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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?

Answer Choices

Right! (Applause.)

Explanation

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.

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