Accuplacer Quantitative Reasoning, Algebra, & Statistics Practice Test

The correct choice is (B). When terms with the same variable are in the same equation, they can be combined:

$y + 3y + 5y = −18$

$9y = −18$

$y = \dfrac{−18}{9}$

$y = −2$

The correct choice is (D). The power is distributed to each term in the parenthesis:

$(x^7 × y^3 )^5 = x^{7 × 5}y^{3 × 5} = x^{35} y^{15}$

The correct choice is (A). The ∪ symbol means union. The union of two sets includes all the values that are in either (or both) of the sets.

The ∩ symbol means intersection. The intersection of a set includes only the numbers that are in both sets. Only two numbers are present in both sets $X$ and $Y$:

$\{11, 13\}$

The correct choice is (C). Mean is just another word for average. To find the average, add up all the numbers, then divide by how many numbers there are:

$\text{Average} =$ $\frac{20 + 14 + 11 + 18 + 14 + 19 + 9}{7}$

$\text{Average} = \frac{105}{7} = 15$

The correct choice is (B). Applying the distributive property to the left side, we get:

$\frac{3}{7}x + \frac{9}{7} + 5 = 3x + 2$

Next, bring all the constants to the left side, and all the variables to the right side. Then simplify each side:

$\frac{9}{7} + 5 - 2 = 3x - \frac{3}{7} x$

$\frac{9}{7} + 3 = 3x - \frac{3}{7} x$

$\frac{9}{7} + \frac{21}{7} = \frac{21x}{7} - \frac{3x}{7}$

$\frac{30}{7} = \frac{18x}{7}$

To solve $\frac{18x}{7} = \frac{30}{7}$, we can equate the numerators since the denominators are equivalent, giving us $18x = 30$. Isolating and simplifying, we get:

$x = \frac{30}{18} = \frac{5}{3}$

The correct choice is (D). Since Pierre keeps his marble, the number of green marbles and the total number of marbles both decrease by 1. So there will be 5 green marbles and 25 total marbles:

Probability = $\dfrac{5}{25} = \dfrac{1}{5}$

The correct choice is (D). We first calculate the total number of shot made by all of the age groups. Using estimation, we can say that the total shots made equal:

$12 + 17 + 21 + 18 + 19 + 9$ $= 96$

The 21–30 age group made 21 shots. Therefore:

$\frac{21}{96} × 100 ≈ 22\%$

The correct choice is (A). Use the slope formula:

$\text{Slope} = \dfrac{\text{Change in } y}{\text{Change in } x}$ $= \dfrac{y_2 - y_1}{x_2 - x_1}$

The slope of the line that is pictured is:

$\dfrac{13-5}{8-2} = \dfrac{8}{6} = \dfrac{4}{3}$

Each of the answer choices is written in slope-intercept form, $y = mx + b$, where $m$ is the slope. Choice (A) has a slope of $\frac{4}{3}$, so (A) is correct.

The correct choice is (B). We are told that $w$ represents the total weight of the truck and its load, and $q$ represents the quantity of castings it is hauling.

If a truck is hauling no castings, $q = 0$.

When $q = 0$, $w = 500(0) + 35,000 = 35,000$.

In other words, the weight of the truck by itself (i.e. hauling no castings) is 35,000 lbs.

The correct answer is (A). We can set up a proportion to solve:

$\dfrac{9 \text{ bottles}}{12 \text{ people}} = \dfrac {x \text{ bottles}}{8 \text{ people}}$

Cross-multiply to solve a proportion:

$(9)(8) = (12)(x)$

$72 = 12x$

$6 = x$

The correct choice is (D). Begin by noticing the form in which the answer choices are written. As no answer choice contains a parenthetical expression, start by distributing the $3x$ through the parentheses. Multiply $3x$ by each of the terms inside of the parentheses and combine any like terms:

$3x(2 + 5y)$

$= 3x(2) + 3x(5y)$

$= 6x + 15xy$

The correct choice is (C). First use the slope forumula to find the slope of line $f$:

$\dfrac{5 - 7}{3 - 0} = - \dfrac{2}{3}$

A line perpendicular to another has a slope that is the negative reciprocal of the slope of the other line. The negative reciprocal of $-\dfrac{2}{3}$ is $\dfrac{3}{2}$.

The correct choice is (A). Begin by distributing the 3 and the 5 through their respective parentheses, then combine like terms on each side of the equal sign:

$3(x + 1) = 5(x − 2) + 7$
$3x + 3 = 5x − 10 + 7$
$3x + 3 = 5x − 3$

Add 3 to both sides to maintain the equality:

$3x + 6 = 5x$

Subtract 3$x$ from both sides and then divide the resulting equation by 2 to solve for $x$ as follows:

$6 = 2x$
$3 = x$

Remember that any time a variable is solved for in an equation, the calculated value can be verified by substituting it into the original equation and determining whether it yields a true statement.

The correct choice is (A). First use any two points to find the slope. We will use (0, 2) and (3, 12.5):

$\dfrac{12.5 - 2}{3 - 0} = \dfrac{10.5}{3} = 3.5$

The point (0, 2) indicates that the $y$-intercept of the line is 2. Plugging in the slope and $y$-intercept into the $y = mx + b$ form, we get $y = 3.5x + 2$.

The correct choice is (A). There are 27 club members, and each will receive a T-shirt. Each box contains 4 shirts, so:

$\dfrac{27}{4} = 6.75 → 7$

7 boxes of T-shirts will be ordered (since a whole number of boxes must be ordered). Each box costs \$23.50, so the total cost for all the shirts is:

$7 × \$23.50 = \$164.50$

The correct choice is (A). The initial charge for Timothy’s Taxi Service is \$2.50 for the first mile, with an additional charge of \$0.75 for each additional mile. We can set up an equation with $c$ being the total charge and $m$ being the total number of additional miles traveled:

$c = 2.5 + 0.75m$

Substitute $10$ in for $c$ and solve for $m$:

$10 = 2.5 + 0.75m$

$7.5 = 0.75m$

$m = \frac{7.5}{0.75} = 10$

Add 1 for the first mile traveled. Our answer is 10 + 1 = 11 miles.

The correct choice is (B). Start by substituting 12 for p in the original equation:

$\frac{6}{z + 4} = 12$

Because the unknown is in the denominator, and the equation represents a simple proportion, we can simplify the problem by cross multiplying and then dividing:

$6 = 12(z + 4)$

Divide both sides by 12:

$\frac{6}{12} = z + 4$

Simplify the fraction and then subtract 4:

$\frac{1}{2} = z + 4$

$\frac{1}{2} - 4 = z$

$-3.5 = z$

The correct choice is (C). Any number raised to the power of 1 equals itself, so 3¹ is equal to 3.

Any number, except zero, that is raised to the 0 power equals 1, so 2⁰ equals 1.

When 1 is raised to any power it always equals 1. The expression becomes:

$3 + 1 − 1 = 3$

The correct choice is (A). Solve with dimensional analysis:

$\require{cancel} 1400 \cancel{\text{ liters}} \cdot$ $\dfrac{1 \cancel{\text{ kiloliter}}}{1000 \cancel{\text{liters}}} \cdot$ $\dfrac{ 220 \text{ gallons}}{1 \cancel{\text{kiloliter}}}$

$= \dfrac{(1400)(220)}{1000} \text{ gallons}$ $= 308 \text{ gallons}$

The correct choice is (C). Recall that the median of a set of data is the value located in the middle of the data set. In the case of a data set that contains an even number of numbers, the median is the average of the two middle numbers. Combine the 2 sets provided, and organize them in ascending order:

$\{1, 2, 4, 5, 7, 9, 12, 13, 15, 18\}$

Since there are an even number of items in the resulting list, the median is the average of the two middle numbers.

$\text{Median} =$ $(7 + 9) ÷ 2 = 8$