ACT Math Practice Test 3

Difficulty Level – 2: Medium

Directions: Solve each problem and then click on the correct answer. You are permitted to use a calculator on this test.

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Question 1

If $x$ is an even integer and $y$ is an odd integer, which of the following must be an odd integer?

A
$2x + 2y$
B
$2x − 2y$
C
$x + y + 1$
D
$x + y + 2$
E
$x − 2y$
Question 1 Explanation: 
The correct answer is (D). To solve this problem, choose an even integer for $x$ and an odd integer for $y$ and evaluate each of the answer choices.

Set $x = 0$ and $y = 1 →$ only $x + y + 2$ will evaluate to an odd integer.
Question 2

35% of 15% of $x$ is equivalent to which of the following?

A
$0.0525x$
B
$0.125x$
C
$0.25x$
D
$0.50x$
E
$2.33x$
Question 2 Explanation: 
The correct answer is (A). 35% of 15% of a number is $0.35 \ast 0.15$ of that number:

$0.35 \ast 0.15 \ast x = 0.0525x$
Question 3

A farmer has a rectangular field that measures 125 feet by 200 feet. He wants to enclose the field with a fence. What is the total length, in feet, he will need for the job?

A
$350$
B
$450$
C
$550$
D
$650$
E
$750$
Question 3 Explanation: 
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:

$125 + 125 + 200 + 200 = 650$

or

$(125 \ast 2) + (200 \ast 2) = 650$
Question 4
$4xyz*2x^2y^2*\dfrac{1}{3}z^3*\dfrac{1}{4}y^2*z$

The equation above is equivalent to which of the following?

A
$\dfrac{1}{3} x y^3 z^3$
B
$\dfrac{2}{3} x^3 y^5 z^5$
C
$\dfrac{4}{3} x^2 y^2 z^2$
D
$\dfrac{3}{4} x^4 y^2 z^2$
E
$\dfrac{8}{3} x^4 y^2 z^3$
Question 4 Explanation: 
The correct answer is (B). Evaluate the expression to find the most simplified form. First evaluate the coefficients:

$4 * 2 * \frac{1}{3} * \frac{1}{4}= \frac{2}{3}$

$x*x^2=x^3$

$y * y^2 * y^2 = y^5$

$z * z^3 * z = z^5$

Combine each of these terms to get answer choice (B).
Question 5

For the equation below, what will be the value of $y$ when $x = 3$?

$y = \dfrac{(13x - 5x) + 12}{4}$

A
$7$
B
$9$
C
$8$
D
$5$
E
$4$
Question 5 Explanation: 
The correct answer is (B). To find $y$, substitute 3 for $x$ in the equation:

$y = \dfrac{(13 \ast 3 - 5 \ast 3) + 12}{4}$

$y = \dfrac{(39 - 15) + 12}{4}$

$y = \dfrac{24 + 12}{4}$

$y = \dfrac{36}{4}$

$y = 9$
Question 6

A and B are reciprocals (when multiplied together their product is 1). If A < −1, then B must be which of the following?

A
$B \gt 1$
B
$B \lt 0$
C
$0 \lt B \lt 1$
D
$−1\lt B \lt0$
E
$B \lt −1$
Question 6 Explanation: 
The correct answer is (D). We are told $A \lt -1$ ($A$ is less than $-1$).

Let's choose a value of $A$ that satisfies this condition:

$A = -2$

We know that $B$ is the reciprocal of $A$:

$B = \frac{1}{A} = \frac{1}{-2} = -\frac{1}{2}$

Since $B = -\frac{1}{2}$, only answer (D) is valid.
Question 7

Magazine subscriptions cost \$9.99 a month per magazine after an initial contract fee of \$24.99. Which expression represents the cost of $m$ magazines in dollars ($)?

A
$9.99 + 24.99m$
B
$9.99m + 24.99$
C
$24.99 - 9.99m$
D
$24.99 + m + 9.99$
E
$33.98m$
Question 7 Explanation: 
The correct answer is (B). Consider the given information: the initial contract fee is a one time price that will be added to the number of magazines, $m$, times the cost per magazine:

$9.99m + 24.99$
Question 8

What is $7\%$ of $7 \frac{1}{7}$ rounded to the nearest hundredth?

A
$0.50$
B
$0.67$
C
$0.42$
D
$0.77$
E
$0.63$
Question 8 Explanation: 
The correct answer is (A). To find the percentage of a number, we multiply:

$7\%$ of $7 \frac{1}{7}$

$7\% \ast 7 \frac {1}{7}$ (Some calculators will let you type this in directly and provide the answer)

$0.07 \ast 7 \frac{1}{7}$

$0.07 \ast \dfrac{50}{7}$

$0.07 \ast 7.1429$ $(50 ÷ 7 ≈ 7.1429)$

$0.50$

Alternate approach:

$7\% \ast 7 \frac{1}{7}$

$\dfrac{7}{100} \ast \dfrac{50}{7} → \dfrac{1}{2} \ast \dfrac{1}{1} $ $ = \dfrac{1}{2}$

$0.50$ is the decimal representation of $\dfrac{1}{2}$.
Question 9

The coordinates $(−3, 5)$ and $(3, 5)$ designate the diameter of a circle, what is its circumference?

A
$π$
B
$2π$
C
$4π$
D
$6π$
E
$12π$
Question 9 Explanation: 
The correct answer is (D). The circumference of a circle is the distance around defined by: $π \ast \text{diameter}$.

The diameter in this case can be found through the difference between the $x$ values:

$3 − (−3) = 6$, so $\pi \ast 6$ is the circumference.
Question 10

Richard wants to try every possible combination of meals available at his favorite restaurant. They offer 4 appetizers, 5 entrees, and 3 desserts. How many total meals will Richard have tried by the time he finishes?

A
$12$
B
$15$
C
$20$
D
$60$
E
$120$
Question 10 Explanation: 
The correct answer is (D). To find the total number of combinations, we multiply the total number of options for each meal available:

$4 \ast 5 \ast 3 = 60$
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