 ## Full Length GED Mathematical Reasoning Practice Test

Taking a practice test for the GED Math, which is similar to an actual exam day, helps you become familiar with how the format of this particular assessment and feel more confident. You will also see if you are prepared to take on such a big challenge as it simulates what could be expected during real-time testing.

If you're going to take the GED test, this complete and realistic practice test can help prepare your mind and body for it. Treat this practice test as a real one - make sure you have scratch paper, pencils, timers, calculators; follow the time limits to the minute. After finishing every question in one sitting-with no distractions!-score your tests using answer keys provided at end of each section. Good luck with everything!

### The Most Comprehensive GED Math Preparation Bundle

$79.99$34.99
56% Off*

Includes GED Math Prep Books, Workbooks, and Practice Tests

## GED Mathematical Reasoning Practice Test

(Non–Calculator)   5 questions Total time for two sections (Non–Calculator, and Calculator sections): 115 Minutes You may not use a calculator in this section.

1- $$[ 8 × (-32) + 12]$$ $$+ (4) \ -$$ $$[ 8 × 2 ]$$ $$÷$$ $$2$$ $$=$$ $$?$$
(A) $$-216$$
(B) $$- 238$$
(C) $$-215$$
(D) $$-248$$
2- Which of the following is equal to the expression below$$?$$
$$(4\ x \ + \ y)\ (3\ x\ -\ 2\ y)$$
(A) $$12\ x^ 2 \ - \ 5\ x\ y \ - \ 2\ y^2$$
(B) $$12\ x^2\ + \ 5\ x\ y \ - \ 2\ y^2$$
(C) $$12\ x^2$$ $$+$$ $$5\ x\ y$$ $$+$$ $$2\ y^2$$
(D) $$12\ x^2$$ $$-$$ $$5\ x\ y$$ $$+$$ $$2y^2$$
3- What is the product of all possible values of $$y$$ in the following equation$$?$$
$$|y-7|$$ $$=$$ $$5$$
(A) $$25$$
(B) $$14$$
(C) $$24$$
(D) $$10$$
4- What is the slope of a line that is perpendicular to the line$$?$$
$$3\ x$$ $$-$$ $$2\ y$$ $$=$$ $$8$$$$?$$
(A) $$-\ \frac{4}{3}$$
(B) $$-\ \frac{2}{3}$$
(C) $$-\ \frac{1}{3}$$
(D) $$-\ \frac{5}{3}$$
5- What is the value of the expression $$2$$ $$(x\ -\ 3\ y)$$ $$+$$ $$(4 \ -\ y)$$$$(4 \ -\ y)$$
when $$x = 1$$ and $$y = 5$$
(A) $$27$$
(B) $$-\ 13$$
(C) $$13$$
(D) $$-\ 27$$

Mathematical Reasoning

Practice Test

(Calculator)   41 questions Total time for two sections (Non–Calculator, and Calculator sections): 115 Minutes   You may use a calculator in this section.

6- If $$60$$% of a number is $$12$$, what is the number?
(A) $$10$$
(B) $$20$$
(C) $$12$$
(D) $$30$$
7- If $$x$$ is $$1.5$$ times of $$y$$ and $$x$$ is $$15$$, what is the value of $$y$$?
(A) $$15$$
(B) $$10$$
(C) $$20$$
(D) $$12$$
8- Jack is $$12$$ miles ahead of Alex running at $$4$$ miles per hour and Alex is running at the speed of $$10$$ miles per hour.
How long does it take Alex to catch Jack?
(A) $$1$$ hours
(B) $$4$$ hours
(C) $$2$$ hours
(D) $$3$$ hours
9- $$30$$ students took an exam and $$6$$ of them failed. What percent of the students passed the exam?
(A) $$25$$%
(B) $$50$$%
(C) $$75$$%
(D) $$80$$%
10- What is the value of $$2^4$$$$?$$
(A) $$64$$
(B) $$32$$
(C) $$8$$
(D) $$16$$
11- Which of the following inequality represents the compound inequality  $$2$$ $$≤$$ $$3x - 4$$ $$<$$ $$5$$
(A) $$2$$ $$≤$$ $$x$$ $$<$$ $$3$$
(B) $$1$$ $$≤$$ $$x$$ $$<$$ $$1.5$$
(C) $$3$$ $$≤$$ $$x$$ $$<$$ $$4.5$$
(D) $$3$$ $$≤$$ $$x$$ $$<$$ $$6$$
12- The diagonal of a rectangle is $$5$$ cm long and the height of the rectangle is $$4$$ cm What is the perimeter of the rectangle in cm?
(A) $$16$$
(B) $$20$$
(C) $$12$$
(D) $$14$$
13- The perimeter of the trapezoid below is $$50$$ cm. What is its area? (A) $$160$$
(B) $$320$$
(C) $$144$$
(D) $$288$$
14- A card is drawn at random from a standard $$63$$–card deck, what is the probability that the card is of diamonds?
(The deck includes $$21$$ of each suit clubs, diamonds, and spades)
(A) $$\frac{1}{21}$$
(B) $$\frac{1}{7}$$
(C) $$\frac{1}{3}$$
(D) $$\frac{12}{21}$$
15- Which of the following shows the numbers in descending order?
$$\frac{1}{3}$$ , $$0.35$$ , $$65\% , 36\%$$
(A) $$36\%<$$$$0.35$$$$<$$$$65\%<$$$$\frac{1}{3}$$
(B) $$36\%<65\%<$$$$0.35$$$$<$$$$\frac{1}{3}$$
(C) $$\frac{1}{3}$$$$<$$$$36\%<$$$$0.35$$$$<$$$$65\%$$
(D) $$\frac{1}{3}$$$$<$$$$0.35$$$$<$$$$36\%<65$$%
16- The mean of $$40$$ test scores was calculated as $$85$$. But, it turned out that one of the scores was
misread as $$92$$ but it was $$72$$. What is the mean?
(A) $$86.5$$
(B) $$87.2$$
(C) $$84.5$$
(D) $$88.5$$
17- Two dice are thrown simultaneously, what is the probability of getting a sum of $$6$$ or $$8$$?
(A) $$\frac{1}{9}$$
(B) $$\frac{1}{12}$$
(C) $$\frac{1}{6}$$
(D) $$\frac{1}{3}$$
18- A swimming pool holds $$1500$$ cubic feet of water.
The swimming pool is $$20$$ feet long and $$7.5$$ feet wide. How deep is the swimming pool?
(A) $$12$$
(B) $$13$$
(C) $$15$$
(D) $$10$$
19- Mr. Carlos's family is choosing a menu for their reception. They have $$4$$ choices of appetizers, $$2$$ choices of entrees, and $$1$$ choices of cake.
How many different menu combinations are possible for them to choose from?
(A) $$4$$
(B) $$2$$
(C) $$8$$
(D) $$1$$
20- Four one–foot rulers can be split among how many users to leave each with $$\frac{1}{3}$$ of a ruler?
(A) $$\frac{4}{3}$$
(B) $$12$$
(C) $$18$$
(D) $$9$$
21- What is the area of a square whose diagonal is $$10$$?
(A) $$50$$
(B) $$\sqrt{50}$$
(C) $$25$$
(D) $$5$$
22- Anita’s trick–or–treat bag contains $$20$$ pieces of chocolate, $$12$$ suckers, $$12$$ pieces of gum, $$16$$  pieces of licorice.
if she randomly pulls a piece of candy from her bag, what is the probability of her pulling out a piece of sucker?
(A) $$\frac{1}{3}$$
(B) $$\frac{1}{4}$$
(C) $$\frac{2}{3}$$
(D) $$\frac{1}{5}$$
23- What is the missing term in the given sequence?
$$2$$, $$4$$, $$7$$, $$11$$, $$16$$, $$22$$, $$29$$, ___, $$46$$
(A) $$32$$
(B) $$35$$
(C) $$36$$
(D) $$37$$
24- The perimeter of a rectangular yard is $$80$$ meters. What is its length if its width is twice its length?
(A) $$15.5$$
(B) $$13.33$$
(C) $$11.47$$
(D) $$12.73$$
25- The average of $$6$$ numbers is $$16$$. The average of $$4$$ of those numbers is $$8$$. What is the average of the other two numbers?
(A) $$64$$
(B) $$32$$
(C) $$96$$
(D) $$16$$
26- What is the value of $$y$$ in the following system of equations?
$$3\ x \ + \ y = 9$$
$$x \ +\ 3\ y = 3$$
(A) $$3$$
(B) $$-3$$
(C) $$1$$
(D) $$0$$
27- The average of four numbers is $$32$$. If a fifth number $$47$$ is added, then, what is the new average?
(A) $$35$$
(B) $$175$$
(C) $$10$$
(D) $$128$$
28- The ratio of boys and girls in a class is $$3: 7$$. If there are $$30$$ students in the class,
how many more boys should be enrolled to make the ratio $$2:3$$?
(A) $$8$$
(B) $$2$$
(C) $$7$$
(D) $$5$$

### GED Math for Beginners 2022

$28.99$14.99
48% Off*

The Ultimate Step by Step Guide to Preparing for the GED Math Test

29- Mr. Jones saves $$$5000$$ out of his monthly family income of$$$30000$$.
What fractional part of his income does he save?
(A) $$\frac{1}{3}$$
(B) $$\frac{2}{3}$$
(C) $$\frac{1}{6}$$
(D) $$\frac{5}{6}$$
30- A football team had $$50000$$ to spend on supplies. The team spent $$38000$$ on new shirts and balls.
New sport shoes cost $$150$$ each. Which of the following inequalities represents the number
of new shoes, the team can purchase?
(A) $$150 \ x \ + \ 38000 ≤ 50000$$
(B) $$150\ x\ + \ 38000 \ ≥ \ 50000$$
(C) $$150\ x \ + \ 50000 \ ≥ 38000$$
(D) $$150\ x\ + \ 5 0000 ≤ 38000$$
31- Jack needs an $$70\%$$ average in his writing class to pass. On his first $$3$$ exams,
he earned scores of $$63\%, 67\%$$, and $$85\%$$. What is the minimum score Jack
can earn on his fourth and final test to pass?
(A) $$63$$
(B) $$64$$
(C) $$67$$
(D) $$65$$
32- What is the value of $$x$$ in the following equation?
$$\frac{1}{4}\ x \ - \ \frac{1}{6} = \frac{-\ 1}{12}$$
(A) $$\frac{-1}{3}$$
(B) $$\frac{1}{3}$$
(C) $$\frac{1}{6}$$
(D) $$\frac{1}{12}$$
33- A bank is offering $$3$$% simple interest on a savings account. If you deposit $$$18000$$, how much interest will you earn in four years? (A) $$540$$ (B) $$72000$$ (C) $$2520$$ (D) $$2160$$ 34- Simplify $$3\ x \ y^2 \ ( 7\ x^4\ y^2) =$$ (A) $$7\ x^5\ y^4$$ (B) $$21\ x^5\ y^6$$ (C) $$21\ x^6 \ y^5$$ (D) $$21\ x^5\ y^4$$ 35- What is the surface area of the cylinder below? (A) $$110\ π\ in^2$$ (B) $$100\ π\ i n^2$$ (C) $$120\ π\ i n^2$$ (D) $$140\ π\ i n^2$$ 36- The square of a number is $$\frac{64}{121}$$. What is the cube of that number? (A) $$\frac{512}{121}$$ (B) $$\frac{512}{1331}$$ (C) $$\frac{64}{1331}$$ (D) $$\frac{64}{121}$$ 37- What is the median of these numbers? $$4$$ ,$$21$$ ,$$2$$ ,$$12$$ ,$$14$$ (A) $$14$$ (B) $$12$$ (C) $$21$$ (D) $$13$$ 38- A cruise line ship left Port A and traveled $$60$$ miles due west and then $$80$$ miles due north. At this point, what is the shortest distance from the cruise to port A in miles? (A) $$75$$ miles (B) $$85$$ miles (C) $$90$$ miles (D) $$100$$ miles 39- What is the equivalent temperature of $$78^\circ$$ F in Celsius? $$C= \frac{5}{9} (F \ -\ 32)$$ (A) $$37$$ (B) $$43.5$$ (C) $$25.55$$ (D) $$17.62$$ 40- If $$250$$ % of a number is $$100$$, then what is the $$85$$ % of that number? (A) $$40$$ (B) $$15$$ (C) $$27$$ (D) $$34$$ 41- What is the slope of the line ( Solve for $$y)$$: $$3\ x \ - \ 3\ y = 1$$ (A) $$2$$ (B) $$0.5$$ (C) $$\frac{1}{3}$$ (D) $$1$$ 42- What is the volume of a box with the following dimensions? Hight = $$3$$ cm Width = $$6$$ cm Length = $$7$$ cm (A) $$178$$ (B) $$118$$ (C) $$193$$ (D) $$126$$ 43- Simplify the expression. ($$3\ x \ + \ 4\ x^3 \ + 3\ x^4 ) \ +\ (-\ x^3 \ -\ 3\ x \ + \ 2\ x^4$$) (A) $$5\ x^4\ -\ x^3$$ (B) $$5\ x^4 \ -\ 2\ x^3\ +\ 6 \ x$$ (C) $$5\ x^4\ -\ 2\ x^3$$ (D) $$5\ x^4\ +\ 3\ x^3$$ 44- In three successive years, the population of a town is increased by $$10\%$$ and $$12\%$$ and$$18\%$$ What percent of the population is increased after three years? (A) $$145\%$$ (B) $$173\%$$ (C) $$121\%$$ (D) $$137$$% 45- Last week $$30000$$ fans attended a football match. This week three times as many bought tickets, but one fifth of them canceled their tickets. How many are attending this week? (A) $$30000$$ (B) $$18000$$ (C) $$72000$$ (D) $$36000$$ 46- What is the perimeter of a square in centimeters that has an area of $$488.41$$ cm$$^2$$? (A) $$86$$ (B) $$44.2$$ (C) $$22.1$$ (D) $$88.4$$  1- Choice D is correct The correct answer is $$- \ 248$$Use PEMDAS (order of operation):$$[ 8 × (-32) + 12]$$ $$+$$ $$4$$ $$-$$ $$[ 8 \ ×\ 2 ]$$ $$÷$$ $$2$$ $$=$$ $$[ - \ 256 \ +\ 12]$$ $$+$$ $$4$$ $$-$$ $$$$ $$÷$$ $$2$$ $$=$$$$[ -\ 256 \ + \ 12]$$ $$+$$ $$4$$ $$-$$ $$$$ $$=$$ $$[ - \ 244]$$ $$+$$ $$4$$ $$-$$ $$$$ $$=$$ $$[ - \ 244]$$ $$+$$ $$4$$ $$-$$ $$8$$ $$=$$ $$- \ 248$$ 2- Choice A is correct The correct answer is $$12\ x^2 \ -\ 5\ x\ y \ - \ 2\ y^2$$Use FOIL method.$$(4\ x \ + \ y) \ (3\ x \ - \ 2\ y)= 12\ x^2 \ -\ 8\ x\ y + 3\ x\ y - 2\ y^2 = 12\ x^2 - 5\ x\ y \ - \ 2 \ y^2$$ 3- Choice C is correct The correct answer is $$24$$To solve absolute values equations, write two equations $$y-7$$ could be positive $$5$$, or negative $$5$$. Therefore, $$y-7$$$$=$$ $$5$$ $$⇒$$ $$y$$ $$=$$ $$12$$$$y-7$$$$=$$ $$-5$$ $$⇒$$ $$y$$ $$=$$ $$2$$Find the product of solutions: $$2$$ $$×$$ $$12$$ $$=$$ $$24$$ 4- Choice B is correct The correct answer is $$-\ \frac{2}{3}$$The equation of a line in slope intercept form is: $$y = mx + b$$Solve for $$y$$.$$3\ x$$ $$-$$ $$2\ y$$ $$=$$ $$8$$ $$⇒$$ $$-\ 2\ y$$ $$=$$ $$8$$ $$-$$ $$3\ x$$ $$⇒$$ $$y$$ $$=$$ $$(8 \ -\ 3\ x)$$ $$÷$$ $$(-\ 2)$$ $$⇒$$$$y$$ $$=$$ $$1.5\ x \ -\ 4$$The slope of this line is $$1.5$$.The product of the slopes of two perpendicular lines is $$-\ 1$$. Therefore, the slope of a line that is perpendicular to this line is:$$𝑚_1 \ ×\ 𝑚_ 2 = −\ 1 ⇒ 1.5 × 𝑚_2 = −\ 1 ⇒ 𝑚_2 = −\ \frac{2}{3}$$ 5- Choice D is correct The correct answer is $$-\ 27$$Plug in the value of $$x$$ and $$y$$. $$x = 1$$ and $$y = 5$$$$2$$ $$(x\ -\ 3\ y)$$ $$+$$ $$(4 \ -\ y)$$$$(4 \ -\ y)$$ $$=$$ $$2$$ $$(1\ -\ 3\ (5))$$ $$+$$ $$(4 \ -\ 5)$$ $$(4 \ -\ 5)$$ $$=$$$$2$$ $$(1\ -\ 15)$$ $$+$$ $$(-\ 1)$$ $$(-\ 1)$$ $$=$$ $$2$$ $$(-\ 14)$$ $$+$$ $$1$$ $$=$$ $$-\ 27$$ 6- Choice B is correct The correct answer is $$20$$Let $$x$$ be the number. Write the equation and solve for $$x$$.$$60$$% of $$x$$ $$=$$ $$12$$ $$⇒$$ $$0.6 \ x$$ $$=$$ $$12$$ $$⇒$$ $$x$$ $$=$$ $$12$$ $$÷$$ $$0.6$$ $$=$$ $$20$$ 7- Choice B is correct The correct answer is $$10$$$$x$$ is $$1.5$$ times of $$y$$, then $$x = 1.5\ y$$ $$⇒$$ ($$x = 15$$) $$15$$ $$=$$ $$1.5$$ $$×$$ $$y$$ $$⇒$$$$y$$ $$=$$ $$15$$ $$÷$$ $$1.5$$ $$=$$ $$10$$ 8- Choice C is correct The correct answer is $$2$$ hoursThe distance between Alex and Jack is $$12$$ miles.Jack running at $$4$$ miles per hour and Alex is running at the speed of $$10$$ miles per hour. Therefore, every hour the distance is $$6$$ miles less. $$12$$ $$÷$$ $$6$$ $$=$$ $$2$$ 9- Choice D is correct The correct answer is $$80$$%The failing rate is $$6$$ out of $$30$$ $$=$$ $$\frac{6}{30}$$Change the fraction to percent:$$\frac{6}{30}$$ × $$100$$% $$=$$ $$20$$%$$20$$ percent of students failed. Therefore, $$80$$ percent of students passed the exam. 10- Choice D is correct The correct answer is $$16$$$$2^4$$$$=$$ $$2$$$$×$$$$2$$$$×$$$$2$$$$×$$$$2$$$$=$$ $$16$$ 11- Choice A is correct The correct answer is $$2$$ $$≤$$ $$x$$ $$<$$ $$3$$ Solve for $$x$$.$$2$$ $$≤$$ $$3x - 4$$ $$<$$ $$5$$ $$⇒$$ (add 4 all sides) $$2 + 4$$ $$≤$$ $$3x$$ $$<$$ $$5 + 4$$ $$⇒$$$$6$$ $$≤$$ $$3x$$ $$<$$ $$9$$ $$⇒$$ (divide all sides by $$3$$) $$2$$ $$≤$$ $$x$$ $$<$$ $$3$$ $$x$$ is between $$2$$ and $$3$$ . 12- Choice D is correct The correct answer is $$14$$Let $$x$$ be the width of the rectangle. Use Pythagorean Theorem:$$a^2 + b^2 = c^2$$$$4^2 + x^2 = 5^2$$ $$⇒$$ $$x^2 + 16 = 25$$ $$⇒$$ $$x^2$$ $$=$$ $$25 - 16$$ $$=$$ $$9$$ $$⇒$$ $$x$$ $$=$$ $$3$$Perimeter of the rectangle $$=$$ $$2$$ (length + width) $$=$$ $$2$$ $$(4 + 3 )$$ $$=$$ $$2$$ $$(7)$$ $$=$$ $$14$$ 13- Choice A is correct The correct answer is $$160$$The perimeter of the trapezoid is $$50$$ cm.Therefore, the missing side (height) is $$= 50 \ – \ 14 \ – \ 12 \ – \ 8 = 16$$Area of a trapezoid: A $$= \frac{1}{2}\ h \ (b_1 \ +\ b_ 2) = \frac{1}{2} \ (16) \ (12 \ + \ 8) = 160$$ 14- Choice C is correct The correct answer is $$\frac{1}{3}$$The probability of choosing a diamond is $$\frac{21}{63}$$ = $$\frac{1}{3}$$ 15- Choice D is correct The correct answer is : $$\frac{1}{3}$$$$<$$$$0.35$$$$<$$$$36\%<65\%$$Change the numbers to decimal and then compare.$$\frac{1}{3}$$ = $$0.333...$$$$0.35$$$$36$$% = $$0.36$$$$65$$% = $$0.65$$$$0.333...$$$$<$$$$0.35$$$$<$$$$0.36$$$$<$$$$0.65$$ 16- Choice C is correct The correct answer is $$84.5$$average (mean) = $$\frac{sum \ of \ terms}{number \ of \ terms}$$$$⇒$$ $$85$$ = $$\frac{sum \ of \ terms}{40}$$$$⇒$$ sum = $$85 × 40 = 3400$$The difference of $$92$$ and $$72$$ is $$20$$. Therefore, $$20$$ should be subtracted from the sum. $$3400 - 20 = 3380$$mean = $$\frac{sum \ of \ terms}{number \ of \ terms}$$$$⇒$$ mean = $$\frac{3380}{40}$$ = $$84.5$$ 17- Choice C is correct The correct answer is $$\frac{1}{6}$$To get a sum of $$6$$ or $$8$$ for two dice, we should get $$3$$ and $$3$$, or $$2$$ and $$4$$, or $$1$$ and $$5$$ or $$3$$ and $$5$$ or $$2$$ and $$6$$ or $$4$$ and $$4$$.Therefore, there are $$6$$ options. Since, we have $$6 × 6 = 36$$ total options, the probability of getting a sum of $$6$$ and $$8$$ is $$6$$ out of $$36$$ or $$\frac{1}{6}$$. 18- Choice D is correct The correct answer is $$10$$Use formula of rectangle prism volume$$V =$$ (length) (width) (height) ⇒ $$1500 = (20$$) ($$7.5$$) (height) ⇒ height $$=1500 \ ÷ \ 150 = 10$$ 19- Choice C is correct The correct answer is $$8$$To find the number of possible outfit combinations, multiply the number of options for each factor:$$4 × 1 × 2 = 8$$ 20- Choice B is correct The correct answer is : $$12$$$$4 \ ÷ \ \frac{1}{3}$$ = $$12$$ 21- Choice A is correct The correct answer is : $$50$$ The diagonal of the square is $$10$$. Let $$x$$ be the side. Use Pythagorean Theorem: $$a^2$$ + $$b^2$$ = $$c^2$$$$x^2$$ $$+$$ $$x^2$$ $$=$$ $$10^2$$ $$⇒$$ $$2\ x^2$$ $$=$$ $$10^2$$ $$⇒$$ $$x^2$$ $$=$$ $$50$$ $$⇒$$ $$x$$ $$=$$ $$\sqrt{50}$$The area of the square is: $$\sqrt{50}$$ $$×$$ $$\sqrt{50}$$ $$=$$ $$50$$ 22- Choice D is correct The correct answer is : $$\frac{1}{5}$$Probability = $$\frac{number \ of \ desired\ outcomes}{number \ of\ total \ outcomes}$$ = $$\frac{12}{20 + 12 + 12 + 16}$$ = $$\frac{1}{5}$$ 23- Choice D is correct The correct answer is $$37$$Find the difference of each pairs of numbers:$$2$$, $$4$$, $$7$$, $$11$$, $$16$$, $$22$$, $$29$$, ___, $$46$$The difference of $$2$$ and $$4$$ is $$2$$, $$4$$ and $$7$$ is $$3$$, $$7$$ and $$11$$ is $$4$$, $$11$$ and $$16$$ is $$5$$,$$16$$ and $$22$$ is $$6$$, $$22$$ and $$29$$ is $$7$$, $$29$$ and next number should be $$8$$. The number is $$29$$ + $$8$$ = $$37$$ 24- Choice B is correct The correct answer is $$13.33$$ The width of the rectangle is twice its length. Let $$x$$ be the length. Then, width$$=2\ x$$Perimeter of the rectangle is $$2$$ (width + length) $$= 2 \ (2\ x \ + \ x ) = 80 ⇒ 6\ x = 80 ⇒ x = 13.33$$The length of the rectangle is $$13.33$$ meters. 25- Choice B is correct The correct answer is : $$32$$average = $$\frac{sum \ of \ terms}{number \ of \ terms}$$ $$⇒$$ (average of $$6$$ numbers) $$16$$ = $$\frac{sum \ of \ terms}{6}$$$$⇒$$ sum of $$6$$ numbers is $$16 × 6 = 96$$ (average of $$4$$ numbers) $$8$$ = $$\frac{sum \ of \ numbers}{4}$$$$⇒$$ sum of $$4$$ numbers is $$4 × 8 = 32$$ sum of $$6$$ numbers - sum of $$4$$ numbers = sum of $$2$$ numbers $$⇒$$ $$96 - 32 = 64$$ (average of $$2$$ numbers) = $$\frac{64}{2}$$ = $$32$$ 26- Choice D is correct The correct answer is $$0$$Solving Systems of Equations by EliminationMultiply the first equation by ($$-3$$), then add it to the first equation.$$-\ 3 \ (3\ x \ +\ y = 9$$)$$x \ +\ 3\ y = 3$$$$⇒$$ $$-\ 9\ x \ -\ 3\ y = -\ 27$$ $$⇒$$ $$-\ 8\ x = -\ 24$$ $$⇒$$ $$x = 3$$$$x \ +\ 3\ y = 3$$Plug in the value of $$x$$ into one of the equations and solve for $$y$$. $$3\ (3$$) + $$y$$ $$=$$ $$9$$ $$⇒$$ $$y = 0$$ 27- Choice A is correct The correct answer is $$35$$Solve for the sum of four numbers. average = $$\frac{sum \ of \ terms}{number \ of \ terms}$$ $$⇒$$ $$32$$ = $$\frac{sum \ of \ 4 numbers}{4}$$$$⇒$$ sum of $$4$$ numbers = $$32 \ ×\ 4 = 128$$ The sum of $$4$$ numbers is $$128$$. If a fifth number $$47$$ is added, then the sum of $$5$$ numbers is $$128 \ +\ 47 = 175$$average = $$\frac{sum \ of \ terms}{number \ of \ terms} = \frac{175}{5}$$ = $$35$$ 28- Choice D is correct The correct answer is $$5$$Th ratio of boy to girls is $$3: 7$$. Therefore, there are $$3$$ boys out of $$10$$ students. To find the answer, first divide the total number of students by $$10$$, then multiply the result by 4.$$30$$ ÷ $$10$$ = $$3$$ ⇒ $$3$$ × $$3$$ = $$9$$There are $$9$$ boys and $$21$$ ($$30 - 9$$) girls. So, $$5$$ more boys should be enrolled to make the ratio $$2:3$$ 29- Choice C is correct The correct answer is $$\frac{1}{6}$$$$5000$$ out of $$30000$$ equals to = $$\frac{5000}{30000}$$ = $$\frac{5}{30}$$ = $$\frac{1}{6}$$ 30- Choice A is correct The correct answer is $$150\ x + 38000 ≤ 50000$$Let $$x$$ be the number of new shoes the team can purchase. Therefore, the team can purchase $$150\ x$$.The team had$$$50000$$ and spent $$38000$$. Now the team can spend on new shoes $$12000$$ at most.Now, write the inequality:$$150\ x \ + \ 38000 ≤ 50000$$ 31- Choice D is correct The correct answer is $$65$$Jack needs an $$70\%$$ average to pass for four exams. Therefore, the sum of $$4$$ exams must be at lease $$4 \ × \ 70 = 280$$The sum of $$3$$ exams is: $$63$$ $$+$$ $$67$$ $$+$$ $$85$$ $$=$$ $$215$$The minimum score Jack can earn on his fifth and final test to pass is:$$280 \ -\ 215 = 65$$ 32- Choice B is correct The correct answer is  $$\frac{1}{3}$$$$\frac{1}{4}\ x \ - \ \frac{1}{6} = \frac{-\ 1}{12}$$ $$⇒$$ $$\frac{1}{4}\ x = \frac{-\ 1}{12} \ + \ \frac{1}{6} = \frac{1}{12}$$ $$⇒$$ $$\frac{1}{4}\ x = \frac{1}{12}$$Multiply both sides by the reciprocal of the coefficient of $$x$$($$\frac{4}{1}$$) $$\frac{1}{4}\ x = \frac{1}{12}$$ ($$\frac{4}{1}$$) $$⇒$$ $$x = \frac{1}{3}$$ 33- Choice D is correct The correct answer is $$2160$$Use simple interest formula:$$I=prt$$($$I =$$ interest, $$p =$$ principal, $$r =$$ rate, $$t =$$ time)$$I = (18000$$) ($$0.03$$) ($$4$$) = $$2160$$ 34- Choice D is correct The correct answer is $$21\ x^5\ y^4$$Simplify. $$3\ x\ y^2 \ (7\ x^4 \ y^2 ) = 21\ x^5 \ y^4$$ 35- Choice A is correct The correct answer is $$110\ π\ i n^2$$Surface Area of a cylinder $$= 2\ π\ r\ (r\ +\ h)$$,The radius of the cylinder is $$5\ (10 \ ÷\ 2)$$ inches and its height is $$6$$ inches. Therefore, Surface Area of a cylinder $$= 2\ π\ (5 )\ (5 \ +\ 6 ) = 110 \ π$$ 36- Choice B is correct The correct answer is $$\frac{512}{1331}$$The square of a number is $$\frac{64}{121}$$, then the number is the square root of $$\frac{64}{121}$$$$\sqrt{\frac{64}{121}}$$ = $$\frac{8}{11}$$The cube of the number is: ($$\frac{8}{11}$$)³ = $$\frac{512}{1331}$$ 37- Choice B is correct The correct answer is $$12$$Write the numbers in order:$$2$$,$$4$$,$$12$$,$$14$$,$$21$$edian is the number in the middle. So, the median is $$12$$. 38- Choice D is correct The correct answer is $$100$$ milesUse the information provided in the question to draw the shape.Use Pythagorean Theorem: $$a^2 + b^2 = c^2$$$$60^2 \ + \ 80^2 = c^2$$ $$⇒$$ $$3600 \ + \ 6400 = c^2$$ $$⇒$$ $$10000 = c^2$$ $$⇒$$ $$c = 100$$ miles 39- Choice C is correct The correct answer is $$25.55$$Plug in $$78$$ for F and then solve for C.C$$= \frac{5}{9} (F \ -\ 32) ⇒$$ C$$=\frac{5}{9}$$($$78 \ -\ 32$$) $$⇒$$ C$$= \frac{5}{9}$$($$46$$) $$= 25.55$$ 40- Choice D is correct The correct answer is $$34$$ First, find the number. Let $$x$$ be the number. Write the equation and solve for $$x$$. $$250$$ % of a number is $$100$$, then:$$2.5 × x = 100$$ $$⇒$$ $$x =100 ÷ 2.5 = 40$$  $$85$$ % of $$40$$ is $$34$$ 41- Choice D is correct The correct answer is $$1$$Solve for $$y$$ .$$3\ x \ -\ 3\ y = 1$$ $$⇒$$ $$-\ 3\ y = 1 \ -\ 3\ x$$ $$⇒ y = x \ - \ \frac{1}{3}$$The slope of the line is $$1$$. 42- Choice D is correct The correct answer is $$126$$Volume of a box = length × width × height = $$3 × 6 × 7 = 126$$ 43- Choice D is correct The correct answer is ($$5\ x^4\ +\ 3\ x^3$$)($$3\ x \ + \ 4\ x^3 \ +\ 3\ x^4) \ +\ (-\ x^3 \ -\ 3\ x\ + \ 2\ x^4$$) $$⇒$$ $$( 3 \ x^4\ + \ 4\ x^3\ +\ 3\ x ) \ +\ ( 2\ x^4\ -\ x^3\ -\ 3\ x$$) $$=$$ ($$5\ x^4 \ + \ 3\ x^3$$) 44- Choice A is correct The correct answer is $$145\%$$the population is increased by $$10\%$$ and $$12\%$$ and $$18\%$$ . $$10\%$$ increase changes the population to $$110\%$$ of original population. For the second increase, multiply the result by $$112\%$$.For the third increase, multiply the result by $$118\%$$($$1.10) \ × \ (1.12) \ × \ ( 1.18) = 1.45 = 145\%$$ 45- Choice C is correct The correct answer is $$72000$$Three times of $$30000$$ is $$90000$$. One fifth of them cancelled their tickets.One fifth of $$90000$$ equals $$18000$$. $$72000$$  ($$90000$$ – $$18000$$ = $$72000$$) fans are attending this week 46- Choice D is correct The correct answer is $$88.4$$The area of the square is $$488.41$$. Therefore, the side of the square is a square root of the area.$$\sqrt{488.41} = 22.1$$Four times the side of the square is the perimeter:$$4 \ ×\ 22.1 = 88.4$$

### The Most Comprehensive GED Math Preparation Bundle

$79.99$34.99
56% Off*

Includes GED Math Prep Books, Workbooks, and Practice Tests

### Practice Test 1

Simulate test day with an official practice test. Then, score your test. The answers come with explanations so you can learn from your mistakes.

### Practice Test 2

Simulate test day with an official practice test. Then, score your test. The answers come with explanations so you can learn from your mistakes.

## More Articles

### Prepare for the ISEE Upper Level Math Test in 7 Days

$19.99$14.99

### AFOQT Math Study Guide 2020 – 2021

$18.99$13.99

### The Most Comprehensive CLEP College Math Preparation Bundle

$76.99$36.99

### CHSPE Math Practice Workbook

$25.99$14.99