ACCUPLACER Arithmetic Practice Test

Here is the first of our Next-Generation Accuplacer math practice tests. Our Arithmetic practice questions have been fully updated for the Next-Generation Accuplacer which was released at the beginning of 2019. This test includes 20 Arithmetic questions covering number operations, fractions, decimals, percents, and number comparisons. You may not use a calculator.

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Question 1

A travel soccer team has 39 players. Each charter van fits 4 players. How many vans does the team need to fit all of their players?

A
$9$
B
$10$
C
$11$
D
$12$
Question 1 Explanation: 
The correct answer is (B). To find the total number of vans, we divide 39 by 4, which gives us a quotient of 9, with a remainder of 3. Since we cannot leave anyone on the team behind, we must have another van for the remaining 3 people. This gives us 9 + 1 = 10 total vans.
Question 2

What is 3.1415 + 6.25 rounded to the nearest thousandths place?

A
$9.391$
B
$9.39$
C
$9.392$
D
$6.287$
Question 2 Explanation: 
The correct answer is (C). To add decimals, vertically align the numbers so that the decimals are lined up. You can pad the shorter decimals by adding zeros to the end, and then add up the numbers:

$\begin{align} 3.1415& \\ \underline{+\quad 6.2500}& \\ 9.3915& \end{align}$

Since the question asks to round the sum to the nearest thousandth, we must look at the third digit after the decimal point which contains the digit 1. Since the number to the right of the digit 1 is 5, we must round the thousandths digit 1 up to 2. Thus, the correct answer is: $9.392$
Question 3

Jason invests $325 in a bank account. The bank has an annual interest rate of 24%. How much interest did his investment earn after one year?

A
$\$403.00$
B
$\$80.00$
C
$\$78.00$
D
$\$13.54$
Question 3 Explanation: 
The correct anser is (C). To solve this problem we can multiply $325$ by $0.24$ or by $\frac{24}{100}$:

$325 × \dfrac{24}{100} = \dfrac{7800}{100}$

$\require{enclose} \dfrac{78\enclose{horizontalstrike}{00}}{1 \enclose{horizontalstrike}{00}} = \dfrac{78}{1} = 78$
Question 4

Katy has 1$\frac{3}{8}$ cups of flour. Her cookie recipe calls for 2 cups of flour. How many more cups of flour does she need for the recipe?

A
$1\dfrac{5}{8}$
B
$\dfrac{5}{8}$
C
$\dfrac{1}{3}$
D
$\dfrac{1}{2}$
Question 4 Explanation: 
The correct answer is (B). In order to find out how many more cups Katy needs for her recipe, we must subtract 1$\frac{3}{8}$ from 2.

When subtracting fractions we need a common denominator. The number 2 can be written as $\frac{16}{8}$ and the number 1$\frac{3}{8}$ can be written as $\frac{11}{8}$:

$\dfrac{16}{8} - \dfrac{11}{8} = \dfrac{16 - 11}{8} = \dfrac{5}{8}$
Question 5

Estimate the value of 1573 + 1211 − 697.

A
$2000$
B
$2073$
C
$2077$
D
$2100$
Question 5 Explanation: 
The correct answer is (D). This question tests the student’s ability to estimate in order to arrive at the best possible answer. Round each number to the nearest hundred:

$1573 ≈ 1600$
$1211 ≈ 1200$
$697 ≈ 700$

The revised equation is:

$1600 + 1200 − 700 = 2100$
Question 6

Students are watching a series of instructional videos that are each 8.7 minutes long. How many minutes will they spend watching all 6 of the videos?

A
$52.2$
B
$48.7$
C
$51.2$
D
$512$
Question 6 Explanation: 
The correct answer is (A). Since there are 6 videos that are each 8.7 minutes long, we need to multiply 6 × 8.7 to get the total number of minutes:

$\begin{align} 8.7& \\ \underline{×\quad 6}& \\ 52.2& \end{align}$
Question 7

Sachin got 14 out of 20 questions correct on a biology exam. What is his grade written in percent form?

A
$65\%$
B
$70\%$
C
$80\%$
D
$85\%$
Question 7 Explanation: 
The correct answer is (B). Sachin’s grade can be found by calculating:

$\dfrac{\text{Total Correct}}{\text{Total Problems}} × 100$

Substituting in 14 for the total number of problems correct, and 20 for the total number of problems, we get:

$\dfrac{14}{20} × 100$
Question 8

On the number line above, where is the number $\frac{7}{3}$ located?

A
$\text{Between}$ $0$ $\text{and}$ $1$
B
$\text{Between}$ $1$ $\text{and}$ $2$
C
$\text{Between}$ $2$ $\text{and}$ $3$
D
$\text{Between}$ $3$ $\text{and}$ $4$
Question 8 Explanation: 
The correct answer is (C). We know that $\frac{7}{3}$ is equivalent to $2 \frac{1}{3}$ since:

$\require{enclose} \begin{array}{rll} 2 & \hbox{r1} \\[-3pt] 3 \enclose{longdiv}{7}\kern-.2ex \\[-3pt] \underline{-6} \\[-3pt] \,1 \end{array}$

$2 \frac{1}{3}$ falls between $2$ and $3$ on the number line.
Question 9

If $a = 1$, $b = 3$, $c = 8$, and $d = 15$, which of the following statements is true?

A
$a + c > b + d$
B
$a + b ≥ c + d$
C
$a - d < b - c$
D
$a ≥ b + c + d$
Question 9 Explanation: 
The correct answer is (C). Substituting in the given values for $a$, $b$, $c$, and $d$ in the inequality $a - d < b - c$, we get:

$1 - 15 < 3 - 8$

$-14 < -5$

This is a true statement.
Question 10

Round $\frac{625}{1000}$ to the nearest hundredths place.

A
$0.625$
B
$0.75$
C
$0.63$
D
$6.25$
Question 10 Explanation: 
The correct answer is (C). First write the fraction as a decimal:

$\frac{625}{1000} = 0.625$

The problem asks to round 0.625 to the nearest hundredths place. We must look at the hundredths digit which is 2, and the digit to the right of it, which is 5. Since the thousandths digit is equal to 5, we must increment the hundredths digit by 1. Therefore, 0.625 rounded up to the nearest hundredths place is 0.63.
Question 11

What is the remainder when 582 is divided by 3?

A
$0$
B
$1$
C
$8$
D
$9$
Question 11 Explanation: 
The correct answer is (A). Use long division to solve this problem. As seen below, 582 divided by 3 equals 194 with no remainder:

$\require{enclose} \begin{array}{rll} 194 & \\[-3pt] 3 \enclose{longdiv}{582}\kern-.2ex \\[-3pt] -\underline{3\phantom{00}} \\ 28\phantom{0} \\ -\underline{27\phantom{0}} \\ \phantom{0}12 \\ -\underline{12} \\ \phantom{0}0 \\ \end{array}$
Question 12

Evaluate: $\frac{1}{2} ÷ 36 + 16 × \frac{1}{72}$

A
$\dfrac{17}{72}$
B
$22.5$
C
$\dfrac{1}{7488}$
D
$6$
Question 12 Explanation: 
The correct answer is (A). To answer this question correctly, we must remember the order of operations (PEMDAS). We must complete multiplication and division moving from left to right. So first, we evaluate $\frac{1}{2} ÷ 36$, which is equivalent to:

$\dfrac{1}{2} × \dfrac{1}{36} = \dfrac{1}{72}$

The next step is:

$16 × \dfrac{1}{72} = \dfrac{16}{72}$

Finally, we must find the sum:

$\dfrac{1}{72} + \dfrac{16}{72} = \dfrac{17}{72}$
Question 13

What percent of 70 is equivalent to 28?

A
$21\%$
B
$40\%$
C
$56\%$
D
$60\%$
Question 13 Explanation: 
The correct answer is (B). We start by setting up our equation as:

$\dfrac{x}{100} × 70 = 28$

In order to isolate $x$, we first multiply both sides of the equation by 100, giving:

$70x = 2800$

Next, we divide both sides of the equation by 70, giving:

$x = 40$

Therefore, 40% of 70 is 28.
Question 14

Sophie went to a candy store and purchased three fudge slices for \$3.98 each. If she paid with a \$20 bill, how much change did she receive?

A
$16.02$
B
$8.06$
C
$11.94$
D
$9.06$
Question 14 Explanation: 
The correct answer is (B). First multiply 3.98 by 3 to figure out the total cost of the fudge:

$\begin{align} 3.98& \\ \underline{×\quad 3}& \\ 11.94& \end{align}$

Then subtract this amount from 20 to get the amount of change:

$\begin{align} 20.00& \\ \underline{-\quad 11.94}& \\ 8.06& \end{align}$
Question 15

Convert $\dfrac{28}{6}$ to a mixed number.

A
$1\dfrac{22}{6}$
B
$3\dfrac{5}{3}$
C
$4\dfrac{1}{2}$
D
$4\dfrac{2}{3}$
Question 15 Explanation: 
The correct answer is (D). We first start by finding how many times 6 goes into 28:

$\require{enclose} \begin{array}{rl} 4 & \text{r}4 \\[-3pt] 6 \enclose{longdiv}{28}\kern-.2ex \\[-3pt] \underline{-24} \\[-3pt] \,4 \end{array}$

So we can rewrite $\frac{28}{6}$ as $4\frac{4}{6}$, which can be simplified to $4\frac{2}{3}$.
Question 16

Subtract:

$9.078 - 1.455 = $

A
$10.533$
B
$8.423$
C
$7.623$
D
$8.623$
Question 16 Explanation: 
The correct answer is (C). Use subtraction with regrouping to solve:

$\begin{align} 9.078& \\ \underline{-\quad 1.455}& \\ 7.623& \end{align}$
Question 17

Divide $8\frac{7}{11}$ by $\frac{5}{11}$.

A
$\dfrac{475}{121}$
B
$19$
C
$3.965$
D
$\dfrac{5}{7}$
Question 17 Explanation: 
The correct answer is (B). First convert the mixed fraction to an improper fraction. $8\frac{7}{11}$ is equivalent to $\frac{95}{11}$. Now write out the division problem:

$\dfrac{95}{11} ÷ \dfrac{5}{11}$

To divide fractions turn the the division sign into a multiplication sign and flip the second fraction over (find its reciprocal):

$\dfrac{95}{11} × \dfrac{11}{5} = \dfrac{95}{5} = 19$
Question 18

Which of the following inequalities is true?

A
$0.095 > 0.1001$
B
$\dfrac{9}{18} < \dfrac{1}{2}$
C
$0.08 > \dfrac{2}{3}$
D
$\dfrac{5}{11} < \dfrac{6}{9}$
Question 18 Explanation: 
The correct answer is (D).

We know that half of 11 is 5.5, so $\frac{5}{11}$ is less than $\frac{1}{2}$.

We know that half of 9 is 4.5, so $\frac{6}{9}$ is greater than $\frac{1}{2}$.

$\dfrac{5}{11} < \dfrac{6}{9}$ is therefore true.
Question 19

Multiply:

$3.17 × 2.8$

A
$2.536$
B
$887.6$
C
$3.17$
D
$8.876$
Question 19 Explanation: 
The correct answer is (D). To multiply decimals, line up the numbers on the right (do not align the decimal points). Then starting on the right, multiply each digit of the top number by each digit of the bottom number. Then add the products:

$\begin{align} 3.17& \\ \underline{×\quad 2.8}& \\ 2536 \\ \underline{+\quad 634\phantom{0}}& \\ 8.876& \end{align}$

Once you add the products, you must place the decimal point correctly. There are two decimal places in 3.17 and one decimal place in 2.8. Adding these decimal places together gives 3. Starting at the right of our answer move 3 places to the left and put the decimal point there.
Question 20

What is the value of $\dfrac{3.65 + 4.75}{0.5}$?

A
$18$
B
$16.8$
C
$16.4$
D
$14.368$
Question 20 Explanation: 
The correct answer is (B). Add the two numbers in the numerator and then divide. Dividing by half (0.5) is the same and multiplying by 2:

$\dfrac{3.65 + 4.75}{0.5} = \dfrac{8.4}{0.5} = 16.8$
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