Weighted Average — Practice Set

Bank code: STA-WAV · Section: Statistics · 30 questions — Easy 5 · Medium 8 · Hard 12 · Extreme 5

Never average the averages: weight each group's mean by how many members it has, and the combined mean always lands closer to the bigger group.

Every question below is live in the question bank under the ID shown — the sheet and the portal are the same questions. Attempt a level with the clock running, then check Part C.

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Part A — Questions

Quantitative Comparison — the four choices are always the same, so they are not reprinted: (A) Column A is greater · (B) Column B is greater · (C) The two quantities are equal · (D) The relationship cannot be determined from the information given

Level 1 · Easy — 5 questions · ~4 min

warm-up — these must be automatic

Q1 · STA-WAV-001 · MCQ · 45s

In a class, 10 students scored an average of 80 on a test and the other 15 students scored an average of 70. What was the average score of all 25 students?

(A) 70
(B) 74
(C) 75
(D) 76
(E) 80

Q2 · STA-WAV-003 · Numeric Entry · 40s

A course grade is computed from two components: a quiz worth 1 credit and an exam worth 2 credits. A student scores 90 on the quiz and 60 on the exam. What is the student's weighted average score? Enter your answer as a number.

Numeric entry — write the number.

Q3 · STA-WAV-008 · MCQ · 50s

Group 1 has average value a and Group 2 has average value b, where a < b. Each group contains at least one member, and the two groups are combined into a single group. Which of the following must be true of the average of the combined group?

(A) It equals (a + b)/2
(B) It is less than a
(C) It is greater than b
(D) It lies strictly between a and b
(E) It is closer to a than to b

Q4 · STA-WAV-009 · QC · 50s

Group X consists of 5 students with an average score of 60. Group Y consists of 15 students with an average score of 80.

Column A: The average score of all 20 students Column B: 70

Q5 · STA-WAV-010 · MCQ · 50s

On a job site, 8 workers each earn $15 per hour and 2 workers each earn $25 per hour. What is the average hourly wage of the 10 workers?

(A) $15
(B) $17
(C) $20
(D) $23
(E) $25

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Level 2 · Medium — 8 questions · ~10 min

two or three steps, one planted trap each

Q6 · STA-WAV-015 · Numeric Entry · 70s

At a company, 25% of the employees work in the Delhi office and the remaining 75% work in the Mumbai office. In the Delhi office, 80% of the employees hold a graduate degree; in the Mumbai office, 40% do. What percent of all the company's employees hold a graduate degree? Enter your answer as a number.

Numeric entry — write the number.

Q7 · STA-WAV-020 · MCQ · 85s

A cafe sells regular coffee at $3 per cup and premium coffee at $8 per cup, and sells nothing else. On Tuesday it sold 40 cups in total for $190. How many cups of premium coffee did it sell?

(A) 14
(B) 20
(C) 24
(D) 26
(E) 38

Q8 · STA-WAV-021 · Numeric Entry · 70s

Three groups of students have average scores of 60, 75, and 90. The groups contain 5, 3, and 2 students respectively. What is the average score of all the students? Enter your answer as a number.

Numeric entry — write the number.

Q9 · STA-WAV-024 · Select all that apply · 90s

For real numbers a and b, define M = (3a + 5b)/8. Which of the following must be true? Select all that apply.

(A) If a < b, then M is closer to b than to a
(B) If a is not equal to b, then M lies strictly between a and b
(C) M > (a + b)/2 for all a and b
(D) If a and b are each increased by 4, then M increases by 4
(E) If a and b are each multiplied by 3, then M is multiplied by 3 and then increased by 8

Q10 · STA-WAV-027 · QC · 85s

A car drives from P to Q at a constant speed of v1 km/h and immediately returns from Q to P along the same road at a constant speed of v2 km/h. Both v1 and v2 are positive, and v1 is not equal to v2.

Column A: The car's average speed for the round trip Column B: (v1 + v2)/2

Q11 · STA-WAV-029 · Numeric Entry · 60s

The average age of a group of 9 people is 30 years. One more person, aged 48, joins the group. What is the average age of the 10 people now? Enter your answer as a number.

Numeric entry — write the number.

Q12 · STA-WAV-030 · Select all that apply · 80s

In a class containing at least one boy and at least one girl, the boys' average test score is 70 and the girls' average test score is 85. Which of the following could be the average score of the whole class? Select all that apply.

(A) 69
(B) 72
(C) 77.5
(D) 84
(E) 86

Q13 · STA-WAV-031 · MCQ · 80s

In a school district, the boys' average math score is 72 and the girls' average math score is 78. The district's overall average math score is 76. What fraction of the students in the district are boys?

(A) 1/4
(B) 1/3
(C) 1/2
(D) 2/3
(E) 3/4

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Level 3 · Hard — 12 questions · ~20 min

where 162+ is won or lost

Q14 · STA-WAV-034 · MCQ · 100s

A school has exactly three sections. Section A has 20 students with an average score of 68 and Section B has 30 students with an average score of 78. All 100 students in the school have an average score of 80. What is the average score of Section C?

(A) 74
(B) 80
(C) 86
(D) 92
(E) 94

Q15 · STA-WAV-035 · QC · 90s

Group A has an average score of 70 and Group B has an average score of 90. Group A has more members than Group B, and each group has at least one member.

Column A: The average score of Groups A and B combined Column B: 80

Q16 · STA-WAV-036 · Numeric Entry · 95s

Three sections P, Q and R contain students in the ratio 3 : 4 : 5. Section P averaged 84 on a test and Section Q averaged 78. All the students in the three sections together averaged 77. What was Section R's average? Enter your answer as a number.

Numeric entry — write the number.

Q17 · STA-WAV-037 · MCQ · 95s

The average salary in Department A is $60,000 and the average salary in Department B is $90,000. When the two departments are combined, the average salary of all their employees is $72,000. If Department B has 12 employees, how many employees does Department A have?

(A) 8
(B) 12
(C) 18
(D) 30
(E) 36

Q18 · STA-WAV-038 · Select all that apply · 100s

A class of 24 students has a test average of 72. A second class, in which every student scored exactly 100 on the same test, is merged with the first. The second class contains at least one student, but its size is not given. Which of the following must be true of the merged class's average? Select all that apply.

(A) It is greater than 72
(B) It is less than 100
(C) If the second class also has 24 students, the merged average is 86
(D) It is 86 regardless of the size of the second class
(E) It is greater than 80 regardless of the size of the second class

Q19 · STA-WAV-039 · MCQ · 100s

A student's grade point average is the sum of (grade x credit hours) over all courses, divided by the total credit hours. This term the student earned: Calculus, 3 credits, grade 3.0; Chemistry, 4 credits, grade 2.7; English, 3 credits, grade 3.5; History, 2 credits, grade 4.0. What is the student's grade point average, rounded to the nearest hundredth?

(A) 3.03
(B) 3.19
(C) 3.30
(D) 3.34
(E) 3.83

Q20 · STA-WAV-040 · QC · 95s

A store sold n items on Monday at an average price of $40 and m items on Tuesday at an average price of $60, where n and m are both positive. The average price of all the items sold over the two days was $52.

Column A: n Column B: m

Q21 · STA-WAV-041 · Numeric Entry · 100s

The average score of 25 students on a test was 72. When the 5 lowest scores were excluded, the average of the remaining 20 students was 76. What was the average of the 5 excluded scores? Enter your answer as a number.

Numeric entry — write the number.

Q22 · STA-WAV-042 · MCQ · 105s

On a certain airline, 80% of passengers travel in Economy and pay an average fare of $300; the other 20% travel in Business and pay an average fare of $1,200. The airline then raises every Economy fare by 10% and cuts every Business fare by 20%. The proportion of passengers in each class is unchanged. What is the new average fare per passenger?

(A) $422
(B) $456
(C) $480
(D) $499
(E) $528

Q23 · STA-WAV-043 · QC · 105s

Team A has 12 players with an average age of 25 and Team B has 8 players with an average age of 30. Two players from Team A, both aged 28, transfer to Team B, and at the same time two players from Team B, both aged 27, transfer to Team A. No other players join or leave.

Column A: The average age of all 20 players on the two teams after the transfers Column B: 27

Q24 · STA-WAV-044 · Select all that apply · 100s

Group A has an average score of 62 and Group B has an average score of 74. Each group contains at least one member, and the average score of the two groups combined is exactly 70. Which of the following must be true? Select all that apply.

(A) Group B has more members than Group A
(B) Group B has exactly twice as many members as Group A
(C) Group A has more members than Group B
(D) Group A has at least 4 members and Group B has at least 8 members
(E) If Group A has 9 members, then the two groups together have 27 members

Q25 · STA-WAV-045 · MCQ · 105s

A factory makes only two kinds of bolt: standard bolts weighing 30 grams each and heavy-duty bolts weighing 60 grams each. Last week the average weight of all bolts produced was 45 grams. This week the factory produces twice as many heavy-duty bolts as it did last week while producing the same number of standard bolts as last week. What is the average weight of all the bolts produced this week?

(A) 45 g
(B) 50 g
(C) 52.5 g
(D) 54 g
(E) 60 g

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Level 4 · Extreme — 5 questions · ~10 min

165+ — expect to need the insight, not the grind

Q26 · STA-WAV-046 · MCQ · 120s

A firm has exactly two divisions. Division A has 300 employees: 40% are managers, who average $120,000, and the remaining 60% are staff, who average $70,000. Division B has 200 employees: 25% are managers, who average $130,000, and the remaining 75% are staff, who average $60,000. What is the average salary of all 500 employees of the firm?

(A) $82,500
(B) $83,750
(C) $85,000
(D) $90,000
(E) $92,000

Q27 · STA-WAV-047 · QC · 125s

Every student at School X and at School Y takes the same annual exam. In 2019 the average score was 80 at School X and 84 at School Y. In 2020 the average score was 88 at School X and 92 at School Y. Each school had at least one student in each of the two years, but a school's enrollment in 2020 need not equal its enrollment in 2019.

Column A: The average score of all students at the two schools combined in 2020 Column B: 8 more than the average score of all students at the two schools combined in 2019

Q28 · STA-WAV-048 · Numeric Entry · 115s

Three plants make identical widgets. Plant A produces 120 widgets per hour and runs for 5 hours; Plant B produces 200 widgets per hour and runs for 6 hours; Plant C produces 100 widgets per hour and runs for 2 hours. It costs $5 to make each widget at Plant A, $3 at Plant B, and $7 at Plant C. Taking all three plants together, what is the average cost per widget, in dollars? Enter your answer as a number.

Numeric entry — write the number.

Q29 · STA-WAV-049 · Select all that apply · 130s

A portfolio is split among stocks, bonds and cash with weights wS, wB and wC, each strictly positive and summing to 1. Stocks return 12%, bonds return 6% and cash returns 2%, and the portfolio's overall return is exactly 7%. Which of the following must be true? Select all that apply.

(A) wS < 1/3
(B) wB > wC
(C) wS < wB + wC
(D) wS + wB > 0.5
(E) wC < 0.5

Q30 · STA-WAV-050 · MCQ · 120s

A train covers the first third of its route at a constant 20 km/h and the remaining two thirds of the route at a constant 60 km/h. What is the train's average speed for the whole route, in km/h?

(A) 30
(B) 36
(C) 40
(D) 44
(E) 46 2/3

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