Question 1

A summer camp hosts 130 kids. Of the 24 kids reporting allergies, 15 bring lunch from home. There are 63 kids bringing lunch from home in total. How many kids do NOT have allergies and bring lunch from home?

Accepted Answer

$$48$$

Question 2

Given the following: 47 properties are at risk for wildfires, 32 for tornadoes, 8 for earthquakes and tornadoes, 5 for all three disasters, 10 for only tornadoes and wildfires, and 7 not at risk for any. How many properties are at risk for tornadoes only?

Accepted Answer

$$14$$

Question 3

In a survey of 700 houses, 80 are not within a mile of any amenities, 220 are within a mile of all three (schools, parks, commercial areas), 45 are near schools only, 135 are near schools and commercial areas but not parks, and 75 are near parks and commercial areas but not schools. How many houses are near commercial areas only?

Accepted Answer

$$60$$

Question 4

A Venn Diagram is used to represent students at the University of Utah. Region D represents students who are:

Accepted Answer

Sophomores taking a math class and living in the dorms

Question 5

If 130 kids attend a camp and 24 have allergies, how many do NOT have allergies?

Accepted Answer

$$106$$

Question 6

In a city of 700 houses, 45 are near schools only, 135 are near schools and commercial areas but not parks, and 220 are near all three amenities. How many houses are near exactly two amenities?

Accepted Answer

$$235$$

Question 7

An insurance company insures 95 properties. 47 are at risk for wildfires, 32 for tornadoes, 8 for earthquakes and tornadoes, 5 for all three disasters, 10 for only tornadoes and wildfires, 7 not at risk for any, and 30 only for wildfires. How many properties are at risk for earthquakes only?

Accepted Answer

$$24$$

Question 8

Which of the following best describes the relationship between lizards, reptiles, mammals, birds, and apes in a Venn Diagram?

Accepted Answer

Lizards are a subset of reptiles; mammals, birds, and apes are separate groups.

Question 9

A camp has 130 kids. 24 have allergies, 15 of whom bring lunch from home. If 63 kids bring lunch from home, how many kids without allergies bring lunch from home?

Accepted Answer

$$48$$

Question 10

In a survey, 430 houses are near schools, 490 near commercial areas, and 220 near all three amenities. If 45 are near schools only and 135 are near schools and commercial areas but not parks, how many houses are near schools and parks but not commercial areas?

Accepted Answer

$$30$$

Question 11

Given 95 properties, 47 at risk for wildfires, 32 for tornadoes, 8 for earthquakes and tornadoes, 5 for all three disasters, 10 for only tornadoes and wildfires, and 7 not at risk for any, how many properties are NOT at risk for earthquakes?

Accepted Answer

$$61$$

Question 12

If a food is vegan, what can you conclude about its relationship to vegetarian and gluten-free foods in a Venn Diagram?

Accepted Answer

All vegan foods are vegetarian, but not all are gluten-free.

Question 13

A city planner wants all houses within 1 mile of schools, parks, and commercial areas. If 80 houses are not near any of these, how many are near at least one amenity?

Accepted Answer

$$620$$

Question 14

In a Venn Diagram of students at the University of Utah, which region represents students who are not taking a math class, do not live in the dorms, and are not sophomores?

Accepted Answer

Region B

Question 15

If 700 houses are surveyed and 55 are near parks only, what does this mean in the context of a Venn Diagram?

Accepted Answer

55 houses are only near parks and not near schools or commercial areas.

Question 16

If 7 properties are not at risk for wildfires, tornadoes, or earthquakes, what does this represent in a Venn Diagram?

Accepted Answer

The region outside all three circles.

Question 17

A student is a sophomore, not living in the dorms, and not taking a math class. In the Venn Diagram of students at the University of Utah, which region would this student be in?

Accepted Answer

Outside all three circles, but within the universal set.

Question 18

If 220 houses are near all three amenities, and 135 are near schools and commercial areas but not parks, how many houses are near schools and commercial areas (including those near all three)?

Accepted Answer

$$355$$

Question 19

If 30 houses are near schools and parks but not commercial areas, and 75 are near parks and commercial areas but not schools, how many houses are near exactly two amenities?

Accepted Answer

$$235$$

Question 20

If 95 properties are insured and 7 are not at risk for wildfires, tornadoes, or earthquakes, what percentage of properties are at risk for at least one disaster? (Round to the nearest whole percent.)

Accepted Answer

$$93\%$$

Quantitative Reasoning Practice: Sets, Venn Diagrams, and Logical Reasoning

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