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Mathematics > Standard Multiple Choice

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

10-7-2013-M41008.png

The table above shows the attendance at the home games of the Central High School football team. If the median attendance for the five games was 456, and no two games had the same attendance, what is the greatest possible value for n?

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You got it!

Explanation

The median of five numbers can be found by putting the numbers in increasing order and picking the middle, or third, number from the list. Putting the four numbers you know in increasing order produces the following list:

399 comma 456 comma 508 comma 550

Thus, if n is less than or equal to 456, the list of the numbers in increasing order will be

n comma 399 comma 456 comma 508 comma 550 or 399 comma n comma 456 comma 508 comma 550

In either case, the median will be 456. However, if n is greater than 456, the list of numbers in increasing order will be

399 comma 456 comma n comma 508 comma 550

or 399 comma 456 comma 508 comma n comma 550

or 399 comma 456 comma 508 comma 550 comma n

In these cases, the median will be either n or 508. Since you know that the median is 456, it must be true that n is less than or equal to 456. Also, since no two games had the same attendance, the number n cannot be equal to 456. Therefore, the greatest possible value of n is 455.

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