Question 1

Given the following survey results about Ben Franklin's inventions: 56 people had a Franklin Stove, 70 had a lightning rod, 30 had a lightning rod and carriage odometer, 25 had a lightning rod and a Franklin Stove, 15 had a carriage odometer and a Franklin Stove, 4 had all three inventions, and 70 people did not own a carriage odometer. How many people owned a carriage odometer?

Accepted Answer

55

Question 2

Using the same survey data, how many people owned none of Ben Franklin's inventions?

Accepted Answer

9

Question 3

How many people owned exactly two of Ben Franklin's inventions (lightning rod, Franklin Stove, carriage odometer)?

Accepted Answer

42

Question 4

Which formula correctly represents the number of elements in the union of three sets $$A$$, $$B$$, and $$C$$?

Accepted Answer

$$n(A \cup B \cup C) = n(A) + n(B) + n(C) - n(A \cap B) - n(A \cap C) - n(B \cap C) + n(A \cap B \cap C)$$

Question 5

If $$A$$ and $$B$$ are sets, which of the following statements is true about their intersection?

Accepted Answer

$$A \cap B$$ contains only elements that are in both $$A$$ and $$B$$

Question 6

Which of the following numbers is NOT a real number?

Accepted Answer

$$\sqrt{-9}$$

Question 7

Which of the following numbers is a rational number?

Accepted Answer

$$\frac{3}{4}$$

Question 8

Which of the following numbers is an irrational number?

Accepted Answer

$$\pi$$

Question 9

If $$A$$ and $$B$$ are disjoint sets, what is $$A \cap B$$?

Accepted Answer

$$\emptyset$$

Question 10

Which of the following numbers is a repeating decimal?

Accepted Answer

$$0.333333333$$

Question 11

Which of the following numbers is a terminating decimal?

Accepted Answer

$$0.78$$

Question 12

If $$A = \{1, 2, 3\}$$ and $$B = \{3, 4, 5\}$$, what is $$A \cup B$$?

Accepted Answer

$$\{1, 2, 3, 4, 5\}$$

Question 13

If $$A = \{0, 1, 2\}$$ and $$B = \{2, 3, 4\}$$, what is $$A \cap B$$?

Accepted Answer

$$\{2\}$$

Question 14

Which of the following numbers is a percentage?

Accepted Answer

$$38\%$$

Question 15

Which of the following numbers is a scientific notation?

Accepted Answer

$$3 	imes 10$$^{-2}$$

Question 16

If $$A = \{1, 2, 3\}$$ and $$B = \{4, 5, 6\}$$, what is $$A \cap B$$?

Accepted Answer

$$\emptyset$$

Question 17

Which of the following numbers is a whole number?

Accepted Answer

$$97$$

Question 18

Which of the following numbers is a negative decimal?

Accepted Answer

$$-0.33$$

Question 19

Which of the following numbers is a perfect square?

Accepted Answer

$$\sqrt{16}$$

Question 20

Which of the following numbers is a fraction?

Accepted Answer

$$\frac{22}{7}$$

Quantitative Reasoning Study Guide: Sets, Venn Diagrams, and Real Numbers

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