# 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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