SAT Math Multiple Choice Practice Question 151: Answer and Explanation

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Question: 151

19. A list of three integers has an average (arithmetic mean) of 6. If the median of the numbers is -1, what is the smallest positive number that could appear in the list?

A. 1
B. 6
C. 18
D. 20
E. 21

Correct Answer: D

Explanation:

D. The median is the middle number when the three numbers are listed in order. So you can list the numbers as a, -1, b. Also, you know that the mean is 6, and therefore the total of the three numbers is 18. (Do you remember why? The total = the average × the number of things, or 18 = 6 × 3. This formula is really worth knowing.)

Now comes the tricky part: a can't be greater than -1, but nothing prevents it from equaling -1. It's tempting to make a = -2, which makes b = 21. But if you let a = -1, then b can equal 20. Because -1 is the biggest you can possibly make a, 20 must be the smallest that b can ever be.

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