# 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 $0.525x$ E $5.25x$
Question 2 Explanation:
The correct answer is (A). 35% of 15% of a number is $0.35 \ast 0.15$ of that number:

$0.35 \ast 0.15 = 0.0525x$
 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:

$(125 *\ast 2) + (200 \ast 2) = 650$
 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

### What is the slope intercept form of $(13x − 5x) + 12 − 2y = 6$?

 A $y = 3x − 9$ B $y = 4x + 3$ C $y = −4x − 3$ D $y = 6x + 2$ E $y = −6x + 5$
Question 5 Explanation:
The correct answer is (B). Recall that slope-intercept form is $y = mx + b$ where $m$ is the slope and $b$ is the $y$-intercept. Solve for $y$:

$8x − 2y = −6$

$2y = 8x + 6$

Divide everything by 2:

$y = 4x + 3$
 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). If the product of two numbers is positive, the two numbers must have the same sign. That is, if $ab \gt 0$, then either $a \gt 0$ and $b \gt 0$, or $a \lt 0$ and $b \lt 0$.

We are told that $A \lt −1$ (which implies that $A \lt 0$).
So we know that $B \lt 0$.
We also know that $AB=1$, so $A=\dfrac{1}{B}$
Since $A=\dfrac{1}{B}$, and $A \lt -1$, we can infer that $\dfrac{1}{B} \lt -1$

If we take reciprocals on both sides of the last inequality, we must flip the inequality sign. Hence: $B \gt −1$

So we know that $B \lt 0$, and $B \gt −1$. We can represent this as a compound inequality: $−1 \lt B \lt 0$
 Question 7

 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,$m$, of magazines times the cost per magazine: 9.99$m$+ 24.99  Question 8 ###$f(x) = −3x^3 + 4x^2 − x + 2$###$g(x) = 2x^2 − x$### What is$f(g(−1))$?  A$−46$B$−22$C$0$D$22$E$46$Question 8 Explanation: The correct answer is (A). This question asks about function composition. Begin by evaluating$g(−1) = 2 + 1 = 3$Now evaluate$f(3) = −3 * 27 + 36 − 3 + 2 = −46$ 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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