### All ACT Math Resources

## Example Questions

### Example Question #1 : Arithmetic Mean

Angela scores 17, 19, 13, 24, and 14 points in the first five games of a seven-game basketball season. If the scoring leader in Angela’s league averages 18 points per game, how many points must Angela score in the final two games combined to end the season with the highest scoring average in the league AND have a higher scoring average than any other player?

**Possible Answers:**

34

37

40

39

32

**Correct answer:**

40

Since a given player’s scoring average can be determined by dividing the sum total of points scored by the number of games, we can determine the total points of the scoring leader by multiplying the average points per game by the total number of games. 18 x 7 = 126. Angela would have to score 1 more point than the current scoring leader. Angela’s current total is 87 points; therefore, she must score 40 (87 + 40 = 127) over the course of the final two games to have the highest average points per game in the league.

### Example Question #2 : How To Find Arithmetic Mean

What is the mean of the following set of numbers: 13, 15, 100, 54, 345, rounded to the nearest 1’s place?

**Possible Answers:**

135

100

105

106

**Correct answer:**

105

mean = sum of all values divided by the number of values.

### Example Question #3 : How To Find Arithmetic Mean

The mean of five numbers is 40. The mean of the smallest two numbers is 25. What is the mean of the other three numbers?

**Possible Answers:**

45

40

50

55

60

**Correct answer:**

50

The equation for the mean of a group of numbers is to find the sum of all of the numbers and then divide by how many numbers are in the group. This means that if we know the mean and how many numbers are in the group, we can find the sum of those numbers.

(sum of all five numbers) / 5 = 40 **-->** sum of all five numbers = 200

(sum of two smallest numbers) / 2 = 25 **-->** sum of two smallest numbers = 50

Subtracting the sum of the two smallest numbers from the sum of all five gives us the sum of the remaining three. We can then divide by three to find the mean of those three remaining numbers.

200 – 50 = 150

150 / 3 = 50

### Example Question #4 : How To Find Arithmetic Mean

LeBron James had played in 7 playoff games. He scored 31, 30, 55, 14, 29, 20, and 12 points in those games. What is his average for those 7 games?

**Possible Answers:**

27.3 points

43 points

29 points

20.5 points

22 points

**Correct answer:**

27.3 points

To find the mean, you have to add all of the items and then divide by the number of items. Finding the sum (31+30+55+14+29+20+12)= 191 and then dividing by 7 would give a result of 27.3. [Side Note: The Median is 29 and the range is 43.]

### Example Question #5 : How To Find Arithmetic Mean

Kobe Bryant has averaged about 29.5 points a game through the first 81 games of the NBA season. His goal is to average at least 30 points per game for the season. What is the least amount of points he needs to score in his last game of the season to achieve his goal? (There are 82 games in a season.)

**Possible Answers:**

41 points

31 points

61 points

71 points

51 points

**Correct answer:**

71 points

To find your answer, you would have to set it up like a weighted average because we don’t know what he scored for the 81 games, but we can approximate how many actual points he scored by multiplying 29.5 times 81. Thus, we would get the equation (29.5(81)+x)/82=30. Multiply both sides by 82 to get 2389.5+x=2460. Thus x=70.5 and we would round up to get 71 points.

### Example Question #6 : How To Find Arithmetic Mean

Peter received the following 4 grades on math tests: 86, 90, 88, and 96. What was Peter's average score for the 4 tests?

**Possible Answers:**

91

92

88

89

90

**Correct answer:**

90

In order to calculate the average, or arithmetic mean, of numbers in a set, we add up all of the numbers, then divide that total sum by the *n* (the count of numbers in the set).

Here we have 86, 90, 88, and 96. This gives us *n* = 4.

We add up 86 + 90 + 88 + 96 = 360. 360 / 4 = **90**.

### Example Question #7 : How To Find Arithmetic Mean

Ashley scored 80, 80, 83, 85, 90, and 77 on her tests this semester. If she wants an average of 85 on all her tests, which would she have to score on her final test?

**Possible Answers:**

100

None of the other answers.

95

85

97

**Correct answer:**

100

One can set up an equation for the average test score. 85=(80+80+83+85+90+77+x)/7.

Solving for x gives 100.

### Example Question #8 : How To Find Arithmetic Mean

An olympic athlete has just completed a four mile run. His average time was 6 minutes per mile. If he ran the first and last mile in 5 minutes, and the other 2 were the same time as each other, what was the average time for the 2 miles in the middle?

**Possible Answers:**

Not enough information given

5 minutes per mile

6 minutes per mile

7 minutes per mile

14 minutes per mile

**Correct answer:**

7 minutes per mile

The total time spent by the athlete was 24 minutes, if two of the miles took 10 minutes, then the other two took 14.

14/2 yields an average of 7 miles per minute

### Example Question #9 : How To Find Arithmetic Mean

On the chart above, what was the class average for Exam 2? Round to 1 decimal point.

**Possible Answers:**

87.4

83.1

84.9

79.9

81.0

**Correct answer:**

79.9

Average = (Sum of Grades) / (# of Grades)

= (85+93+65+70+90+72+65+86+93) / 9

= 719 / 9 = 79.9

### Example Question #10 : How To Find Arithmetic Mean

Anthony makes $4,000 a month as a bartender 10 months of the year, and for 2 months, he works in a jazz club where he makes $6,000 a month.

What is Anthony's average monthly salary in a year?

**Possible Answers:**

**Correct answer:**$4,333

In a year, Anthony makes $4,000 x 10 = $40,000

and an additional $6,000 x 2 = $12,000

totaling $52,000

The average monthly salary would be 52,000 ÷ 12 = 4,333