SAT Prep
Average Problems
1. The average (arithmetic mean) of a, b, s, and t is 6 and the average of s and t is 3. What
is the average of a and b?
A) 3 B) 9/2 C) 6 D) 9 E) 12
2. Seven students played a game and their scores from least to greatest were 20, 30, 50, 70,
80, 80, and 90. Which of the following is true of the scores?
I. The average (arithmetic mean) is greater than 70.
II. The median is greater than 70.
III. The mode is greater than 70.
A) None B) III only C) I and II D) II and III E) I, II and III
x y z
3. If p 4 , then in terms of p, what is the average (arithmetic mean) of x, y, and
3
z?
A) 4p B) 3p C) p/3 D) p/4 E) p/12
4. For the numbers r, s, and t, the average (arithmetic mean) is twice the median. If r < s <
t, r = 0, and t = ns, what is the value of n?
5. If the average (arithmetic mean) of 5 and k is equal to the average of 2, 6, and k, what is
the value of k?
A) 1 B) 2 C) 5 D) 6 E) 8
6. In a certain club, the median age of the members is 11. Which of the following must be
true?
I. The oldest member in the club is at least 1 year older than the youngest.
II. If there is a 10 year old in the club, there is also a 12 year old.
III. The mode of the members’ ages is 11.
A) None B) I only C) II only D) III only E) II and III
7. The average (arithmetic mean) of 5 positive integers is 350. Two of the integers are 99
and 102 and the other integers are greater than 102. If all 5 integers are different, what is
the greatest possible value for any of the five integers?
8. If a, b, and c, represent three numbers where b = a + 3 and c = b + 6, what is the result
when the median of the three numbers is subtracted from the average (arithmetic mean)
of the numbers?
A) 0 B) 1 C) 1.5 D) 2 E) 2.5
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SAT Prep
Average Problems
9. From the list of numbers {1, 3, 4, 5, and 11}, two different numbers will be chosen. Of
the following, which could be the average (arithmetic mean) of the two numbers?
I. 3 II. 4 III. 6
A) I only B) II only C) III only D) I and II E) I, II, and III
10. If the average (arithmetic mean) of 5 consecutive even integers is n, what is the median
of these 5 integers?
A) 0 B) 2 C) n D) n – 2 E) n – 4
11. Which of the following set of numbers is the average (arithmetic mean) greater than the
median?
A) {1, 2, 3, 4, 5}
B) {1, 2, 3, 4, 6}
C) {1, 3, 3, 3, 5}
D) {-1, 2, 3, 4, 5}
E) {-1, 2, 3, 4, 6}
12. A class of 20 students took a 3-question quiz. The table shows the possible scores on this
quiz and the numbers of students who received each of these scores.
Quiz Score # of Students
0 3
1 6
2 7
3 4
What is the average (arithmetic mean) of the scores for this class?
A) 1.0 B) 1.5 C) 1.6 D) 1.9 E) 2.0
13. The average (arithmetic mean) of the test scores of a class of p students is 70, and the
average of the test scores of a class of n students is 92. When the scores of both classes
p
are combined, the average score is 86. What is the value of .
n
14. The average (arithmetic mean) of 3 numbers is 60. If two of the numbers are 50 and 60,
what is the third number?
A) 50 B) 55 C) 60 D) 65 E) 70
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