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SSAT Upper Level Math : Number Concepts and Operations

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

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All SSAT Upper Level Math Resources

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Example Questions

Example Question #5 : Ratios & Proportional Relationships

If it takes Dennis 120 minutes to paint walls, how many minutes does it take him to paint wall?

Possible Answers:

Correct answer:

Explanation:

Divide the time it take Dennis to paint walls by the number of walls he painted to find how long it will take him to paint one wall.

$120\div8=15$

It will take Dennis minutes to paint one wall.

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Example Question #6 : Ratios & Proportional Relationships

An arcade charges players $\$1.25$ to play on the machine for minutes. How much money would it cost a player if she wanted to play for an hour?

Possible Answers:

$\$35$

$\$20$

$\$30$

$\$25$

Correct answer:

$\$25$

Explanation:

First, find out how much money it costs to play for one minute.

$1.25\div3=0.41667$

Now, multiply this amount by the number of minutes in an hour to find how much it will cost for the player to play for one hour.

$0.41667\times60=25$

It will cost her $\$25$ to play for one hour.

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Example Question #7 : 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:

$\$375$

$\$350$

$\$250$

$\$400$

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 #8 : 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:

$\$275$

$\$250$

$\$300$

$\$325$

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 #21 : Proportion / Ratio / Rate

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 : Grade 7

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:

500

300

6000

400

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 #23 : Rational Numbers

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

Possible Answers:

$245\textup { min}$

$270\textup { min}$

$315\textup { min}$

$300\textup { min}$

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 #3 : How To Find The Ratio Of A Fraction

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:

4:11

11:3

3:10

1:4

11:36

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 #1132 : Gre Quantitative Reasoning

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:

7:5

7:8

3:5

5:7

7:3

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 #1133 : Gre Quantitative Reasoning

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

Possible Answers:

165:800

15:200

121 : 800

45 : 191

22:375

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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All SSAT Upper Level Math Resources

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SSAT Upper Level Math : Number Concepts and Operations

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

All SSAT Upper Level Math Resources

Example Questions

Example Question #5 : Ratios & Proportional Relationships

Example Question #6 : Ratios & Proportional Relationships

Example Question #7 : Ratios & Proportional Relationships

Example Question #8 : Ratios & Proportional Relationships

Example Question #21 : Proportion / Ratio / Rate

Example Question #12 : Grade 7

Example Question #23 : Rational Numbers

Example Question #3 : How To Find The Ratio Of A Fraction

Example Question #1132 : Gre Quantitative Reasoning

Example Question #1133 : Gre Quantitative Reasoning

All SSAT Upper Level Math Resources

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