ParaPro Math Practice Test

The correct answer is (D). This question is really asking for the perimeter of the field. Add up all of the sides to find the perimeter:

$(125 \cdot 2) + (200 \cdot 2) = 650$

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.

The correct answer is (B).

$\require{cancel} 270 \cancel{\text{minutes}} \cdot \dfrac{1 \text{ hour}}{60 \cancel{\text{minutes}}}$ $= \dfrac{270}{60} \text{hours}$ $= \dfrac{27}{6} \text{hours}$

$\dfrac{27}{6} = \dfrac{9}{2} = 4 \dfrac{1}{2}$

The correct answer is (B). Calculate the number of defective balls in each container and then add these two amounts:

$40\% \text{ of } 80 $ $= 0.40 \cdot 80 = 32$

$20\% \text{ of } 90$ $ = 0.20 \cdot 90 = 18$

$32 + 18 = 50$

The correct answer is (A). From Ayana's initial amount of \$305, a flat \$21.00 delivery charge is deducted:

$\$305 − \$21.00 = \$284.00$

We can then divide this amount by the cost per bag to find the total number of bags that Ayana can buy:

$\$284.00 ÷ \$8.00 $ $= 35.5 \text{ bags}$

However, the question states that the mulch can only be sold in full bags, so we must round our answer down to ensure that Ayana doesn't exceed her budget.

The correct answer is (C). When dealing with addition and subtraction involving fractions we must remember to always convert everything to a common denominator. If the family consumed $\frac{7}{8}$ of one and $\frac{1}{4}$ or $\frac{2}{8}$ of the other pizza, they consumed a total of $\frac{9}{8} = \frac{11}{8}$. We can now subtract the $\frac{1}{8}$ from the last remaining pizza to find $\frac{7}{8}$.

the correct answer is (D). To determine the total amount owed, we need to determine the sales tax:

$6\%$ of $\$50 = .06 \cdot 50 = \$3$

(Or, you might recognize that 6% of \$100 = \$6, so 6% of \$50 must be half of \$6, or \$3.)

Total amount owed $= \$50 + \$3 = \$53$

Three $\$20$ bills $= 3 \cdot \$20 = \$60$

$\$60 − \$53 = \$7$ change.

The correct answer is (A). Given $x + 17 = 11$, to solve we want to isolate the variable, $x$. To do this most efficiently, we subtract $17$ from both sides:

$\require{cancel} x + \cancel{17} = 11$
$~~~\require{cancel} − \cancel{17} −17$

$x = −6$

The correct answer is (C). The average of a set of data points is the sum of the data points divided by the total number of data points. In this case, we are given 5 out of 6 data points, the number of data points, and the desired average. Substitute the given values into the formula for the average, using a variable to represent the unknown test score, and then solve for the variable:

Average $=$ sum of data points $÷$ number of data points

$75 = (50 + 52 + 77 + 88 + 91 + x) ÷ 6$

Now solve for $x$. Start with the addition:

$75 = (358 + x) ÷ 6$

Next, eliminate the denominator by multiplying both sides by $6$:

$450 = 358 + x$

The last step is to subtract $358$ from both sides:

$x = 92$

The correct answer is (B). When subtracting a larger number from a smaller number you will end up with a negative number. To solve this type of problem, switch the order of the two numbers and do the subtraction as you normally would, but add a negative sign in front of the result:

$8.77 − 10.16$ $= -(10.16 − 8.77)$

$\begin{align} 10.16& \\ \underline{-\quad 8.77}& \\ 1.39& \end{align}$

So the answer is $-1.39$.

The correct answer is (A). The cost of the 9 pens can be found by multiplying \$1.10 by 9. This can be written as:

$(9)(\$1.10)$

Since Jodi paid with a \$20 bill, her change will be the difference between \$20 and the cost of the 9 pens. Thus, her change is:

$\$20 − (9)(\$1.10)$

The correct answer is (C).

5 packs of hotdogs × 8 hotdogs per pack = 40 hotdogs

Buns are sold in packs of 6.

7 packs of buns × 6 buns per pack = 42 buns

The correct answer is (B). Begin by writing out the formula for the area of a circle. Next, substitute the given value for the area, and then solve for the radius. Recall that the square root of both sides must be evaluated in order to isolate $r$. Multiplying the value of $r$ by $2$ gives the diameter:

$A = πr^2$
$100π = πr^2$
$100 = r^2$
$10 = r$
$D = 20$

The correct answer is (B). The factors of a number are values that divide evenly into that number. For example, the factors of 4 are 1, 2, and 4 because 4 can be divided by each without producing a remainder. To determine the greatest common factor of 33 and 44, begin by listing the factors of each number:

Factors of 33 are: $1, 3, 11, 33$
Factors of $44$ are: $1, 2, 4, 11, 22, 44$

The greatest common factor is the largest number that is in both lists of factors: $11$.

The correct answer is (C). There are two useful methods for directly comparing the values of fractions: converting each fraction to a decimal and rewriting each fraction with a common denominator. In this case, the least common denominator would be $60$ $(5 × 4 × 3)$, and as a result, the optimal approach entails converting each fraction to a decimal, instead:

$\dfrac{7}{5} = 1.4$, $\dfrac{15}{4} = 3.75$, $\dfrac{3}{2} = 1.5$, $\dfrac{11}{4} = 2.75$, $\dfrac{13}{3} = 4.33$

Now, order the decimals from least to greatest, and match the resulting list with its corresponding list of fractions: $1.4, 1.5, 2.75, 3.75$, and $4.33$ which corresponds to:

$\dfrac{7}{5}, \dfrac{3}{2}, \dfrac{11}{4}, \dfrac{15}{4}, \dfrac{13}{3}$

The correct answer is (B). The price quote, $P$, will be equal to the total amount of charges. It’s given that there is a $\$25$ base charge, so we can begin by writing the price quote as $P = \$25$. To this base charge of $\$25$, $\$8$ per each bathroom, represented by the variable $B$, is added; our price quote is now $P = \$25 + \$8B$. Lastly, $\$4$ per each other room, $R$, is added, and the actual price quote is $P = \$25 + \$8B + \$4R$, or $P = 25 + 8B + 4R$.

The correct answer is (A).

Area of a circle $= πr^2$
$400π$ square inches $= πr^2$
$400 = r^2$

We may need to "guess and check" to determine that $r = 20$ works, since $20^2 = 20 \cdot 20 = 400$.

We are asked to find the diameter, which is twice the radius:

$D = 2r$
$D = 2(20)$
$D = 40 \text{ inches}$

The correct answer is (A). To determine which value is the greatest, convert the fractions to decimals and compare each value. The fraction $\frac{2}{3}$ is equivalent to $2 ÷ 3$ or $0.66$; the fraction $\frac{13}{22}$ evaluates to $0.59$.

The correct answer is (D). Remember that 0.5 is equivalent to $\frac{1}{2}$. Our fraction needs to be less than $\frac{1}{2}$.

Since 5.5 is half of 11, $\frac{6}{11}$ is greater than $\frac{1}{2}$. No good.

Since $11.5$ is half of $23$, $\frac{12}{23}$ is greater than $\frac{1}{2}$. No good.

This means our answer is either $\frac{3}{10}$ or $\frac{9}{20}$.

$\frac{3}{10}$ is equivalent to $0.3$, which is less than $0.4$. No good.

$\frac{9}{20}$ must be correct. You could also solve by recognizing that $0.4 = \frac{4}{10} = \frac{8}{20}$ and $0.5 = \frac{5}{10} = \frac{10}{20}$, so $\frac{9}{20}$ works.

The correct answer is (C). Calculate the amount he spent on each item and then add these totals together:

$\require{cancel} 20 \cancel{\text{cones}} \cdot \dfrac{\$1.25}{\cancel{\text{cone}}} = \$25.00$

$\require{cancel} 3 \cancel{\text{balls}} \cdot \dfrac{\$25}{\cancel{\text{ball}}} = \$75.00$

$\require{cancel} 12 \cancel{\text{vests}} \cdot \dfrac{\$3.50}{\cancel{\text{vest}}} = \$42.00$

$\$25.00 + \$75.00 + \$42.00$ $= \$142.00$

The correct answer is (A). We can use PEMDAS to evaluate the expression. (PEMDAS is a technique for remembering the order of operations. It stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction) According to the rules, we must evaluate the expression in the parentheses first:

$26 − 7(3 + 5) ÷ 4 + 2$
$= 26 − 7(8) ÷ 4 + 2$

Then we perform multiplication and division in order from left to right as follows:

$26 − 7(8) ÷ 4 + 2$
$= 26 − 56 ÷ 4 + 2$
$= 26 − 14 + 2$

Finally, we perform addition and subtraction in order from left to right as follows:

$26 − 14 + 2$
$= 12 + 2$
$= 14$

The correct answer is (D). Order of Operations ("PEMDAS") says exponents must be dealt with first in this problem.

$5^3 = 5 × 5 × 5 = 25 × 5 = 125$

$8^2 = 8 × 8 = 64$

$5^3 × 8^2$ becomes $125 × 64$ (answer D)

Note: Adding or multiplying exponents only applies when the base is the same:

$5^3 × 5^2 = 5^{3 + 2} = 5^5$
$(5^3)^2 = 5^{3 × 2} = 5^6$

In these two examples, the base is $5$.

The correct answer is (B). The number 3995 is close to 4000, and the number 102 is close to 100. The estimated product can then be written as:

$4000 × 100 = 400{,}000$

The correct answer is (B). First calculate the area of the wall:

$\text{Area} = \text{Length} × \text{Height}$

$= 66 \text{ ft} × 18 \text{ ft}$
$= 1{,}188 \text{ square feet}$

To determine the number of cans:

$\require{cancel} 1,188 \cancel{\text{sq ft}} \cdot \dfrac{1 \text{can}}{200 \cancel{\text{sq ft}}} = 5.94 ≈ 6 \text{ cans}$

You could also realize that:

$5 \text{ cans} = 5 × 200 = 1000 \text{ sq ft}$ (not enough)
$6 \text{ cans} = 6 × 200 = 1200 \text{ sq ft}$ (just enough)

The correct answer is (B). Let $x$ equal the sum of the seven numbers. The student should have divided $x$ by 7 to get the average, giving the correct result of $\frac{x}{7}$. Since the student accidentally multiplied by 7, the calculator shows 7$x$.

To get the correct answer, the student needs to divide by 7 twice, which is the same as dividing by 49:

$\dfrac{7x}{49} = \dfrac{x}{7}$

The correct answer is (A). Three books at \$2.65 would equal a total of \$7.95. The change would equal:

$\$20 − \$7.95 = \$12.05$

The correct answer is (A). If we remove both pairs of parentheses we have:

$6 × 15 − 8 − 3 − 10$

Order of operations ("PEMDAS") says the multiplication must be performed first.

$6 × 15 − 8 − 3 − 10$
$90 − 8 − 3 − 10$

Now we simply proceed from left to right.

$90 − 8 − 3 − 10$
$82 − 3 − 10$
$79 − 10$
$69$

The correct answer is (A). We can add up the fractions received by Emma, Olivia, and Ava as follows:

$\dfrac{1}{8} + \dfrac{1}{4} + \dfrac{3}{8}$

$= \dfrac{1}{8} + \dfrac{2}{8} + \dfrac{3}{8}$

$= \dfrac{6}{8} = \dfrac{3}{4}$

We can find the fraction Amelia receives by subtracting the sum of the other three fractions from one, since all the fractions must add up to one. Amelia will receive:

$1 − \dfrac{3}{4} = \dfrac{1}{4}$

The correct answer is (D). There were 5 accidents in 2015, 4 in 2016, 9 in 2017, and 10 in 2018:

$\text{Average} = \dfrac{5 + 4 + 9 + 10}{4}$ $= \dfrac{28}{4} = 7$