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SSAT Elementary Level Math : SSAT Elementary Level Quantitative (Math)

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Example Questions

Example Question #1 : How To Find A Proportion

Sofia goes to the movies with $\$24$ $\displaystyle \$24$ . She spends $\$12$ $\displaystyle \$12$ on her ticket and $\$4$ $\displaystyle \$4$ on food and drink.

What fraction of Sofia's original $\$24$ $\displaystyle \$24$ was not spent?

Possible Answers:

$\frac{1}{6}$ $\displaystyle \frac{1}{6}$

$\frac{1}{4}$ $\displaystyle \frac{1}{4}$

$\frac{2}{5}$ $\displaystyle \frac{2}{5}$

$\frac{1}{8}$ $\displaystyle \frac{1}{8}$

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

Correct answer:

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

Explanation:

Adding Sofia's expenses shows that she spent a total of $\displaystyle 12 + 4 = 16$ dollars. Subtracting this from the original amount of money she had gives the unspent portion: $\$24 - \$16 = \$8$ $\displaystyle \$24 - \$16 = \$8$ .

The ratio of the unspent portion to the original amount gives the fraction of the money that was not spent: $\frac{8}{24} = \frac{1}{3}$ $\displaystyle \frac{8}{24} = \frac{1}{3}$ .

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Example Question #21 : Numbers And Operations

A $\$75$ $\displaystyle \$75$ sweater is on sale for $\$45$ $\displaystyle \$45$ . What percentage of the original price has been discounted for the sale?

Possible Answers:

$30\%$ $\displaystyle 30\%$

$35\%$ $\displaystyle 35\%$

$15\%$ $\displaystyle 15\%$

$45\%$ $\displaystyle 45\%$

$40\%$ $\displaystyle 40\%$

Correct answer:

$40\%$ $\displaystyle 40\%$

Explanation:

Set up a proportion of the new price to the old price to see how they relate.

$\frac{\$45}{\$75} = \frac{3}{5}$ $\displaystyle \frac{\$45}{\$75} = \frac{3}{5}$ of the original price

Subtract $\frac{3}{5}$ $\displaystyle \frac{3}{5}$ from $\displaystyle 1$ to find the amount that was discounted.

$1 - \frac{3}{5} = \frac{2}{5}$ $\displaystyle 1 - \frac{3}{5} = \frac{2}{5}$

Convert $\frac{2}{5}$ $\displaystyle \frac{2}{5}$ to a decimal by multiplying both the top and bottom of the fraction by $\displaystyle 2$ , then convert to a percentage.

$\frac{2}{5} \times\frac{2}{2}=\frac{4}{10}$ $\displaystyle \frac{2}{5} \times\frac{2}{2}=\frac{4}{10}$ , which is equivalent to 0.4 $\displaystyle 0.4$ or $40\%$ $\displaystyle 40\%$

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Example Question #23 : Ratio And Proportion

Mary wants to enlarge a picture that she has in her office. The original picture is $\displaystyle 5$ cm (width) by $\displaystyle 8$ cm (length). What would be the length of the enlarged picture if the width is $\displaystyle 10$ cm?

Possible Answers:

$21\ cm$ $\displaystyle 21\ cm$

$15\ cm$ $\displaystyle 15\ cm$

$12\ cm$ $\displaystyle 12\ cm$

$16\ cm$ $\displaystyle 16\ cm$

Correct answer:

$16\ cm$ $\displaystyle 16\ cm$

Explanation:

To find the length of the enlarged picture, we must set up a proportion:

$\frac{5}{10}=\frac{8}{x}$ $\displaystyle \frac{5}{10}=\frac{8}{x}$

cross multiply:

5x=80 $\displaystyle 5x=80$

Divide both sides by 5:

$\displaystyle x=16$

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Example Question #1 : How To Find A Proportion

Solve for y:

$\frac{y}{8} = \frac{5}{4}$ $\displaystyle \frac{y}{8} = \frac{5}{4}$

Possible Answers:

$\displaystyle 8$

$\displaystyle 9$

$\displaystyle 10$

$\displaystyle 12$

$\displaystyle 11$

Correct answer:

$\displaystyle 10$

Explanation:

Multiply both sides by 8 to yield:

$8\times\frac{y}{8} = 8\times\frac{5}{4}$ $\displaystyle 8\times\frac{y}{8} = 8\times\frac{5}{4}$

Therefore:

$y = \frac{40}{4}$ $\displaystyle y = \frac{40}{4}$

Therefore:

y = 10 $\displaystyle y = 10$

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Example Question #21 : Ratio And Proportion

Solve for the variable:

$\frac{x}{6}=\frac{10}{12}$ $\displaystyle \frac{x}{6}=\frac{10}{12}$

Possible Answers:

Correct answer:

Explanation:

Cross multiply:

$(x) \times 12=6\times10$ $\displaystyle (x) \times 12=6\times10$

12x=60 $\displaystyle 12x=60$

Solve for x by dividing 60 by 12:

x=5 $\displaystyle x=5$

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Example Question #21 : Ssat Elementary Level Quantitative (Math)

Solve for the variable:

$\frac{5}{9}=\frac{x}{27}$ $\displaystyle \frac{5}{9}=\frac{x}{27}$

Possible Answers:

$\displaystyle 9$

$\displaystyle 5$

135 $\displaystyle 135$

$\displaystyle 45$

$\displaystyle 15$

Correct answer:

$\displaystyle 15$

Explanation:

Cross multiply:

$\displaystyle 5\times27=9\times x$

$\displaystyle 135=9x$

Solve for $\displaystyle x$ by dividing 135 by 9:

x=15 $\displaystyle x=15$

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Example Question #22 : Ssat Elementary Level Quantitative (Math)

Solve for the variable:

$\frac{3}{4}=\frac{6}{x}$ $\displaystyle \frac{3}{4}=\frac{6}{x}$

Possible Answers:

$\displaystyle 12$

$\displaystyle 10$

$\displaystyle 9$

$\displaystyle 8$

$\displaystyle 14$

Correct answer:

$\displaystyle 8$

Explanation:

There are two ways to solve. First, you may see that the top numbers are related by multiplying by 2.

3*2=6 $\displaystyle 3*2=6$

This means that the bottom numbers must also be related by multiplying by 2.

4*2=x $\displaystyle 4*2=x$

8=x $\displaystyle 8=x$

The missing number is therefore 8.

The other way to solve is to cross multiply:

$\frac{3}{4}=\frac{6}{x}$ $\displaystyle \frac{3}{4}=\frac{6}{x}$

$3\times (x) = 4\times6$ $\displaystyle 3\times (x) = 4\times6$

3x = 24 $\displaystyle 3x = 24$

Solve for $\displaystyle x$ by dividing 24 by 3:

$x = \frac{24}{3}=8$ $\displaystyle x = \frac{24}{3}=8$

$\frac{3}{4}=\frac{6}{8}$ $\displaystyle \frac{3}{4}=\frac{6}{8}$

The answer is again 8.

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Example Question #13 : How To Find A Proportion

Find the unknown value: $\frac{2}{3}= \frac{8}{x}$ $\displaystyle \frac{2}{3}= \frac{8}{x}$

Possible Answers:

$\frac{3}{16}$ $\displaystyle \frac{3}{16}$

$\frac{16}{3}$ $\displaystyle \frac{16}{3}$

$\frac{2}{3}$ $\displaystyle \frac{2}{3}$

$\displaystyle 12$

$\frac{1}{12}$ $\displaystyle \frac{1}{12}$

Correct answer:

$\displaystyle 12$

Explanation:

To solve the proportion, cross multiply and find the value of the missing variable.

$2x=8\times3$ $\displaystyle 2x=8\times3$

2x=24 $\displaystyle 2x=24$

Divide by $\displaystyle 2$ on both sides.

x=12 $\displaystyle x=12$

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Example Question #14 : How To Find A Proportion

Solve: $\frac{3}{7}= \frac{10}{x}$ $\displaystyle \frac{3}{7}= \frac{10}{x}$

Possible Answers:

$\frac{30}{7}$ $\displaystyle \frac{30}{7}$

$\frac{7}{30}$ $\displaystyle \frac{7}{30}$

$\frac{21}{10}$ $\displaystyle \frac{21}{10}$

$\frac{3}{70}$ $\displaystyle \frac{3}{70}$

$\frac{70}{3}$ $\displaystyle \frac{70}{3}$

Correct answer:

$\frac{70}{3}$ $\displaystyle \frac{70}{3}$

Explanation:

Solve by cross multipling the two fractions.

$3x=10\times7$ $\displaystyle 3x=10\times7$

3x=70 $\displaystyle 3x=70$

Divide by $\displaystyle 3$ on both sides.

$x=\frac{70}{3}$ $\displaystyle x=\frac{70}{3}$

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Example Question #21 : Ssat Elementary Level Quantitative (Math)

What is $10\%$ $\displaystyle 10\%$ of 200 $\displaystyle 200$ ?

Possible Answers:

$\displaystyle 10$

$\displaystyle 5$

$\displaystyle 40$

$\displaystyle 2$

$\displaystyle 20$

Correct answer:

$\displaystyle 20$

Explanation:

$10\%$ $\displaystyle 10\%$ of 200 $\displaystyle 200$ is calculated by multiplying . $\displaystyle 10$ by 200 $\displaystyle 200$ .

$.10\times 200=20$ $\displaystyle .10\times 200=20$

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All SSAT Elementary Level Math Resources

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SSAT Elementary Level Math : SSAT Elementary Level Quantitative (Math)

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

All SSAT Elementary Level Math Resources

Example Questions

Example Question #1 : How To Find A Proportion

Example Question #21 : Numbers And Operations

Example Question #23 : Ratio And Proportion

Example Question #1 : How To Find A Proportion

Example Question #21 : Ratio And Proportion

Example Question #21 : Ssat Elementary Level Quantitative (Math)

Example Question #22 : Ssat Elementary Level Quantitative (Math)

Example Question #13 : How To Find A Proportion

Example Question #14 : How To Find A Proportion

Example Question #21 : Ssat Elementary Level Quantitative (Math)

All SSAT Elementary Level Math Resources

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