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SSAT Upper Level Math : SSAT Upper Level Quantitative (Math)

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Example Questions

Example Question #4 : Ratios & Proportional Relationships

If a doctor charges $\$500$ per hour for her services, how much would it cost to hire this doctor for minutes?

Possible Answers:

$\$375$

$\$400$

$\$350$

$\$250$

Correct answer:

$\$375$

Explanation:

First, convert the minutes to hours.

$45\div60=0.75$

Since minutes is 0.75 hours, multiply this by the doctor's hourly rate to find how much it will cost to hire this doctor for minutes.

$500\times0.75=375$

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Example Question #5 : Ratios & Proportional Relationships

A dentist charges $\$50$ per hour for the first three hours of an appointment. Any amount of time greater than three hours is charged at $\$25$ per hour. If a patient had a hour long appointment, how much would this appointment cost?

Possible Answers:

$\$325$

$\$250$

$\$300$

$\$275$

Correct answer:

$\$275$

Explanation:

Use the dentist's rate to find how much the first three hours of the appointment will cost.

$50\times 3=150$

Next, use the dentist's second rate to find out how much the last five hours of the appointment will cost.

$25\times5=125$

Now, add these values together to get the cost of the entire appointment.

150+125=275

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Example Question #11 : Compute Unit Rates Associated With Ratios Of Fractions: Ccss.Math.Content.7.Rp.A.1

On a map, $4\textup{ centimeters}=20\textup{ miles}$ . If two cities are $10\textup{ cm}$ apart on the map, how many miles apart are they in reality?

Possible Answers:

Correct answer:

Explanation:

Set up the following proportion:

$\frac{4}{10}=\frac{20}{x}$ ,

where is the number of miles the cities are apart.

Now, solve for .

4x=200

x=50

The two cities are miles apart.

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Example Question #12 : Compute Unit Rates Associated With Ratios Of Fractions: Ccss.Math.Content.7.Rp.A.1

Chuck is building a driveway that measures feet by feet. He needs to use pounds of cement for every square foot of driveway. How many pounds of cement does he need to complete the driveway?

Possible Answers:

6000

500

400

300

Correct answer:

6000

Explanation:

First, find the area of the driveway.

$15\times20=300 ft^2$

Since it takes pounds of cement per square feet,

$300\times20=6000$ pounds will be needed to complete the driveway.

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Example Question #81 : Number Concepts And Operations

Joanna can finish math problems in minutes. How many minutes would it take her to finish math problems?

Possible Answers:

$245\textup { min}$

$300\textup { min}$

$315\textup { min}$

$270\textup { min}$

Correct answer:

$270\textup { min}$

Explanation:

First, find out how long it will take her to finish math problem.

$45\div10=4.5$

Since it takes Joanna 4.5 minutes to finish one problem, multiply this number by the amount of questions she needs to do.

$4.5\times60=270$

It will take her 270 minutes to finish questions.

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Example Question #132 : Fractions

A pie is made up of $\frac{1}{9}$ crust, $\frac{1}{3}$ apples, and $\frac{1}{4}$ sugar, and the rest is jelly. What is the ratio of crust to jelly?

Possible Answers:

3:10

11:3

4:11

11:36

1:4

Correct answer:

4:11

Explanation:

A pie is made up of $\frac{1}{9}$ crust, $\frac{1}{3}$ apples, $\frac{1}{4}$ sugar, and the rest is jelly. What is the ratio of crust to jelly?

To compute this ratio, you must first ascertain how much of the pie is jelly. This is:

$1-\frac{1}{4}-\frac{1}{3}-\frac{1}{9}$

Begin by using the common denominator :

$1-\frac{1}{4}-\frac{1}{3}-\frac{1}{9}=\frac{36}{36}-\frac{9}{36}-\frac{12}{36}-\frac{4}{36}$

$\frac{36}{36}-\frac{9}{36}-\frac{12}{36}-\frac{4}{36}=\frac{11}{36}$

So, the ratio of crust to jelly is:

$\frac{1}{9}:\frac{11}{36}$

This can be written as the fraction:

$\frac{\frac{1}{9}}{\frac{11}{36}}=\frac{1}{9}*\frac{36}{11}=\frac{4}{11}$ , or 4:11

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Example Question #2 : How To Find The Ratio Of A Fraction

In a solution, $\frac{1}{3}$ of the fluid is water, $\frac{1}{5}$ is wine, and $\frac{7}{15}$ is lemon juice. What is the ratio of lemon juice to water?

Possible Answers:

5:7

7:5

7:8

7:3

3:5

Correct answer:

7:5

Explanation:

This problem is really an easy fraction division. You should first divide the lemon juice amount by the water amount:

$\frac{lemon\:juice}{water}=\frac{\frac{7}{15}}{\frac{1}{3}}$

Remember, to divide fractions, you multiply by the reciprocal:

$\frac{\frac{7}{15}}{\frac{1}{3}} = \frac{7}{15}*3=\frac{7}{5}$

This is the same as saying:

7:5

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Example Question #2 : How To Find The Ratio Of A Fraction

If $x=\frac{11}{100}$ and $y=\frac{15}{8}$ , what is the ratio of to ?

Possible Answers:

15:200

165:800

22:375

45 : 191

121 : 800

Correct answer:

22:375

Explanation:

To find a ratio like this, you simply need to make the fraction that represents the division of the two values by each other. Therefore, we have:

$x:y=\frac{\frac{11}{100}}{\frac{15}{8}}$

Recall that division of fractions requires you to multiply by the reciprocal:

$\frac{\frac{11}{100}}{\frac{15}{8}} = \frac{11}{100}*\frac{8}{15}=\frac{11}{25}*\frac{2}{15}$ ,

which is the same as:

$\frac{22}{375}$

This is the same as the ratio:

22:375

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Example Question #31 : Fractions

A smoothie is made up of $\frac{1}{5}$ pineapple juice and $\frac{1}{4}$ mango juice; the rest is orange juice. What is the ratio of orange juice to pineapple juice?

Possible Answers:

4:11

11:4

11:3

1:5

Correct answer:

11:4

Explanation:

First, find out how much of the smoothie is orange juice.

$1-\frac{1}{5}-\frac{1}{4}=\frac{11}{20}$

Since we want the ratio of orange juice to pineapple juice, we want to set up the fractions like this:

$\frac{orange\: juice}{pineapple \:juice}=\frac{\frac{11}{20}}{\frac{1}{5}}$

Now, divide these fractions.

$\frac{\frac{11}{20}}{\frac{1}{5}}=\frac{11}{20}\div\frac{1}{5}=\frac{11}{20}\times\frac{5}{1}=\frac{55}{20}=\frac{11}{4}= 11:4$

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Example Question #32 : Proportion / Ratio / Rate

A bakery sells three different types of cookies. $\frac{2}{5}$ of the cookies sold are chocolate chip, $\frac{3}{8}$ sold are oatmeal raisin, and the rest sold are sugar cookies. What is the ratio of sugar cookies to oatmeal raisin cookies that the bakery sells?

Possible Answers:

3:5

5:3

4:5

5:4

Correct answer:

3:5

Explanation:

First, find the fraction of sugar cookies that are sold.

$1-\frac{3}{8}-\frac{2}{5}=\frac{9}{40}$

Since we want the ratio of sugar cookies to oatmeal raisin cookies:

$\frac{\text{Sugar cookies}}{\text{Oatmeal raisin}}=\frac{\frac{9}{40}}{\frac{3}{8}}$

Now, multiply and simplify the resulting fraction.

$\frac{\frac{9}{40}}{\frac{3}{8}}=\frac{9}{40}\div\frac{3}{8}=\frac{9}{40}\times\frac{8}{3}=\frac{3}{5}\times\frac{1}{1}=\frac{3}{5}=3:5$

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SSAT Upper Level Math : SSAT Upper Level Quantitative (Math)

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

All SSAT Upper Level Math Resources

Example Questions

Example Question #4 : Ratios & Proportional Relationships

Example Question #5 : Ratios & Proportional Relationships

Example Question #11 : Compute Unit Rates Associated With Ratios Of Fractions: Ccss.Math.Content.7.Rp.A.1

Example Question #12 : Compute Unit Rates Associated With Ratios Of Fractions: Ccss.Math.Content.7.Rp.A.1

Example Question #81 : Number Concepts And Operations

Example Question #132 : Fractions

Example Question #2 : How To Find The Ratio Of A Fraction

Example Question #2 : How To Find The Ratio Of A Fraction

Example Question #31 : Fractions

Example Question #32 : Proportion / Ratio / Rate

All SSAT Upper Level Math Resources

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