Overlapping Sets — Practice Set

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

Adding two groups double counts whoever is in both, so Total = A + B - both + neither; build the 2x2 table and make every row and column add up.

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-OVL-003 · Numeric Entry · 50s

In a group of 60 students, 35 study French and 28 study Spanish. Every student studies at least one of the two languages. How many students study both French and Spanish? Enter your answer as a number.

Numeric entry — write the number.

Q2 · STA-OVL-004 · MCQ · 40s

In a class, 18 students play chess and 14 students play checkers. Exactly 6 students play both games. How many students play chess but not checkers?

(A) 6
(B) 8
(C) 12
(D) 14
(E) 18

Q3 · STA-OVL-010 · QC · 50s

In a class of 50 students, 28 like math, 22 like science, and 10 like both subjects.

Column A: The number of students who like math but not science Column B: The number of students who like science but not math

Q4 · STA-OVL-011 · MCQ · 45s

Of 100 students surveyed, 55 have a dog, 40 have a cat, and 15 have both a dog and a cat. How many students have neither a dog nor a cat?

(A) 5
(B) 10
(C) 15
(D) 20
(E) 25

Q5 · STA-OVL-012 · Select all that apply · 60s

In a group of 40 people, 24 own a smartphone and 18 own a tablet. Which of the following could be the number of people who own both a smartphone and a tablet? Select all that apply.

(A) 0
(B) 2
(C) 10
(D) 18
(E) 20

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Level 2 · Medium — 8 questions · ~10 min

two or three steps, one planted trap each

Q6 · STA-OVL-014 · MCQ · 70s

In a survey of 150 people, 85 like action movies, 70 like comedy movies, and 30 like neither genre. How many people like both action and comedy?

(A) 5
(B) 30
(C) 35
(D) 50
(E) 120

Q7 · STA-OVL-018 · MCQ · 80s

A survey asked 200 people about two social media platforms. 130 use Facebook, 95 use Instagram, and 25 use neither platform. How many people use exactly one of the two platforms?

(A) 75
(B) 80
(C) 125
(D) 150
(E) 175

Q8 · STA-OVL-023 · MCQ · 90s

In a neighborhood of 250 households, 60 percent subscribe to a streaming service. Of the households that subscribe to a streaming service, one third also subscribe to a cable service. 40 households subscribe to neither service. How many households subscribe to a cable service?

(A) 50
(B) 60
(C) 100
(D) 110
(E) 150

Q9 · STA-OVL-024 · QC · 65s

In a study, 70 percent of participants exercise regularly, 60 percent maintain a healthy diet, and 10 percent do neither.

Column A: The percent of participants who both exercise regularly and maintain a healthy diet Column B: 40%

Q10 · STA-OVL-025 · MCQ · 90s

A bookstore surveyed 180 customers about two categories of books. 110 customers bought fiction, and 45 of those 110 also bought non-fiction. Of the customers who did not buy fiction, 40 percent bought non-fiction. How many of the 180 customers bought neither category?

(A) 25
(B) 28
(C) 42
(D) 45
(E) 72

Q11 · STA-OVL-026 · Select all that apply · 85s

In a class of 50 students, 30 study French and 25 study German. Every student studies at least one of the two languages. Which of the following must be true? Select all that apply.

(A) Exactly 5 students study both languages
(B) At least 5 students study both languages
(C) More students study only French than study only German
(D) Exactly 20 students study only French
(E) Exactly 45 students study only French

Q12 · STA-OVL-027 · Numeric Entry · 70s

A hotel surveyed its guests: 40 percent ordered room service, 35 percent used the spa, and 25 percent used neither service. What percent of guests used both room service and the spa? Enter your answer as a number.

Numeric entry — write the number.

Q13 · STA-OVL-029 · MCQ · 75s

In a survey of 500 people, 55 percent watch TV daily and 40 percent use social media daily. If 20 percent do neither, what percent watch TV daily but do NOT use social media daily?

(A) 15%
(B) 25%
(C) 35%
(D) 40%
(E) 55%

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Level 3 · Hard — 12 questions · ~20 min

where 162+ is won or lost

Q14 · STA-OVL-034 · MCQ · 105s

In a school of 300 students, every student studies at least one of three subjects: math, science, or history. 160 study math, 140 study science, and 130 study history. 60 study both math and science, 50 study both math and history, and 40 study both science and history; each of these three pairwise counts includes the 20 students who study all three subjects. How many students study exactly one subject?

(A) 130
(B) 150
(C) 170
(D) 190
(E) 210

Q15 · STA-OVL-035 · Numeric Entry · 95s

In a survey of 200 people about three streaming services X, Y, and Z, 110 use X, 95 use Y, and 80 use Z. 45 use both X and Y, 35 use both X and Z, and 30 use both Y and Z; each of these pairwise counts includes everyone who uses all three services. Every person surveyed uses at least one of the three services. How many people use all three services? Enter your answer as a number.

Numeric entry — write the number.

Q16 · STA-OVL-036 · MCQ · 95s

Of 500 adults surveyed, 60 percent drink coffee, 45 percent drink tea, and 25 percent drink both. One adult is chosen at random from among those who drink at least one of the two beverages. What is the probability that the chosen adult drinks tea?

(A) 1/4
(B) 5/16
(C) 9/20
(D) 9/16
(E) 3/4

Q17 · STA-OVL-037 · QC · 100s

In a class, 70 percent of the students passed exam A and 80 percent passed exam B. Nothing else is known about how the two groups overlap.

Column A: The smallest possible percent of the class that passed both exams Column B: The largest possible percent of the class that passed neither exam

Q18 · STA-OVL-038 · Numeric Entry · 100s

In a group of 120 people, 75 have taken a cooking class, 60 have taken a pottery class, and 45 have taken a painting class. 30 have taken both cooking and pottery, 25 have taken both cooking and painting, and 20 have taken both pottery and painting; each of these three pairwise counts includes the 10 people who have taken all three classes. Some people have taken none of the three. How many people have taken exactly two of the three classes? Enter your answer as a number.

Numeric entry — write the number.

Q19 · STA-OVL-039 · MCQ · 100s

A company has 400 employees, each of whom works at exactly one of three locations: the city office, remotely, or the satellite office. 50 percent work at the city office and 35 percent work remotely. Of the city office workers, 30 percent lead a team; of the remote workers, 20 percent lead a team; of the satellite office workers, 20 percent lead a team. What percent of the company's team leaders work at the city office?

(A) 20%
(B) 25%
(C) 30%
(D) 50%
(E) 60%

Q20 · STA-OVL-040 · QC · 95s

In a large group of people, 65 percent like product A. Of the people who like product A, 40 percent also like product B. 10 percent of the group like neither product.

Column A: The percent of the group who like product B but not product A Column B: 20%

Q21 · STA-OVL-041 · Select all that apply · 100s

In a group of 100 people, 70 speak language A and 60 speak language B. No other information is given. Which of the following must be true? Select all that apply.

(A) At least 30 people speak both languages
(B) At most 60 people speak both languages
(C) At least 10 people speak neither language
(D) At most 30 people speak neither language
(E) If no one in the group speaks neither language, then exactly 30 people speak both

Q22 · STA-OVL-042 · Numeric Entry · 110s

In a school of 80 students, every student belongs to at least one of three clubs: A, B, or C. Club A has 50 members, club B has 45 members, and club C has 38 members. Exactly 15 students belong to A and B but not C, exactly 12 belong to A and C but not B, and exactly 10 belong to B and C but not A. How many students belong to all three clubs? Enter your answer as a number.

Numeric entry — write the number.

Q23 · STA-OVL-043 · MCQ · 95s

In a survey of 500 people, 55 percent like red, 45 percent like blue, and 30 percent like green. 20 percent like both red and blue, 15 percent like both red and green, and 12 percent like both blue and green; each of these pairwise percents includes the 8 percent who like all three colors. What percent of the people surveyed like none of the three colors?

(A) 1%
(B) 8%
(C) 9%
(D) 17%
(E) 25%

Q24 · STA-OVL-044 · QC · 100s

In a class of 60 students, 35 study art and 28 study music. No information is given about how many study both.

Column A: The number of students who study both art and music Column B: The number of students who study neither art nor music

Q25 · STA-OVL-045 · Select all that apply · 110s

In a group of 100 people, 80 like product A, 70 like product B, and 60 like product C. Which of the following could be the number of people who like all three products? Select all that apply.

(A) 5
(B) 10
(C) 30
(D) 60
(E) 70

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Level 4 · Extreme — 5 questions · ~10 min

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

Q26 · STA-OVL-046 · MCQ · 125s

At a conference with 200 attendees, every person speaks at least one of three languages: English, French, or Mandarin. 140 speak English, 120 speak French, and 90 speak Mandarin. What is the greatest possible number of attendees who speak all three languages?

(A) 50
(B) 60
(C) 75
(D) 90
(E) 150

Q27 · STA-OVL-047 · Numeric Entry · 125s

In a survey of 400 people, 60 percent like product A, 50 percent like product B, and 35 percent like product C. Every person likes at least one of the three products, and the number of people who like exactly two of the products is three times the number who like all three. How many people like exactly one product? Enter your answer as a number.

Numeric entry — write the number.

Q28 · STA-OVL-048 · QC · 125s

In a group of 100 students, 50 belong to club X, 40 belong to club Y, and 30 belong to club Z. Every student belongs to at least one of the three clubs. Nothing is given about the pairwise overlaps.

Column A: The number of students who belong to all three clubs Column B: 5

Q29 · STA-OVL-049 · Select all that apply · 125s

In a class of 100 students, 55 passed math, 50 passed English, and 45 passed science. 25 passed both math and English, 20 passed both math and science, and 18 passed both English and science; each of these three pairwise counts includes the x students who passed all three subjects. Some students may have passed none of the three. Which of the following could be the value of x? Select all that apply.

(A) 8
(B) 13
(C) 18
(D) 20
(E) 25

Q30 · STA-OVL-050 · Numeric Entry · 130s

A company has 300 employees, each of whom speaks at least one of three languages: English, Spanish, and French. The number who speak English only is twice the number who speak Spanish only, and the number who speak Spanish only is twice the number who speak French only. Exactly 30 speak English and Spanish but not French, exactly 10 speak English and French but not Spanish, exactly 5 speak Spanish and French but not English, and exactly 10 speak all three languages. How many employees speak English? Enter your answer as a number.

Numeric entry — write the number.

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