SSAT Upper Level Math : Number Concepts and Operations

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

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Example Questions

Example Question #1 : Number Concepts And Operations

What is the ratio of \dpi{100} 6\ inches\(\displaystyle \dpi{100} 6\ inches\) to \dpi{100} 12\ feet\(\displaystyle \dpi{100} 12\ feet\)

Possible Answers:

\dpi{100} 1:2\(\displaystyle \dpi{100} 1:2\)

\dpi{100} 1:6\(\displaystyle \dpi{100} 1:6\)

\dpi{100} 1:12\(\displaystyle \dpi{100} 1:12\)

\dpi{100} 1:24\(\displaystyle \dpi{100} 1:24\)

Correct answer:

\dpi{100} 1:24\(\displaystyle \dpi{100} 1:24\)

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}\(\displaystyle \dpi{100} \frac{6\ inches}{12\ inches}=\frac{1}{2}\).

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

\dpi{100} 12\div \frac{1}{2}=12\times \frac{2}{1}=12\times 2=24\(\displaystyle \dpi{100} 12\div \frac{1}{2}=12\times \frac{2}{1}=12\times 2=24\).

So the ratio is 1:24.

Example Question #1 : Number Concepts And Operations

What is the ratio of 3 gallons to 5 quarts?

Possible Answers:

\dpi{100} 5:3\(\displaystyle \dpi{100} 5:3\)

\dpi{100} 3:5\(\displaystyle \dpi{100} 3:5\)

\dpi{100} 12:5\(\displaystyle \dpi{100} 12:5\)

\dpi{100} 3:1\(\displaystyle \dpi{100} 3:1\)

Correct answer:

\dpi{100} 12:5\(\displaystyle \dpi{100} 12:5\)

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\(\displaystyle \dpi{100} 4\times 3=12\) quarts.

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

Example Question #2 : Number Concepts And Operations

Bob gets paid \(\displaystyle \$5.25\) an hour for the regular hours he works and \(\displaystyle \$6\) 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:

\(\displaystyle \$285\)

\(\displaystyle \$495\)

\(\displaystyle \$231\)

\(\displaystyle \$264\)

\(\displaystyle \$234\)

Correct answer:

\(\displaystyle \$234\)

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, \(\displaystyle 40\times5.25 = \$210\). For overtime, it is \(\displaystyle 4\times6 = 24\). Add the amount made in overtime and the normal hours and you get \(\displaystyle \$234\).

Example Question #2 : 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:

\(\displaystyle 325\ students\)

\(\displaystyle 85\ students\)

\(\displaystyle 75\ students\)

\(\displaystyle 450\ students\)

\(\displaystyle 425\ students\)

Correct answer:

\(\displaystyle 425\ students\)

Explanation:

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

Example Question #3 : Number Concepts And Operations

1 mile = 5280 feet

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

Possible Answers:

\(\displaystyle 27,566\ feet\)

\(\displaystyle 25,324\ feet\)

\(\displaystyle 26,000\ feet\)

\(\displaystyle 27,984\ feet\)

\(\displaystyle 26,400\ feet\)

Correct answer:

\(\displaystyle 27,984\ feet\)

Explanation:

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

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 \(\displaystyle 100\). So \(\displaystyle 15.68 = 1568\)%.

Example Question #4 : Number Concepts And Operations

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

Possible Answers:

\(\displaystyle 5\)

\(\displaystyle 4\)

\(\displaystyle 9\)

\(\displaystyle 13\)

\(\displaystyle 7\)

Correct answer:

\(\displaystyle 4\)

Explanation:

\(\displaystyle 1536\div4 = 384\)

Example Question #4 : Number Concepts And Operations

Candidate A gets \(\displaystyle \frac{2}{7}\) 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:

\(\displaystyle 120,000\)

\(\displaystyle 225,000\)

\(\displaystyle 360,000\)

\(\displaystyle 180,000\)

\(\displaystyle 150,000\)

Correct answer:

\(\displaystyle 180,000\)

Explanation:

First we need to get \(\displaystyle \frac{2}{7}\) 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.

\(\displaystyle \frac{7}{20}-\frac{2}{7}=\frac{49}{140}-\frac{40}{140}=\frac{9}{140}\).

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

Example Question #5 : Number Concepts And Operations

\(\displaystyle \frac{4}{9}\) 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:

60%

55%

70%

65%

75%

Correct answer:

60%

Explanation:

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

\(\displaystyle \frac{4}{9}\cdot 36=16\)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 \(\displaystyle 20-2=18\) girls and \(\displaystyle 16-4=12\) boys.

\(\displaystyle \frac{18}{30}=60\%\)

Example Question #6 : Number Concepts And Operations

The menu of a local coffeehouse reads as follows:

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

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.

\(\displaystyle \$ 2.97\)

\(\displaystyle \$4.85\)

\(\displaystyle \$3.78\)

\(\displaystyle \$4.59\)

Correct answer:

\(\displaystyle \$ 2.97\)

Explanation:

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

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

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

The espresso costs \(\displaystyle \$1.79\).

Add these amounts to get the cost before tax:

\(\displaystyle \$ 6.87 + 3.18 + 4.38 + 1.79 = \$ 16.22\)

The tax is five percent of \(\displaystyle \$16.22\) or:

\(\displaystyle \$16.22 \times 0.05 \approx \$ 0.81\)

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

\(\displaystyle \$16.22 + 0.81 = \$ 17.03\)

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

\(\displaystyle \$20.00- 17.03= \$ 2.97\)

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