SAT SUBJECT TEST MATH LEVEL 1

STATISTICS, COUNTING, AND PROBABILITY

CHAPTER 16 Basic Concepts of Statistics, Counting, and Probability

Exercises

1. If a + b = 9, b + c = 13, and c + a = 14, what is the average (arithmetic mean) of a, b, and c ?

(A) 6

(B) 9

(C) 12

(D) 18

(E) 36

2. Let m be the median and M the mode of the following set of numbers: 1, 7, 2, 4, 7, 9, 2, 7. What is the average (arithmetic mean) of m and M?

(A) 5

(B) 5.5

(C) 6

(D) 6.25

(E) 6.5

3. Palindromes are numbers such as 44 and 383 and 1,441 that read the same from right to left as they do from left to right. If a 4-digit number is chosen at random, what is the probability that it will be a palindrome?

(A)

(B)

(C)

(D)

(E)

4. The following chart presents the number of employees at Acme Air-Conditioning in three age groups and the average monthly salary of the workers in each group.

What is the average (arithmetic mean) monthly salary, in dollars, for all the employees?

(A) 3,652

(B) 3,700

(C) 3,744

(D) 3,798

(E) 3,800

5. If five fair coins are flipped, what is the probability that all five land on heads?

(A)

(B)

(C)

(D)

(E)

6. What is the average (arithmetic mean) of 3⁶, 3⁹, and 3¹⁸?

(A) 3⁹

(B) 3¹¹

(C) 3²³

(D) 3² + 3³ + 3⁶

(E) 3⁵ + 3⁸ + 3¹⁷

7. Each question on a multiple-choice test has five equally likely answers. If Nicole guesses randomly on four questions, what is the probability she will answer at least one correctly?

(A) .25

(B) .47

(C) .5

(D) .59

(E) .8

8. If Ari, Ben, and Carol each choose a number at random between 1 and 5, inclusive, what is the probability that all of them choose different numbers?

(A)

(B)

(C)

(D)

(E)

9. The following stem-and-leaf plot displays the number of points scored in January by each member of the Central High School basketball team.

1 | 0

2 | 1 7 7

3 |

4 | 2 4 4 4 6 8 9

5 | 3 7 7

6 | 1 8

Legend: 4 | 2 = 42 points What percent of the team’s members scored between 35 and 55 points?

(A) 25%

(B) 43.75%

(C) 50%

(D) 56.25%

(E) 75%

10. Consider the following boxplot diagram for a set of data:

If R, I, and M represent the range, interquartile range, and median of the data, respectively, what is the value of R + I + M?

(A) 295

(B) 325

(C) 560

(D) 810

(E) 825

ANSWERS EXPLAINED

Answer Key

Solutions

Each of the problems in this set of exercises is typical of a question you could see on a Math 1 test. When you take the model tests in this book and, in particular, when you take the actual Math 1 test, if you get stuck on questions such as these, you do not have to leave them out—you can almost always answer them by using one or more of the strategies discussed in the “Tactics” chapter. The solutions given here do not depend on those strategies; they are the correct mathematical ones.

See Important Tactics for an explanation of the symbol ⇒, which is used in several answer explanations.

1. (A) Add the three equations:

2. (D) First arrange the numbers in increasing order: 1, 2, 2, 4, 7, 7, 7, 9. Since there are an even number of numbers, the median is the average of the middle two: The mode, M, is 7, the number that appears most often. Finally, the averge of m and M is .

3. (A) First use the counting principle to calculate the number of 4-digit palindromes. There are 9 choices for the first digit (1–9) and 10 choices for the second digit (0–9). For the third digit, there is only 1 choice (it must be the same as the second digit), and for the fourth digit there is only 1 choice (it must be the same as the first digit). So in total there are 9 × 10 × 1 × 1 = 90 four-digit palindromes. Since there are 9,000 four-digit integers, the probability that a four-digit number chosen at random will be a palindrome is .

4. (C) Use a weighted average:

5. (A) Since there are two equally possible outcomes for each coin (a head or a tail), there are 2 × 2 × 2 × 2 × 2 = 32 different equally possible outcomes. Only one of them consists of five heads, so the probability of getting five heads is . Alternatively, you could recognize that for each coin, the probability of getting a head is . Then the probability of getting five straight heads is .

6. (E) The average is

7. (D) The only way to fail to get at least one right is to get all four wrong. On each question Nicole has a probability of of guessing the correct answer and of guessing the wrong answer. So the probability that Nicole gets all four wrong is . The probability that she gets at least one correct is 1 – .41 = .59.

8. (E) Ari can choose any number. For Ben’s number to be different from Ari’s number, he must choose one of the 4 remaining numbers; the probability he will do that is . Similarly, the probability that Carol’s number will be different from the two numbers already chosen is . Therefore, the probability that the three numbers chosen are all different is .

9. (C) Of the 16 members on the team, 8 scored between 35 and 55 points—all 7 players whose scores were in the 40s and the 1 player who scored 53 points. So of the members scored between 35 and 55 points.

10. (A) The range is the difference between the greatest data point (230) and the least data point (125), so R = 105. The interquartile range is the difference between Q₃ (175, the right-hand end of the box ) and Q₁ (140, the left-hand end of the box), so I = 35. The median, M, is 155, the vertical line inside the box. So, R + I + M = 105 + 35 + 155 = 295.