Question 1
Simplify the expression below. Which of the following is correct?
$5{,}344− 57$
A | $5{,}277$ |
B | $5{,}283$ |
C | $5{,}287$ |
D | $5{,}288$ |
Question 1 Explanation:
The correct answer is (C). This can be solved with a calculator or subtraction by regrouping.
Question 2
Solve the equation below. Which of the following is correct?
$3(x− 4) = 18$
A | $x = \frac{3}{2}$ |
B | $x = \frac{22}{3}$ |
C | $x = 6$ |
D | $x = 10$ |
Question 2 Explanation:
The correct answer is (D). First divide both sides by 3:
$\require{cancel} \dfrac{\cancel{3}(x − 4)}{\cancel{3}} = \dfrac{18}{3}$
$x − 4 = \dfrac{18}{3}$
$x − 4 = 6$
Then solve for $x$:
$x − 4 = 6$
$x = 6 + 4$
$x = 10$
Question 3
The above is known as what type of graph?
A | $\text{Line Graph}$ |
B | $\text{Scatterplot}$ |
C | $\text{Bar Graph}$ |
D | $\text{Histogram}$ |
Question 3 Explanation:
The correct answer is (B). The above graph is known as a scatterplot, which is a plot of points on $x$ and $y$ axes. In this case, each point would have an $x$ value equal to the temperature in degrees Celsius, and a $y$ value equal to the amount of money in dollars.
Question 4
Simplify the expression below.
$(5x− 1) (3x + 2)$
Which of the following is correct?
A | $15x^2 − 7x + 3$ |
B | $15x^2 + 7x − 2$ |
C | $15x^2 + 7x − 3$ |
D | $15x^2 − 7x − 2$ |
Question 4 Explanation:
The correct answer is (B). The “FOIL method” is the easiest way to remember how to multiply two-termed expressions. Multiply the
First two terms, then the
Outer two terms, then the
Inner two terms, and then the
Last two terms, then sum all four to arrive at the answer:
$15x^2 + 10x − 3x − 2$
$= 15x^2 + 7x − 2$
Question 5
Timmy can usually make six paper airplanes in an hour. However, if he gets interrupted by his parents, he can only make four per hour. His friend John can make seven paper airplanes per hour.
One day, Timmy and John decide to have a three-hour long contest to see who can make the most paper airplanes. During the contest, Timmy is interrupted once every hour. John also had to take a break and do chores for an hour. How many more paper airplanes does the winner make?
A | $1$ |
B | $2$ |
C | $3$ |
D | $4$ |
Question 5 Explanation:
The correct answer is (B). Because Timmy is interrupted during each hour, he can only make four paper airplanes per hour, multiplied by 3 hours, for a total of 12 airplanes. John makes seven paper airplanes during the two hours he works without chores, for a total of 14 airplanes. 14 airplanes minus 12 airplanes equals 2.
Question 6
If a car travels 360 kilometers in 5 hours, how far will it travel in 9 hours?
A | $72$ |
B | $268$ |
C | $426$ |
D | $648$ |
Question 6 Explanation:
The correct answer is (D). Given that it took 5 hours to travel 360km, we can set up a ratio equation to figure out how far the car will travel in 9 hours:
$\dfrac{360}{5} = \dfrac{x}{9}$
$72 = \dfrac{x}{9}$
$72 \ast 9 = x$
$x = 648$
Question 7
What degrees Fahrenheit is it at 30 degrees Celsius?
$\text{Note: °F} = (\text{°C} * \frac{9}{5} + 32)$
A | $86$ |
B | $89$ |
C | $92$ |
D | $95$ |
Question 7 Explanation:
The correct answer is (A). Plug in °C = 30 into the given formula and solve for °F:
$\text{°F} = (\text{°C} * \frac{9}{5} + 32)$
$\text{°F} = (30 * \frac{9}{5} + 32)$
$\text{°F} = 54 + 32$
$\text{°F} = 86$
Question 8
A toy manufacturer makes 15,000 toys a year. The company randomly selects 300 of the toys to sample for inspection. The company discovers that there are 5 faulty toys in the sample. Based on the sample, how many of the 15,000 total toys are likely to be faulty?
A | $25$ |
B | $250$ |
C | $300$ |
D | $600$ |
Question 8 Explanation:
The correct answer is (B). The sample indicates that 5 out of every 300 randomly selected toys will be faulty. Consequently, a proportion can be set up that relates the unknown number of faulty toys in the total number of toys to the ratio of faulty toys to the sample:
$\dfrac{5}{300} = \dfrac{T}{15{,}000}$
$T$ is the unknown number of faulty toys in the total. Multiply both sides by 15,000 and then divide the left side by 300 to solve for $T$:
$\dfrac{15{,}000 \ast 5}{300} = T$
$\dfrac{50 \ast 5}{1} = T = 250$
Question 9
At a comic book store, Robert purchased three comics for \$2.65 each. If he paid with a \$20 bill, how much change did he receive?
A | $\$10.95$ |
B | $\$12.05$ |
C | $\$13.15$ |
D | $\$13.85$ |
Question 9 Explanation:
The correct answer is (B). Three comics at \$2.65 would equal a total of \$7.95. The change would equal:
$\$20 − \$7.95 = \$12.05$
Question 10
Simplify the expression below.
$7\dfrac{1}{4} × \dfrac{1}{18}$
Which of the following is correct?
A | $\dfrac{14}{54}$ |
B | $\dfrac{22}{67}$ |
C | $\dfrac{29}{72}$ |
D | $\dfrac{18}{126}$ |
Question 10 Explanation:
The correct answer is (C). The first step is to convert the mixed fraction 7$\frac{1}{4}$ into an improper fraction. To do this:
- Multiply the whole number by the denominator.
- Add the answer from step 1 to the numerator.
- Write the answer from step 2 above the denomintor.
$7 \ast 4 + 1 = 29 → \dfrac{29}{4}$
To mulitply fractions simply multiply across the top and the bottom:
$\dfrac{29}{4} \ast \dfrac{1}{18} = \dfrac{29 \ast 1}{4 \ast 18}$ $=\dfrac{29}{72}$
Question 11
Express $\dfrac{5}{8}$ as its closest rounded percentage.
A | $56\%$ |
B | $60\%$ |
C | $63\%$ |
D | $66\%$ |
Question 11 Explanation:
The correct answer is (C). 5 ÷ 8 = 0.625, which equals 62.5%. Rounding up gives us 63%.
Question 12
Amanda wants to paint the walls of a room. She knows that each can of paint contains one gallon. Ahalf gallon will cover a 55 square feet of wall. Each of the four walls is 10 feet high. Two of the walls are 10 feet wide and two of the walls are 15 feet wide. How many 1-gallon buckets of paint does Amanda need to buy in order to fully paint the room?
A | $4$ |
B | $5$ |
C | $9$ |
D | $10$ |
Question 12 Explanation:
The correct answer is (B). First, we must calculate the area of the walls Amanda wants to paint. Two of the walls are 10 x 10 and two of the walls are 10 x 15:
2 (10 x 10) = 200
2 (10 x 15) = 300
So the total square footage of the walls is 500.
If a half gallon of paint will cover 55 square feet, then each gallon will cover 110 square feet. Four gallons would only cover 440 square feet. Five gallons will cover 550 square feet, which will be enough for all 500 square feet of walls.
Question 13
How many millimeters are there in 5 meters?
A | $500$ |
B | $5{,}000$ |
C | $50{,}000$ |
D | $500{,}000$ |
Question 13 Explanation:
The correct answer is (B). The prefix “milli—” means one-thousandth. A millimeter is one-thousandth of a meter, which means there are 1,000 millimeters in 1 meter. So there must be 5,000 millimeters in 5 meters.
Question 14
Kyra has a budget of \$300 for her holiday spending. Kyra decides to buy shoes for her grandchildren. If each pair of shoes costs \$40, and Kyra has $n$ grandchildren, which of the following inequalities represents Kyra’s budget constraint?
A | $40n > 300$ |
B | $40 + n > 300$ |
C | $40 + n ≤ 300$ |
D | $40n ≤ 300$ |
Question 14 Explanation:
The correct answer is (D). If Kyra buys $n$ pairs of shoes at a cost of \$40 each, she pays \$40$n$. Since she only has \$300 to spend, \$40$n$ must be less than or equal to \$300:
$40n ≤ 300$
Question 15
Simplify the expression below. Which of the following is correct?
$2− 8÷ (2^4÷2) =$
A | $−6$ |
B | $−\frac{3}{4}$ |
C | $1$ |
D | $2$ |
Question 15 Explanation:
The correct answer is (C). Remember your order of operations:
- Complete operations within parentheses first.
- Calculate exponents.
- Then multiply and divide in order from left to right.
- Then add and subtract in order from left to right.
$2 − 8 ÷ (2^4 ÷ 2) =$
$2 − 8 ÷ (16 ÷ 2) =$
$2 − 8 ÷ 8 =$
$2 − 1 =$
$1$
Question 16
Which type of graph would best indicate the percentage of a school’s annual scholarship fund spent on freshman students?
A | $\text{pie chart}$ |
B | $\text{line graph}$ |
C | $\text{scatterplot}$ |
D | $\text{histogram}$ |
Question 16 Explanation:
The correct answer is (A). A pie chart represents percentages of a total, and would thus be the best graphic representation of a budget breakdown.
Question 17
Order the list of numbers below from least to greatest.
$−\frac{1}{4},\; π,\; \frac{3}{8},\; −0.2$
Which of the following is correct?
A | $−0.2,\; −\frac{1}{4},\; \frac{3}{8},\; π$ |
B | $−\frac{1}{4},\; −0.2,\; \frac{3}{8},\; π$ |
C | $−0.2,\; −\frac{1}{4},\; π,\; \frac{3}{8}$ |
D | $−\frac{1}{4},\; −0.2,\; π,\; \frac{3}{8}$ |
Question 17 Explanation:
The correct answer is (B). The smallest number is the greatest negative value:
$−\frac{1}{4} (−0.25)$
The next smallest is:
$−0.2$
The largest value is:
$π (3.14)$
Question 18
Simplify:
$(7y^2 + 3xy− 9)− (2y^2 + 3xy− 5)$
A | $5y^2 − 4$ |
B | $9y^2 + 6xy− 14$ |
C | $5y^2 + 4$ |
D | $5y^2 + 6xy− 14$ |
Question 18 Explanation:
The correct answer is (A). When subtracting polynomials the first step is to distribute the negative sign through the parentheses. This changes the sign on each term inside the parentheses:
$7y^2 + 3xy− 9− 2y^2 − 3xy+ 5$
Arrange like terms next to each other (optional):
$7y^2 − 2y^2 + 3xy− 3xy − 9+ 5$
Combine like terms to compute the answer:
$5y^2 − 4$
Question 19
Which of the following is the solution set for the equation below?
$| 2x− 5 | = 19$
A | $\{−7, −12\}$ |
B | $\{7, 12\}$ |
C | $\{−7, 12\}$ |
D | $\{7, −12\}$ |
Question 19 Explanation:
The correct answer is (C). Absolute value equations can be rewritten in two ways to solve:
$2x − 5 = 19\;$ and $\;2x − 5 = −19$
Solve both:
$2x − 5 = 19$
$2x = 24$
$x = 12$
$2x − 5 = −19$
$2x = −14$
$x = −7$
The two solutions are: $−7$ $\text{and}$ $12$
Question 20
If Maria left a \$10.16 tip on a breakfast that cost \$86.89, approximately what percentage was the tip?
A | $12\%$ |
B | $17\%$ |
C | $25\%$ |
D | $31\%$ |
Question 20 Explanation:
The correct answer is (A). The easiest way to answer this question is to round the numbers. Let’s say the tip is \$10 and the total was \$87. \$10/$87 = approximately 11%. (A) is the closest answer to our approximation.
Question 21
A nurse working at a medical clinic earns \$17.81 per hour.The nurse works three 8-hour shifts and one 12-hour shift every week, and is paid weekly. Weekly deductions are: federal tax \$102.80, state tax \$24.58, federal insurance \$18.13, and family health insurance \$52.15. What isthe nurse'stake-home pay each week?
A | $\$158.54$ |
B | $\$443.50$ |
C | $\$514.74$ |
D | $\$641.16$ |
Question 21 Explanation:
The correct answer is (B). First you must calculate how many hours the nurse works each week. Three 8-hour shifts plus one 12-hour shift equals 36 hours per week.
Beginning Salary = 36 x \$17.81 = \$641.16
Deductions = \$102.80 + \$24.58 + \$18.13 + \$52.15 = \$197.66
Take-Home Pay = \$641.16 − \$197.66 = \$443.50
Question 22
How many imperial gallons are there in 1,400 liters?
Note: 1 kiloliter = 220 imperial gallons
A | $308$ |
B | $3{,}080$ |
C | $30{,}800$ |
D | $308{,}000$ |
Question 22 Explanation:
The correct answer is (A). There are 1,000 liters in 1 kiloliter:
1,400 liters = 1.4 kiloliters.
1.4 x 220 = 308 imperial gallons
Question 23
Derek purchased concert tickets in the month of June for \$73, \$66, \$96, \$17, and \$66 dollars. Which of the following is an accurate estimate of the total amount he spent on concert tickets in June?
A | $\$300$ |
B | $\$330$ |
C | $\$360$ |
D | $\$400$ |
Question 23 Explanation:
The correct answer is (B). The easiest way to make an estimate is to round each number so there is only one nonzero digit. Then you can easily add up the numbers:
$73 ≈ 70$
$66 ≈ 70$
$96 ≈ 100$
$17 ≈ 20$
$66 ≈ 70$
$70 + 70 + 100 + 20 + 70 = 330$
Question 24
Solve the inequality below.
$5y− 8 > 32$
Which of the following is correct?
A | $y > 8$ |
B | $y < 8$ |
C | $y > 6$ |
D | $y < 6$ |
Question 24 Explanation:
The correct answer is (A). To solve an inequality, simply treat the inequality symbol as if it’s an equals sign:
$5y − 8 > 32$
$5y > 40$
$y > 8$
Question 25
There are 48 students studying a foreign language at the community college. If the only two foreign languages offered are French and Spanish, and 28 students are studying French, which of the following represents the ratio of students studying Spanish to the total number of foreign language students?
A | $\dfrac{2}{7}$ |
B | $\dfrac{1}{2}$ |
C | $\dfrac{1}{3}$ |
D | $\dfrac{5}{12}$ |
Question 25 Explanation:
The correct answer is (D). If there are 48 total, and 28 study French, then 20 study Spanish. The ratio of 20 to 48 can be written as a fraction and then simplified:
$\dfrac{20}{48} = \dfrac{10}{24} = \dfrac{5}{12}$
Question 26
What is 181.5% of 18?
A | $3.267$ |
B | $14.67$ |
C | $32.67$ |
D | $3267$ |
Question 26 Explanation:
The correct answer is (C). First you must convert the fraction to a decimal by moving the decimal point 2 places to the left, which gives you 1.815. Then multiply this by 18:
$1.815 × 18 = 32.67$
Question 27
Which of the following is equivalent to $0.0009$?
A | $0.0009\%$ |
B | $0.009\%$ |
C | $0.09\%$ |
D | $0.9\%$ |
Question 27 Explanation:
The correct answer is (C). In order to convert a decimal to a percent you need to move the decimal point two places to the right and add the percent symbol.
Question 28
A father is planning a birthday party for his son. He is expecting a total attendance of 7 adults and 13 children. Food costs will be \$11.00 for each adult and \$5.00 for each child. He will also need to spend \$2.00 per child for party favors. Which of the following is the total cost of the birthday party?
A | $\$142.00$ |
B | $\$168.00$ |
C | $\$182.00$ |
D | $\$192.00$ |
Question 28 Explanation:
The correct answer is (B). The cost for each adult is \$11.00 and there are 7 adults:
$7 × \$11 = \$77$
The cost for each child is \$7.00 (\$5.00 for food plus \$2.00 for the party favors) and there are 14 children:
$13 × \$7 = \$91$
$\text{Total Cost} = \$77 + \$91 = \$168$
Question 29
Simplify the expression below.
$7 × 4 + (9− 6) + 13$
Which of the following is correct?
A | $34$ |
B | $37$ |
C | $41$ |
D | $44$ |
Question 29 Explanation:
The correct answer is (D). According to the order of operations, do what is inside the parenthesis first:
$7 × 4 + (3) + 13$
Next, move left to right, doing any multiplication or division:
$28 + 3 + 13$
Finally, move left to right, doing any addition or subtraction:
$31 + 13 = 44$
Question 30
Write the number 1906 in Roman numerals.
A | $\text{MCMLXVIII}$ |
B | $\text{MCMXVI}$ |
C | $\text{MCMVI}$ |
D | $\text{XIXVI}$ |
Question 30 Explanation:
The correct answer is (C). In the Roman numeral system, M = 1000, D = 500, C = 100, L = 50, X = 10, V = 5, and I = 1. The ones, tens, hundreds and thousands must be treated as separate items. If a smaller item precedes a larger item, as in CM, it is treated as the difference of the two, so CM = 1000 − 100 = 900.
1000=M
900= CM
6=VI
Question 31
Simplify the expression below.
$3\dfrac{2}{5} + 1\dfrac{4}{7}$
Which of the following is correct?
A | $\dfrac{145}{34}$ |
B | $\dfrac{174}{35}$ |
C | $\dfrac{168}{35}$ |
D | $\dfrac{159}{34}$ |
Question 31 Explanation:
The correct answer is (B). To add mixed number fractions, first convert them to improper fractions, then find a common denominator and add the numerators, placing them over the common denominator. Reduce the final fraction if necessary.
$3\dfrac{2}{5} = \dfrac{17}{5} \qquad$ $1\dfrac{4}{7} = \dfrac{11}{7}$
Now find the lowest common denominator between 5 and 7. Since they are both prime numbers, their lowest common denominator is their product, 35. We can rewrite both fractions:
$\dfrac{17}{5} = \dfrac{119}{35} \qquad$ $\dfrac{11}{7} = \dfrac{55}{35}$
Now that the denominators are the same, we can add the numerators:
$\dfrac{119 + 55}{35} = \dfrac{174}{35}$
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