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Mathematics > Standard Multiple Choice

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

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Explanation

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