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Data Analysis, Statistics, and Probability

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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