- If y= 2 x+1, what is the average (arithmetic
mean) of 2x, 2 x, y,and 3y,in terms of x?
(A) 2x (B) 2x+ 1 (C) 3x
(D) 3x+ 1 (E) 3x+ 2 - The average (arithmetic mean) of seven inte-
gers is 11. If each of these integers is less than
20, then what is the least possible value of any
one of these integers?
(A) − 113 (B) − 77 (C) − 37
(D) − 22 (E) 0 - The median of 8, 6, 1, and kis 5. What is k?
- The average (arithmetic mean) of two numbers is
z.If one of the two numbers is x,what is the value
of the other number in terms of xand z?
(A) z−x (B) x−z (C) 2z−x
(D) x− 2 z (E) - A set of nnumbers has an average (arithmetic
mean) of 3kand a sum of 12m,where kand m
are positive. What is the value of nin terms of k
and m?
(A) (B) (C)(D) (E) 36km- The average (arithmetic mean) of 5, 8, 2, and k
is 0. What is the median of this set?
(A) 0 (B) 3.5 (C) 3.75
(D) 5 (E) 5.5
m
4 kk
4 m4 k
m4 m
kxz+
2- A die is rolled 20 times, and the outcomes are as
tabulated above. If the average (arithmetic
mean) of all the rolls is a,the median of all the
rolls is b,and the mode of all the rolls is c,then
which of the following must be true?
I. a=b II. b> c III. c= 5
(A) I only (B) II only
(C) I and II only (D) II and III only
(E) I, II, and III - If a 30% salt solution is added to a 50% salt so-
lution, which of the following could be the con-
centration of the resulting mixture?
I. 40%
II. 45%
III. 50%
(A) I only (B) I and II only
(C) I and III only (D) II and III only
(E) I, II, and III- Set A consists of five numbers with a median of
m.If Set B consists of the five numbers that are
two greater than each of the numbers in Set A,
which of the following must be true?
I. The median of Set B is greater
than m.
II. The average (arithmetic mean) of
Set B is greater than m.
III. The greatest possible difference
between two numbers in Set B is
greater than the greatest possible
difference between two numbers
in Set A.
(A) I only (B) I and II only
(C) I and III only (D) II and III only
(E) I, II, and IIISAT Practice 2: Mean/Median/Mode Problems
CHAPTER 9 / SPECIAL MATH PROBLEMS 339
Roll Frequency
15
23
33
43
53
63....1 2 3 4 5 7 8 9610 2 3 4 5 7 8 9610 2 3 4 5 7 8 9610 2 3 4 5 7 8 96