# Full-Length AFOQT Math Practice Test-Answers and Explanations

Did you take the AFOQT Math Practice Test? If so, then it’s time to review your results to see where you went wrong and what areas you need to improve.

## AFOQT Mathematical Reasoning Practice Test Answers and Explanations

1- **Choice C is correct**

\(\frac{198}{18} = 11\)

2- **Choice A is correct**

Area of a rectangle\( =\) width \(×\) length \(= 12 × 27 = 324\)

3- **Choice C is correct**

\(44 ÷ 4 = 11 \)hours for one course, \(11 × 36 = 396 ⇒ $396\)

4- **Choice A is correct**

8 dozen of magazines are 96 magazines:\( 8 × 12 = 96, 96 – 32 = 64\)

5- **Choice A is correct**

Michelle \(=\) Karen \(– 6\), Michelle \(=\) David \(– 3\), Karen \(+\) Michelle \(+\) David \(= 45\) Karen \(=\) Michelle \(+ 6\), David \(=\) Michelle \(+ 3\), Karen \(+ \)Michelle \(+\) David\( = 45 \)

Now, replace the ages of Karen and David by Michelle.

Then: Michelle \(+ 6 +\) Michelle \(+\) Michelle \(+ 3 = 45\), 3Michelle \(+ 9 = 45 ⇒\) 3Michelle \(= 45 – 9 \)

3Michelle\( = 36\), Michelle \(= 12\)

6- **Choice D is correct**

distance\(=\)speed \(×\)time ⇒time\(=\frac{distance}{speed}=\frac{900}{60}=15 \)

(Round trip means that the distance is 900 miles)

The round trip takes 15 hours. Change hours to minutes, than: \(15×60=900\)

7- **Choice A is correct**

Write proportion and solve. \(\frac{1}{124} = \frac{19}{x} ⇒ x = 19 × 124 = 2,356\)

8- **Choice A is correct**

average\(=\frac{sum}{total}\), Sum \(= 4 + 7 + 14 + 19 + 24 + 36 + 39 + 41 = 184\) Total number of numbers \(= 8\), average\(=\frac{184}{8} = 23\)

9- **Choice C is correct**

Each worker can walk 3 dogs: \(15 ÷ 5 = 3, 8\) workers can walk 24 dogs. \(8 × 3 = 24\)

10- **Choice B is correct**

The base rate is $12. The fee for the first 30 visits is: \(30×0.15=4.5\) The fee for the visits 31 to 45 is: \(15×0.10=1.5\), Total charge: \(12 + 4.5 + 1.5 = 18\)

11- **Choice C is correct**

average\(=\frac{sum}{total}=\frac{45+33+27}{3}=\frac{105}{3}=35\)

12- **Choice A is correct**

The amount they have \(= $9.85 + $15.45 + $12.75 = 38.05\)

13- **Choice D is correct**

Change 8 hours to minutes, then:\( 8 × 60 = 480\) minutes, \(\frac{480}{40}= 12\)

14- **Choice C is correct**

Since Julie gives 6 pieces of candy to each of her friends, then, the number of pieces of candies must be divisible by 6.

A. \(98 ÷ 6 = 16.33 \)

B. \(128 ÷ 6 = 21.33 \)

C. \(210 ÷ 6 = 35 \)

D. \(385 ÷ 6 = 64.166 \)

Only choice C gives a whole number

15- **Choice D is correct**

probability\(=\frac{desired outcomes}{possible outcomes}=\frac{5}{5+3+10+7}=\frac{5}{25}=\frac{1}{5}\)

16- **Choice B is correct**

1 ton \(= 2,000\) pounds, 10 ton \(= 20,000\) pounds, \(\frac{27,000}{10,000} = 2.7 \)

William needs to make at least 3 trips to deliver all of the food.

17- **Choice A is correct**

\(145 – 30 – 40 = 75\)

18- **Choice B is correct**

3 weeks \(= 21\) days, \(21 × 5 = 105\) hours, \(105 × 60 = 6,300\) minutes

19- **Choice B is correct**

Find the value of each choice:

A. \(2 × 2 × 3 × 7 = 84\)

B. \(2 × 3 × 3 × 3 × 7 = 378 \)

C. \(2 × 3 × 5 × 5 × 7 = 1,050 \)

D. \(3 × 3 × 5 × 7 × 7 = 1,960\)

20- **Choice D is correct**

\(25\% × 80 = \frac{25}{100} × 80 = 20\),

The coupon has \($20\) value. Then, the selling price of the sweater is \($60\).

\(80 – 20 = 60\), Add \(9\%\) tax, then: \(\frac{9}{100} × 60 = 5.4\) for tax, Total: \(60 + 5.4 = $65.4\)

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21- **Choice C is correct**

1 quart \(= 0.25\) gallon, 28 quarts \(= 28 × 0.25 = 7\) gallons, then: \(\frac{7}{2} = 3.5\) weeks

22- **Choice D is correct**

The difference of the file added, and the file deleted is:

\(487,236 – 397,756 = 89,480, 987,345 + 89,480 = 1,076,825\)

23- **Choice C is correct**

40 students did not have to go to summer school. \(50 – 10 = 40, \frac{40}{50} = \frac{4}{5}\)

24- **Choice B is correct**

Diameter \(= 2r ⇒4 = 2r⇒r = 2\), Circumference \(= 2πr ⇒ C = 2π (2) ⇒ C = 4π\)

25- **Choice D is correct**

Write a proportion and solve. \(\frac{\frac{1}{4}}{1}= \frac{60}{x}\)

\(x = \frac{60}{\frac{1}{4}} = 240\)

26- **Choice A is correct**

All angles in a triable add up to 180 degrees. \(90^\circ + 60^\circ = 150^\circ ⇒ x = 180^\circ − 150^\circ = 30^\circ\)

27- **Choice C is correct**

\(\sqrt{81} = 9, \sqrt{49} = 7, 9 × 7 = 63\)

28- **Choice D is correct**

If \(a = 5\) then: \(b = \frac{a^3}{5} -2 ⇒ b = \frac{5^3}{5} -2 = 25 -2 = 23\)

29- **Choice B is correct**

An obtuse angle is an angle of greater than 90 degrees and less than 180 degrees. Only choice A is an obtuse angle.

30- **Choice D is correct**

Only choice D is not equal to \(3^2\)

31- **Choice B is correct**

\(\sqrt[4]{625} = 5, (5^4=5×5×5×5=625)\)

32- **Choice B is correct**

(\(r =\) radius) Area of a circle \(= πr^2 = π × (4)^2 = 3.14 × 16 = 50.26\)

33- **Choice D is correct**

Volume \(=\) length \(×\) width \(× \)height, Volume \(= 8 × 3 × 4\), Volume \(= 96\) cm\(^3\)

34- **Choice A is correct**

\(-9a = 81 ⇒ a = \frac{81}{-9}= – 9\)

35- **Choice C is correct**

Area of a square \(=\) (one side)\(^2 ⇒ A = (8)^2 ⇒ A = 64\)

36- **Choice B is correct**

Use Pythagorean Theorem: \(a^2 + b^2 = c^2 ⇒ (6)^2 + (3)^2 = c^2 ⇒36 + 9 = 45 = C^2⇒C =\sqrt{45} = 6.708\)

37- **Choice B is correct**

Use FOIL (first, out, in, last) method.

\((-3x +7) (3x-4) = -9x^2 + 12x + 21x – 28 = -9x^2 + 33x – 28\)

38- **Choice D is correct**

\(3(a–7)=34 ⇒ 3a-21=34 ⇒3a=34+21=45 , ⇒ 3a=45⇒a=\frac{45}{3}=15\)

39- **Choice C is correct**

Use exponent multiplication rule: \(x^a. x^b = x^{a + b}\)

Then:\( 2^{18}=2^5× 2^x=2^{5+x}⇒ 18 = 5 + x ⇒x=18-5=13\)

40- **Choice C is correct**

To factor the expression \(x^2 + 4x –21\), we need to find two numbers whose sum is 4 and their product is \(-21\). Those numbers are 7 and \(-3\). Then:\(x^2+4x-21=(x+7)(x-3)\)

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41- **Choice B is correct**

Slope of a line:\(\frac{y_2- y_1}{x_2 – x_1 } = \frac{rise}{run}, \frac{y_2- y_1}{x_2 – x_1 } = \frac{1- 4}{7 – 4} = \frac{-3}{3} = -1\)

42- **Choice B is correct**

\(\sqrt[3]{4,913} = 17\)

43- **Choice C is correct**

In scientific notation form, numbers are written with one whole number times 10 to the power of a whole number. Number 87,456 has 5 digits. Write the number and after the first digit put the decimal point. Then, multiply the number by 10 to the power of 4 (number of remaining digits). Then: \(87,456 = 8.7456 × 10^4\)

44- **Choice B is correct**

The area of the non-shaded region is equal to the area of the bigger rectangle subtracted by the area of the smaller rectangle.

Area of the bigger rectangle \(= 5 × 7 = 35\)

Area of the smaller rectangle \(= 5 × 3 = 15 \)

Area of the non-shaded region \(= 35 – 15 = 20\)

45- **Choice B is correct**

Diameter \(= 2r ⇒ 7 = 2r⇒r = 3.5\), Circumference \(= 2πr ⇒ C = 2π (3.5) ⇒ C = 7π\)

46- **Choice A is correct**

average\(=\frac{sum}{total}=\frac{270}{45} = 6\)

47- **Choice A is correct**

Factor of \(56: {1, 2, 4, 7, 8, 14, 28, 56}\)

Factor of \(18: {1, 2, 3, 6, 9, 18}\), Then, factors they have in common is \({1, 2}\)

48- **Choice C is correct**

Diameter\( = 2r ⇒ 10 = 2r ⇒r = 5\), Circumference \(= 2πr ⇒ C = 2π (5) ⇒ C = 10 × 3.14 = 31.4\)

49- **Choice C is correct**

The straight line is 180 degrees. Then: \(a = 180^\circ – 45^\circ = 135^\circ\)

50- **Choice C is correct**

\(\sqrt{49x^4 }=\sqrt{49}×\sqrt{x^4 }=7×x^2=7x^2\)

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## More from Effortless Math for AFOQT Test …

### What tips you should follow to prevent failure again AFOQT?

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**Here are some tips to help you make the most of your test day:** **AFOQT Math-Test Day Tips**

## The Perfect Prep Books** **for the AFOQT Math Test

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