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SSAT Middle Level Math : SSAT Middle Level Quantitative (Math)

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Example Questions

Example Question #1 : Venn Diagrams

Vt_custome_venn_diagram_series_

Using the Venn diagram above shows whether respondents only like Super Hero , only like Super Hero , or if they like both Super Heroes. What percentage of respondents like both Super Heroes?

Possible Answers:

$22\%$

$34\%$

$17\%$

$15\%$

Correct answer:

$17\%$

Explanation:

The total number of survey respondents is equal to 100 percent. Since the common part of the Venn diagram represents the respondents that like both Super Heroes.

Thus, the solution is:

100-(34+49)=

100-83=17

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Example Question #2 : Venn Diagrams

Vt_custome_venn_diagram_series_

The Venn diagram shown above displays whether respondents only use Social Media site , only use Social Media site , or use both of the Social Media sites.

What percent of respondents use both Social Media sites?

Possible Answers:

$15\%$

$6\%$

$45\%$

$13\%$

Correct answer:

$13\%$

Explanation:

The total number of survey respondents is equal to 100 percent. Since the common part of the Venn diagram represents the respondents that use both of the Social Media sites, the solution is:

100-(36+51)=

100-87=13

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Example Question #4 : Venn Diagrams

Vt_custome_venn_diagram_series_

What fraction represents the amount of respondents that use both Social Media site and Social Media site ?

Possible Answers:

$\frac{13}{10}$

$\frac{13}{100}$

$\frac{17}{100}$

$\frac{17}{50}$

Correct answer:

$\frac{13}{100}$

Explanation:

The total number of survey respondents is equal to 100 percent. Since the common part of the Venn diagram represents the respondents that use both social media sites, the solution is:

100-(36+51)=

100-87=13

$13\%=\frac{13}{100}$

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Example Question #6 : Venn Diagrams

Vt_custome_venn_diagram_series_

The above Venn diagram shows the amount of survey respondents that only like tacos, only like tamales, and those that like both tacos and tamales.

What fraction of respondents like both tacos and tamales?

Possible Answers:

$\frac{1}{10}$

$\frac{1}{5}$

$\frac{2}{5}$

$\frac{4}{10}$

Correct answer:

$\frac{1}{5}$

Explanation:

The total number of survey respondents is equal to 100 percent, which equals $\frac{5}{5}$ .

The total number of respondents that do not like both tacos and tamales: $\frac{3}{5}+\frac{1}{5}=\frac{4}{5}$ .

The remaining amount equals the respondents that like both tacos and tamales.

Thus, the solution is:

$\frac{5}{5}-\frac{4}{5}=\frac{1}{5}$

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Example Question #11 : Venn Diagrams

Vt_custome_venn_diagram_series_

The above Venn diagram shows the amount of survey respondents that only like tacos, only like tamales, and those that like both tacos and tamales.

What percent of the respondents like both tamales and tacos?

Possible Answers:

$25\%$

$20\%$

$1\%$

$5\%$

Correct answer:

$20\%$

Explanation:

The remaining amount equals the respondents that like both tacos and tamales.

Thus, the solution is:

$\frac{5}{5}-\frac{4}{5}=\frac{1}{5}$

Now we need to convert the fraction into a percent.

$\frac{1}{5}=\frac{1}{5}\times \frac{20}{20}=\frac{20}{100}=20\%$

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Example Question #12 : Venn Diagrams

Vt_custome_venn_diagram_series_

The above Venn diagram shows the results from a recent survey. Respondents had the choice of being only a fan of TEAM , only a fan of TEAM , or a fan of both of the teams. What percentage of the respondents are fans of both the teams?

Possible Answers:

$21\%$

$26\%$

$23\%$

$33\%$

Correct answer:

$23\%$

Explanation:

In order to find the value of the common area of this Venn diagram, find the sum of percent and percent.

Then find the difference from the sum to 100 percent.

The solution is:

56+21=77

100-77=23

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Example Question #1 : How To Use A Venn Diagram

Venn_diagram

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

Possible Answers:

$A \cap \overline{B}$

$A \cup \overline{B}$

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

$\overline{A} \cup B$

$\overline{A} \cap B$

Correct answer:

$\overline{A} \cap B$

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 $\overline{A} \cap B$ .

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Example Question #641 : Ssat Middle Level Quantitative (Math)

Venn_diagram_2

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

Possible Answers:

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

$\overline{A }\cup B$

$A \cup \overline{B}$

$\overline{A }\cap B$

$\overline{A }\cap \overline{B}$

Correct answer:

$A \cup \overline{B}$

Explanation:

The gray region represents all elements that either are in , are not in - that is, are in $\overline{B}$ - or both. This is the union of and $\overline{B}$ , or $A \cup \overline{B}$ .

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Example Question #1 : How To Find The Union Of A Venn Diagram

Given the Venn diagram below, which of the following does not belong to $A \cup B$ ?

Possible Answers:

Correct answer:

Explanation:

The symbol $\cup$ stands for the union between two sets. Therefore, $A\cup B$ means the set of all numbers that are in either A or B. Looking at our choices, the only number that isn't in either A, B, or both is 23.

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Example Question #642 : Ssat Middle Level Quantitative (Math)

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?

Possible Answers:

4,077

3,438

9,349

8,544

4,572

Correct answer:

4,077

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.

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All SSAT Middle Level Math Resources

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SSAT Middle Level Math : SSAT Middle Level Quantitative (Math)

Study concepts, example questions & explanations for SSAT Middle Level Math

All SSAT Middle Level Math Resources

Example Questions

Example Question #1 : Venn Diagrams

Example Question #2 : Venn Diagrams

Example Question #4 : Venn Diagrams

Example Question #6 : Venn Diagrams

Example Question #11 : Venn Diagrams

Example Question #12 : Venn Diagrams

Example Question #1 : How To Use A Venn Diagram

Example Question #641 : Ssat Middle Level Quantitative (Math)

Example Question #1 : How To Find The Union Of A Venn Diagram

Example Question #642 : Ssat Middle Level Quantitative (Math)

All SSAT Middle Level Math Resources

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