Venn Diagrams

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SSAT Middle Level Quantitative › Venn Diagrams

Questions 1 - 10

Vt_custome_venn_diagram_series_

What fraction of the above Venn diagram represents the number of students that took both math and social studies during summer school?

$\frac{1}{11}$

$\frac{1}{4}$

$\frac{4}{10}$

$\frac{4}{5}$

Explanation

The common portion of this Venn diagram is equal to , which depicts the number of students that took both math and social studies during summer school.

The denominator of the fraction is equal to the total number of students: \

Thus,

$\frac{4}{44}=\frac{1}{11}$

Vt_custome_venn_diagram_series_

What fraction of the above Venn diagram represents the number of students that took both math and social studies during summer school?

$\frac{1}{11}$

$\frac{1}{4}$

$\frac{4}{10}$

$\frac{4}{5}$

Explanation

The common portion of this Venn diagram is equal to , which depicts the number of students that took both math and social studies during summer school.

The denominator of the fraction is equal to the total number of students: \

Thus,

$\frac{4}{44}=\frac{1}{11}$

Venn_4

Let set $U = \mathbb{N}$ , the set of all natural numbers.

= { | is a multiple of 6 }

= { | is a multiple of 9 }

Which of the following numbers would appear in the gray region of the Venn diagram?

Explanation

The gray area represents the portion of that is not in - in other words, all multiples of 9 that are not also multiples of 6.

$4,572 \div 6 = 762$

$3,438 \div 6 = 573$

$8,544 \div 6 =1,424$

Therefore, 4,572, 3,438, and 8,544 can be eliminated.

$9,349 \div 9 = 1,038 ;R; 7$ , so 9,349 can be eliminated because it isn't a multiple of 9.

$4,077 \div 6 = 679 ; R ; 3$ and $4,077 \div 9 = 453$ , so, as both a nonmultiple of 6 and a multiple of 9, 4.077 is the correct choice.

Venn_4

Let set $U = \mathbb{N}$ , the set of all natural numbers.

= { | is a multiple of 6 }

= { | is a multiple of 9 }

Which of the following numbers would appear in the gray region of the Venn diagram?

Explanation

The gray area represents the portion of that is not in - in other words, all multiples of 9 that are not also multiples of 6.

$4,572 \div 6 = 762$

$3,438 \div 6 = 573$

$8,544 \div 6 =1,424$

Therefore, 4,572, 3,438, and 8,544 can be eliminated.

$9,349 \div 9 = 1,038 ;R; 7$ , so 9,349 can be eliminated because it isn't a multiple of 9.

$4,077 \div 6 = 679 ; R ; 3$ and $4,077 \div 9 = 453$ , so, as both a nonmultiple of 6 and a multiple of 9, 4.077 is the correct choice.

Venn_diagram

See the above Venn diagram. Which of the following sets is represented by the gray region?

$\overline{A} \cap B$

$A \cap \overline{B}$

$A \cup \overline{B}$

$\overline{A} \cup B$

$\overline{A} \cup \overline{B}$

Explanation

The shaded area represents the set of all elements that are both in and not in . This the intersection of and the complement of , or $\overline{A} \cap B$ .

Venn_diagram

See the above Venn diagram. Which of the following sets is represented by the gray region?

$\overline{A} \cap B$

$A \cap \overline{B}$

$A \cup \overline{B}$

$\overline{A} \cup B$

$\overline{A} \cup \overline{B}$

Explanation

The shaded area represents the set of all elements that are both in and not in . This the intersection of and the complement of , or $\overline{A} \cap B$ .

Vt custom venn series ssat middle

Kayla used a popular social media website to survey her friends' hobbies. All of her friends either play sports or enjoy playing video games, and some of her friends do both.

What fraction of her friends only play sports?

$\frac{1}{2}$

$\frac{3}{5}$

$\frac{3}{10}$

$\frac{1}{5}$

$\frac{2}{10}$

Explanation

In order to calculate the fraction of Kayla's friends who only play sport, first find the sum of the common portion and video game portion of the Venn diagram. Then subtract that sum from whole.

The solution is:

$\frac{3}{10}+\frac{2}{10}=\frac{5}{10}$

Note: $\frac{10}{10}=1$

Thus, $\frac{10}{10}-\frac{5}{10}=\frac{5}{10}=\frac{5\div 5}{10\div 5}=\frac{1}{2}$

This means that half of Kayla's friends only play sports.

Vt custom venn series ssat middle

Kayla used a popular social media website to survey her friends' hobbies. All of her friends either play sports or enjoy playing video games, and some of her friends do both.

What fraction of her friends only play sports?

$\frac{1}{2}$

$\frac{3}{5}$

$\frac{3}{10}$

$\frac{1}{5}$

$\frac{2}{10}$

Explanation

In order to calculate the fraction of Kayla's friends who only play sport, first find the sum of the common portion and video game portion of the Venn diagram. Then subtract that sum from whole.

The solution is:

$\frac{3}{10}+\frac{2}{10}=\frac{5}{10}$

Note: $\frac{10}{10}=1$

Thus, $\frac{10}{10}-\frac{5}{10}=\frac{5}{10}=\frac{5\div 5}{10\div 5}=\frac{1}{2}$

This means that half of Kayla's friends only play sports.

Vt custom venn series ssat middle

Kayla used a popular social media website to survey her friends' hobbies. All of her friends either play sports or enjoy playing video games, and some of her friends do both.

What percentage of Kayla's friends play sports and video games?

Explanation

In order to solve this problem, identify that the common portion of this Venn diagram represents Kayla's friends who play sports and video games. Since $\frac{3}{10}$ of her friends play sports and video games, convert this fraction to a percent.

The solution is:

$\frac{3}{10}=\frac{3\times 10}{10\times 10}=\frac{30}{100}=30%$

Note: the most efficient way to convert this fraction to a percent is to find an equivalent fraction to $\frac{3}{10}$ with a denominator of .

Vt custom venn series ssat middle

Kayla used a popular social media website to survey her friends' hobbies. All of her friends either play sports or enjoy playing video games, and some of her friends do both.

What percentage of Kayla's friends play sports and video games?

Explanation

The solution is:

$\frac{3}{10}=\frac{3\times 10}{10\times 10}=\frac{30}{100}=30%$

Note: the most efficient way to convert this fraction to a percent is to find an equivalent fraction to $\frac{3}{10}$ with a denominator of .

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