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# SAT Sets and Venn Diagrams


The Venn diagram above shows the distribution of students enrolled in soccer, basketball, both, and neither. If $$A = 4$$ and $$B=14,$$ what fraction of all students are enrolled in soccer?

(A) $$\ \ \frac{4}{43}$$

(B) $$\ \ \frac{14}{43}$$

(C) $$\ \ \frac{19}{43}$$

(D) $$\ \ \frac{14}{29}$$

(E) $$\ \ 14$$



The Venn diagram above shows the distribution of students enrolled in soccer, basketball, both, and neither. If $$A = 4, B=8, C=12,$$ and $$D=18,$$ how many students are enrolled in basketball but are NOT enrolled in soccer?

(A) $$\ \ 4$$
(B) $$\ \ 8$$
(C) $$\ \ 12$$
(D) $$\ \ 20$$
(E) $$\ \ 42$$

The intersection of sets $$X$$ and $$Y$$ is the set $$Z$$. Which of the following statements must be true?

$$\begin{array}{r r l} &\text{I.} & \text{If}\ 3\ \text{is in}\ X,\ \text{then}\ 3\ \text{is in}\ Y.\\ &\text{II.} & \text{If}\ 4\ \text{is in}\ Y,\ \text{then}\ 4\ \text{is in}\ Z.\\ &\text{III.} & \text{If}\ 5\ \text{is in}\ Z, \text{then}\ 5\ \text{is in}\ X.\\ \end{array}$$

(A)$$\ \$$ I only
(B)$$\ \$$ II only
(C)$$\ \$$ III only
(D)$$\ \$$ I and II only
(E)$$\ \$$ I and III only

Which of the following sets is a subset of $$S = \{1, 4, 7, 10, 17\}?$$

(A) $$\ \ A=\{1, 15\}$$
(B) $$\ \ B=\{10, 17\}$$
(C) $$\ \ C=\{7, 10, 19\}$$
(D) $$\ \ D=\{4, 7, 10, 13\}$$
(E) $$\ \ E=\{1, 4, 7, 10, 17, 20\}$$



As shown in the diagram above, sets $$A, B$$ and $$C$$ intersect each other. Set $$A$$ is the set of all odd numbers. Set $$B$$ is the set of all numbers $$3m,$$ where $$m$$ is a natural number. Set $$C$$ is the set of all numbers $$3^n,$$ where $$n$$ is a whole number. Which of the following numbers belongs to the set represented by the shaded region?

(A) $$\ \ -3$$
(B) $$\ \ 0$$
(C) $$\ \ 15$$
(D) $$\ \ 45$$
(E) $$\ \ 27$$

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