Number Concepts and Operations - SSAT Upper Level Quantitative

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Question

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

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Answer

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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Question

What is the ratio of 3 gallons to 5 quarts?

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Answer

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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Question

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?

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Answer

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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Question

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?

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Answer

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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Question

1 mile = 5280 feet

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

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Answer

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

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Question

Joe drove an average of 45 miles per hour along a 60-mile stretch of highway, then an average of 60 miles per hour along a 30-mile stretch of highway. What was his average speed, to the nearest mile per hour?

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Answer

At 45 mph, Joe drove 60 miles in $60 \div 45 = \frac{60}{45}= \frac{4}{3}$ hours.

At 60 mph, he drove 30 miles in $30 \div 60 = \frac{1}{2}$ hours.

He made the 90-mile trip in $\frac{4}{3} + \frac{1}{2} = \frac{8}{6} + \frac{3}{6} = \frac{11}{6}$ hours, so divide 90 by $\frac{11}{6}$ to get the average speed in mph:

$90 \div \frac{11}{6} = \frac{90}{1} \div \frac{11}{6} = \frac{90}{1} \cdot \frac{6}{11} = \frac{540} {11} \approx49$

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Question

Convert 15.68 to a percent.

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Answer

To convert a number to a percent, you just multiply it by . So %.

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Question

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

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Answer

$1536\div4 = 384$

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Question

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?

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Answer

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.

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

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Question

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?

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Answer

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 , which equals 180,000.

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Question

$\frac{4}{9}$ 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?

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Answer

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 girls and boys.

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

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Question

Bill decides to donate 15% of his $4000 and Ted decides to donate 25% of his $8000. What percentage of their combined fortunes do Bill and Ted donate?

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Answer

This is a simple problem, so long as you don't forget that Bill and Ted have different amounts of money, so you can't simply average 15% and 25% to get 20%.

Calculate how much each donates:

4000(.15)= 600

8000(.25)= 2000

Now divide the total donation by their total wealth:

$\frac{2600}{12000}=0.21\frac{2}{3}$

Now multiply this answer by 100, and then round to the nearest tenth to get 21.7%.

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Question

$\dpi{100} .24+2.5+\frac{1}{4}=$

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Answer

First, convert $\dpi{100} \frac{1}{4}$ into a decimal. We are left with

$\dpi{100} .24+2.5+.25$

Now add the three numbers, being careful to line the decimal points up exactly. From right to left we will add:

4 and 5 = 9

5, 2, and 2 = 9

2 is alone = 2

This leaves us with 2.99 for the final answer.

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Question

$Solve: 7+(3-9)^{2}+36\div 4$

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Answer

Use order of operations, so you would first complete the operation in the parentheses, which would give you .

Then you do exponenets, so $\left ( -6\right)^{2} = 36$ .

Then you do division which is $36\div4 = 9$ .

Then you do addition from left to right, so .

Last, you add to , which is .

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Question

What is the sum of the two percentages in decimal form?

7 percent and 135 percent

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Answer

You add the percentages and you get 142 percent. To convert a percent to a decimal, you divide by 100, so the answer is 1.42.

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Question

Which of the following angles is supplementary to an angle that is 45 degrees?

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Answer

Supplementary angles add up to 180 degrees. Given that , the correct answer is 135.

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Question

$3+8\div4-(2\times 5)^{^{2}}$

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Answer

Do the expression in the parantheses and you get . Then you do $10^{2}$ and you get . Then you do $8\div4$ and you get . Then you add .

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Question

If Susie bought a pair of shoes for $\$ 75.98$ , a shirt for $\$23.48$ , and a pair of pants for $\$ 48.34$ . How much did she spend in total?

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Answer

You add all three values and you get $\$147.80$ .

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Question

and are prime integers. and . What is the greatest possible value of ?

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Answer

To find the greatest possible value of , add the greatest possible value of to the greatest possible value of . This happens when is equal to the greatest prime between 35 and 45, which is 43, and when is equal to the greatest prime between 85 and 95, which is 89. Add the two numbers:

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Question

and are prime integers: and . How many possible values of are there?

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Answer

can be equal to any of the prime numbers between 45 and 55, of which there are two - 47 or 53.

can be equal to any of the prime numbers between 15 and 25, of which there are three - 17, 19, and 23.

Their sum can be any of the following:

This makes five possible sums.

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