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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

6 Diagnostic Tests 311 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : How To Solve Arithmetic Word Problems

What is the ratio of $\dpi{100} 6\ inches$ to $\dpi{100} 12\ feet$

Possible Answers:

$\dpi{100} 1:2$

$\dpi{100} 1:6$

$\dpi{100} 1:12$

$\dpi{100} 1:24$

Correct answer:

$\dpi{100} 1:24$

Explanation:

First, we need to convert 6 inches into feet.

There are 12 inches in a foot. $\dpi{100} \frac{6\ inches}{12\ inches}=\frac{1}{2}$ .

So 6 inches is equal to $\dpi{100} \frac{1}{2}$ feet. Now our ratio is $\dpi{100} \frac{1}{2}$ to $\dpi{100} 12$ . To find this ratio we divide 12 by $\dpi{100} \frac{1}{2}$ .

$\dpi{100} 12\div \frac{1}{2}=12\times \frac{2}{1}=12\times 2=24$ .

So the ratio is 1:24.

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Example Question #1 : How To Solve Arithmetic Word Problems

What is the ratio of 3 gallons to 5 quarts?

Possible Answers:

$\dpi{100} 3:5$

$\dpi{100} 12:5$

$\dpi{100} 5:3$

$\dpi{100} 3:1$

Correct answer:

$\dpi{100} 12:5$

Explanation:

First convert gallons to quarts. There are 4 quarts in a gallon. So 3 gallons is equivalent to $\dpi{100} 4\times 3=12$ quarts.

Now we have 12 quarts to 5 quarts. This ratio cannot reduce, so our answer is 12:5.

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Example Question #1 : How To Solve Arithmetic Word Problems

Bob gets paid $\$5.25$ an hour for the regular hours he works and $\$6$ an hour for any overtime hours he works. All hours over 40 in a week are considered overtime. If Bob works 44 hours this week, how much did he make?

Possible Answers:

$\$264$

$\$234$

$\$231$

$\$285$

$\$495$

Correct answer:

$\$234$

Explanation:

You first calculate how much he makes for normal hours, which is the number of hours works multiplied by the wage. So for normal hours, $40\times5.25 = \$210$ . For overtime, it is $4\times6 = 24$ . Add the amount made in overtime and the normal hours and you get $\$234$ .

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Example Question #3 : How To Solve Arithmetic Word Problems

There are 500 students at the high school. There are only two menu options: chicken or fish. If 15% of students ordered fish, how many students ordered chicken?

Possible Answers:

$425\ students$

$450\ students$

$75\ students$

$85\ students$

$325\ students$

Correct answer:

$425\ students$

Explanation:

If 15% of students ordered fish, then 85% of the students must have ordered chicken. Then multiply 85% or $.85\times 500 = 425$ .

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Example Question #2 : How To Solve Arithmetic Word Problems

1 mile = 5280 feet

If Greg's house is 5.3 miles away, how far is it in feet?

Possible Answers:

$26,400\ feet$

$27,984\ feet$

$25,324\ feet$

$26,000\ feet$

$27,566\ feet$

Correct answer:

$27,984\ feet$

Explanation:

Using the conversion formula, you would multiply 5.3 miles by 5280 feet and you will get 27,984 feet.

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Example Question #1 : How To Solve Arithmetic Word Problems

Convert 15.68 to a percent.

Possible Answers:

1.568%

1568%

15680%

15.68%

156.8%

Correct answer:

1568%

Explanation:

To convert a number to a percent, you just multiply it by 100 . So 15.68 = 1568 %.

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Example Question #1 : Arithmetic Word Problems

What number can 1536 be divided by that would give no remainder?

Possible Answers:

Correct answer:

Explanation:

$1536\div4 = 384$

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Example Question #2 : How To Solve Arithmetic Word Problems

Candidate A gets $\frac{2}{7}$ of the votes in an election.

Candidate B gets 35% of the votes.

If 2.8 million people votes, how many more votes than Candidate A did Candidate B receive?

Possible Answers:

180,000

225,000

120,000

150,000

360,000

Correct answer:

180,000

Explanation:

First we need to get $\frac{2}{7}$ and 35% in the same terms so that we can subtract one from the other. Since 7ths are repeating decimals, it will be easiest to use fractions.

$\frac{7}{20}-\frac{2}{7}=\frac{49}{140}-\frac{40}{140}=\frac{9}{140}$ .

Now we multiply this fraction by 2.8 million, which reduces nicely to 9(20,000) , which equals 180,000.

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Example Question #5 : How To Solve Arithmetic Word Problems

$\frac{4}{9}$ of a class of 36 students are boys. If 2 girls and 4 boys were to drop the class, what percentage of the class would be girls?

Possible Answers:

70%

65%

75%

60%

55%

Correct answer:

60%

Explanation:

First determine how many boys and girls are currently in the class.

$\frac{4}{9}\cdot 36=16$ boys in the class, which means that there are 20 girls.

When the 6 students drop the new class size will be 30, which will be made up of 20-2=18 girls and 16-4=12 boys.

$\frac{18}{30}=60\%$

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Example Question #3 : How To Solve Arithmetic Word Problems

The menu of a local coffeehouse reads as follows:

$\begin{matrix} \textrm{Espresso}\; \; \; & \$1.79 \\ \textrm{Cafe Latte} & \$2.19 \\ \textrm{Cappucino} & \$2.29 \\ \textrm{Americano} & \$2.39 \\ \textrm{Turkish\; \; } & \$2.09 \\ \textrm{Iced Tea}\; \; \; & \$1.59 \end{matrix}$

Sandy orders some drinks for herself and some friends. She orders three cappuccinos, two iced teas, two cafe lattes, and an espresso. The sales tax is five percent. How much change does she receive back for a twenty-dollar bill?

Possible Answers:

A twenty-dollar bill isn't enough to buy the drinks.

$\$ 2.97$

$\$3.78$

$\$4.59$

$\$4.85$

Correct answer:

$\$ 2.97$

Explanation:

The three cappuccinos cost: $\$2.29 \times 3 = \$6.87$

The two iced teas cost $\$1.59 \times 2 = \$3.18$

The two cafe lattes cost $\$2.19 \times 2 = \$4.38$

The espresso costs $\$1.79$ .

Add these amounts to get the cost before tax:

$\$ 6.87 + 3.18 + 4.38 + 1.79 = \$ 16.22$

The tax is five percent of $\$16.22$ or:

$\$16.22 \times 0.05 \approx \$ 0.81$

Add both values in order to obtain the total cost after tax.

$\$16.22 + 0.81 = \$ 17.03$

As a result, the change from a twenty-dollar bill is as follows:

$\$20.00- 17.03= \$ 2.97$

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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 #1 : How To Solve Arithmetic Word Problems

Example Question #1 : How To Solve Arithmetic Word Problems

Example Question #1 : How To Solve Arithmetic Word Problems

Example Question #3 : How To Solve Arithmetic Word Problems

Example Question #2 : How To Solve Arithmetic Word Problems

Example Question #1 : How To Solve Arithmetic Word Problems

Example Question #1 : Arithmetic Word Problems

Example Question #2 : How To Solve Arithmetic Word Problems

Example Question #5 : How To Solve Arithmetic Word Problems

Example Question #3 : How To Solve Arithmetic Word Problems

All SSAT Upper Level Math Resources

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