# 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, 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
$$\sqrt{49x^4 }=\sqrt{49}×\sqrt{x^4 }=7×x^2=7x^2$$

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