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, then: \(15×60=900\)

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, then 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 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**

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