SAT Math Multiple Choice Practice Question 607: Answer and Explanation

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Question: 607

21. In a list of seven integers, 13 is the smallest member, 37 is the largest member, the mean is 23, the median is 24, and the mode is 18. If the numbers 8 and 43 are then added to the list, which of the following will change?

I. The mean

II. The median

III. The mode

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III

Correct Answer: A


A Come up with a list of numbers that fits the description in the question. We know the smallest, largest, and middle numbers out of 7 spots:

13, __, __, 24, __, __, 37

Because the mode is 18, there must be more than one 18 in the list, and there is only one place they would fit:

13, 18, 18, 24, __, __, 37

The last piece of information we have is that the mean, or average, is 23. Since there are 7 numbers, the total sum is 7 × 23 = 161. The numbers we already know from the list add up to 13 + 18 + 18 + 24 + 37 = 110. The last two integers must equal 51 when added together, so only 25 and 26 fit in the two spaces left in our list. Now add 8 and 43 to the list and evaluate statements I, II, and III. The mode will not change: 18 still occurs the most, so III is not true. Eliminate C, D, and E for containing III. The numbers 8 and 43 are lower and higher, respectively, than anything on the original list, so the median stays the same, so II is not true. Eliminate B because it contains II, leaving only A.

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