*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.*

Congratulations - you have completed .
You scored %%SCORE%% out of %%TOTAL%%.
Your performance has been rated as %%RATING%%

Your answers are highlighted below.

Question 1 |

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

$2x + 2y$ | |

$2x − 2y$ | |

$x + y + 1$ | |

$x + y + 2$ | |

$x − 2y$ |

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.

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?

$0.0525x$ | |

$0.125x$ | |

$0.25x$ | |

$0.50x$ | |

$2.33x$ |

Question 2 Explanation:

The correct answer is (A). 35% of 15% of a number is $0.35 \ast 0.15$ of that number:

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

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

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?

$350$ | |

$450$ | |

$550$ | |

$650$ | |

$750$ |

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

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

$125 + 125 + 200 + 200 = 650$

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?

$\dfrac{1}{3} x y^3 z^3$ | |

$\dfrac{2}{3} x^3 y^5 z^5$ | |

$\dfrac{4}{3} x^2 y^2 z^2$ | |

$\dfrac{3}{4} x^4 y^2 z^2$ | |

$\dfrac{8}{3} x^4 y^2 z^3$ |

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).

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

$x*x^2=x^3$

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

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

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

Question 5 |

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

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

$7$ | |

$9$ | |

$8$ | |

$5$ | |

$4$ |

Question 5 Explanation:

The correct answer is (B). To find $y$, substitute 3 for $x$ in the equation:

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

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

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

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

$y = 9$

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

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

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

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

$y = 9$

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?

$B \gt 1$ | |

$B \lt 0$ | |

$0 \lt B \lt 1$ | |

$−1\lt B \lt0$ | |

$B \lt −1$ |

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.

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 ($)?

$9.99 + 24.99m$ | |

$9.99m + 24.99$ | |

$24.99 - 9.99m$ | |

$24.99 + m + 9.99$ | |

$33.98m$ |

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:

$9.99m + 24.99$

$9.99m + 24.99$

Question 8 |

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

$0.50$ | |

$0.67$ | |

$0.42$ | |

$0.77$ | |

$0.63$ |

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 $\dfrac{1}{2}$.

$7\%$ 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?

$π$ | |

$2π$ | |

$4π$ | |

$6π$ | |

$12π$ |

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.

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?

$12$ | |

$15$ | |

$20$ | |

$60$ | |

$120$ |

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:

$4 \ast 5 \ast 3 = 60$

$4 \ast 5 \ast 3 = 60$

Once you are finished, click the button below. Any items you have not completed will be marked incorrect.

There are 10 questions to complete.

List |

**Next Practice Test:
ACT Math Practice Test 4 >>
**

**More Practice Tests:**

ACT Math – Main Menu >>

ACT Science Practice >>

ACT English Practice >>

ACT Reading Practice >>