D

解析：

It could not be true that each of the ten cars contained exactly 2 people, as this would give a total of only 20. If nine of the cars contained exactly 2 people, the remaining car could have no more than 4 people, for a total of only 22. Continuing in the same way, a pattern develops. If eight of the cars contained exactly 2 people, the remaining two cars could have no more than 4 people each, for a total of only 24. If seven of the cars contained exactly 2 people, the total number of people could be only 26. From the pattern, you can see that if four of the cars contained exactly 2 people, and the remaining six cars contained the maximum of 4 people, the total number would be 32, as given in the question. Therefore, at most four of the ten cars could have contained exactly 2 people.