## Full Length GED Mathematical Reasoning Practice Test

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## 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- $$[6\ ×\ (–\ 24)\ +\ 8]\ –\ (–\ 4)\ +\ [4\ ×\ 5]\ ÷\ 2 = ?$$
(A) $$-64$$
(B) $$-56$$
(C) $$-120$$
(D) $$-122$$
2- Which of the following is equal to the expression below?
$$(2\ x\ +\ 2\ y)\ (2 \ x\ -\ y)$$
(A) $$4\ x^2\ -\ 2\ y^2$$
(B) $$2\ x^2\ + \ 6\ x\ y\ -\ 2 \ y^2$$
(C) $$2\ 4\ x^2\ +\ 2\ x\ y\ -\ 2 \ y^2$$
(D) $$4\ x^2\ +\ 2\ x\ y \ - \ 2 \ y^2$$
3- What is the product of all possible values of $$x$$ in the following equation?
$$|x\ -\ 10| = 3$$
(A) $$3$$
(B) $$7$$
(C) $$13$$
(D) $$91$$
4- What is the slope of a line that is perpendicular to the line
$$4\ x\ -\ 2\ y=12$$ ?
(A) $$-\ 2$$
(B) $$-\ \frac{1}{2}$$
(C) $$4$$
(D) $$12$$
5- What is the value of the expression $$5\ (x\ -\ 2\ y)\ +\ (2\ -\ x)^2$$ when $$x=3$$ and  $$=-\ 2$$ ?
(A) $$-\ 4$$
(B) $$20$$
(C) $$36$$
(D) $$50$$

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 $$40\%$$ of a number is $$4$$, what is the number?
(A) $$4$$
(B) $$8$$
(C) $$10$$
(D) $$12$$
7- If $$A$$ is $$4$$ times of $$B$$ and $$A$$ is $$12$$, what is the value of $$B$$ ?
(A) $$3$$
(B) $$4$$
(C) $$48$$
(D) $$12$$
8- Jason is $$9$$ miles ahead of Joe running at $$5.5$$ miles per hour and Joe is running at
the speed of $$7$$ miles per hour. How long does it take Joe to catch Jason?
(A) $$3$$ hours
(B) $$4$$ hours
(C) $$6$$ hours
(D) $$8$$ hours
9- $$55$$ students took an exam and $$11$$ of them failed.
What percent of the students passed the exam?
(A) $$20\%$$
(B) $$40\%$$
(C) $$60\%$$
(D) $$80\%$$
10- What is the value of $$3^6$$?
(A) $$891$$
(B) $$243$$
(C) $$2187$$
(D) $$729$$
11- Which of the following graphs represents the compound inequality $$-\ 2\ ≤\ 2\ x\ - \ 4 \ < \ 8$$?
(A)
(B)
(C)
(D)
12- The diagonal of a rectangle is $$10$$ inches long and the height of the rectangle is $$8$$ inches.
What is the perimeter of the rectangle in inches?
(A) $$48$$
(B) $$30$$
(C) $$26$$
(D) $$28$$
13- The perimeter of the trapezoid below is $$36$$ cm. What is its area?
(A) $$576$$ cm$$^2$$
(B) $$70$$ cm$$^2$$
(C) $$48$$ cm$$^2$$
(D) $$24$$ cm$$^2$$
14- A card is drawn at random from a standard $$52\ –$$ card deck,
what is the probability that the card is of Hearts?
(The deck includes $$13$$ of each suit clubs, diamonds, hearts, and spades)
(A) $$\frac{1}{3}$$
(B) $$\frac{1}{4}$$
(C) $$\frac{1}{6}$$
(D) $$\frac{1}{52}$$
15- Which of the following shows the numbers in descending order?
$$\frac{2}{3} ,\ 0.68 ,\ 67\% ,\frac{4}{5}$$
(A) $$67\%,\ 0.68, \ \frac{2}{3} ,\ \frac{4}{5}$$
(B) $$67\%,\ 0.68,\ \frac{4}{5},\ \frac{2}{3}$$
(C) $$0.68,\ 67\%,\ \frac{2}{3},\ \frac{4}{5}$$
(D) $$\frac{2}{3} ,\ 67\%,\ 0.68,\ \frac{4}{5}$$
16- The mean of $$50$$ test scores was calculated as $$88$$.
But, it turned out that one of the scores was misread as $$94$$ but it was $$69$$. What is the mean?
(A) $$85$$
(B) $$87$$
(C) $$87.5$$
(D) $$88.5$$
17- Two dice are thrown simultaneously, what is the probability of getting a sum of $$6$$?
(A) $$\frac{1}{3}$$
(B) $$\frac{1}{4}$$
(C) $$\frac{1}{6}$$
(D) $$\frac{5}{36}$$
18- A swimming pool holds $$2,000$$ cubic feet of water.
The swimming pool is $$25$$ feet long and $$10$$ feet wide. How deep is the swimming pool?
(A) $$9$$
(B) $$10$$
(C) $$6$$
(D) $$8$$
19- Mr. Carlos's family is choosing a menu for their reception.
They have $$3$$ choices of appetizers, $$5$$ choices of entrees, $$4$$ choices of cake.
How many different menu combinations are possible for them to choose from?
(A) $$12$$
(B) $$32$$
(C) $$60$$
(D) $$120$$
20- Four one $$–$$ foot rulers can be split among how many users to leave each with $$\frac{1}{6}$$ of a ruler?
(A) $$4$$
(B) $$6$$
(C) $$12$$
(D) $$24$$
21- What is the area of a square whose diagonal is $$8$$?
(A) $$16$$
(B) $$32$$
(C) $$36$$
(D) $$64$$
22- Anita’s trick$$–$$or$$–$$treat bag contains $$12$$ pieces of chocolate,
$$18$$ suckers, $$18$$ pieces of gum, $$24$$ 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) $$\frac{1}{6}$$
(D) $$\frac{1}{12}$$
23- What is the missing term in the given sequence?
$$2,\ 3,\ 5,\ 8,\ 12,\ 17,\ 23,$$ ___$$,38$$
(A) 30
(B) 30
(C) 30
(D) 30
24- The perimeter of a rectangular yard is $$60$$ meters.
What is its length if its width is twice its length?
(A) $$10$$ meters
(B) $$18$$ meters
(C) $$20$$ meters
(D) $$24$$ meters
25- The average of $$6$$ numbers is $$12$$. The average of $$4$$ of those numbers is $$10$$.
What is the average of the other two numbers?
(A) $$10$$
(B) $$12$$
(C) $$14$$
(D) $$16$$
26- $$6$$. What is the value of $$x$$ in the following system of equations?
$$2 \ x \ + \ 5 \ y=11\\ 4 \ x \ - \ 2 \ y=-\ 14$$
(A) $$-\ 1$$
(B) $$1$$
(C) $$-\ 2$$
(D) $$4$$
27- The average of five numbers is $$24$$. If a sixth number $$42$$ is added, then,
what is the new average?
(A) $$25$$
(B) $$26$$
(C) $$27$$
(D) $$28$$
28- The ratio of boys and girls in a class is $$4:7$$. If there are $$44$$ students in the class,
how many more boys should be enrolled to make the ratio $$1:1$$?
(A) $$8$$
(B) $$10$$
(C) $$12$$
(D) $$14$$
29- Mr. Jones saves $$2,500$$ out of his monthly family income of $$55,000$$.
What fractional part of his income does he save?
(A) $$\frac{1}{22}$$
(B) $$\frac{1}{11}$$
(C) $$\frac{3}{25}$$
(D) $$\frac{2}{15}$$

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30- A football team had $$20,000$$ to spend on supplies.
The team spent $$14,000$$ on new balls. New sport shoes cost $$120$$ each.
Which of the following inequalities represent the number of new shoes the team can purchase.
(A) $$120\ x\ +\ 14,000\ ≤\ 20,000$$
(B) $$120\ x\ +\ 14,000\ ≥\ 20,000$$
(C) $$14,000\ x\ +\ 120\ ≤\ 20,000$$
(D) $$14,000\ x\ +\ 12,0\ ≥\ 20,000$$
31- Jason needs an $$75\%$$ average in his writing class to pass.
On his first $$4$$ exams, he earned scores of $$68\%,\ 72\%,\ 85\%,$$ and $$90\%$$.
What is the minimum score Jason can earn on his fifth and final test to pass?
(A) $$70$$
(B) $$72$$
(C) $$63$$
(D) $$60$$
32- What is the value of $$x$$ in the following equation?
$$\frac{2}{3}\ x\ +\frac{1}{6}= \frac{1}{3}$$
(A) $$6$$
(B) $$\frac{1}{2}$$
(C) $$\frac{1}{3}$$
(D) $$\frac{1}{4}$$
33- A bank is offering $$3.5\%$$ simple interest on a savings account.
If you deposit $$12,000$$, how much interest will you earn in two years?
(A) $$420$$
(B) $$840$$
(C) $$4200$$
(D) $$8400$$
34- Simplify $$6\ x^2\ y^3\ (2\ x^2\ y)^3$$=
(A) $$12\ x^4\ y^6$$
(B) $$12\ x^8\ y^6$$
(C) $$48\ x^4\ y^6$$
(D) $$48\ x^8\ y^6$$
35- What is the surface area of the cylinder below?
(A) $$48\ π\ i n^2$$
(B) $$57\ π\ i n^2$$
(C) $$66\ π\ i n^2$$
(D) $$288\ π\ i n^2$$
36- The square of a number is  $$\frac{25}{64}$$. What is the cube of that number?
(A) $$\frac{5}{8}$$
(B) $$\frac{25}{254}$$
(C) $$\frac{125}{512}$$
(D) $$\frac{125}{64}$$
37- What is the median of these numbers? $$2,\ 27,\ 28,\ 19,\ 67,\ 44,\ 35$$
(A) $$19$$
(B) $$28$$
(C) $$44$$
(D) $$35$$
38- A cruise line ship left Port A and traveled $$80$$ miles due west and then $$150$$ miles due north.
At this point, what is the shortest distance from the cruise to port A in miles?
(A) $$155$$
(B) $$165$$
(C) $$160$$
(D) $$170$$
39- What is the equivalent temperature of $$104^\circ$$F in Celsius?
$$C = \frac{5}{9}\ (F\ -\ 32)$$
(A) $$32$$
(B) $$40$$
(C) $$48$$
(D) $$52$$
40- If $$150\%$$ of a number is $$75$$, then what is the $$90\%$$ of that number?
(A) $$45$$
(B) $$50$$
(C) $$70$$
(D) $$85$$
41- What is the slope of the line: $$4\ x\ -\ 2\ y=6$$
(A) $$-3$$
(B) $$3$$
(C) $$-2$$
(D) $$2$$
42- What is the volume of a box with the following dimensions?
Hight $$= 4$$ cm        Width $$= 5$$ cm            Length $$= 6$$ cm
(A) $$15$$ cm$$^3$$
(B) $$60$$ cm$$^3$$
(C) $$90$$ cm$$^3$$
(D) $$120$$ cm$$^3$$
43- Simplify the expression.
$$(6\ x^3\ -\ 8\ x^2\ +\ 2\ x^4 )\ -\ (4\ x^2\ -\ 2\ x^4 \ +\ 2\ x^3 )$$
(A) $$4\ x^4\ +\ 4\ x^3\ -\ 12\ x^2$$
(B) $$4\ x^3\ -\ 12\ x^2$$
(C) $$8\ x^4\ +\ 4\ x^3\ -\ 12\ x^2$$
(D) $$8\ x^3\ -\ 12\ x^2$$
44- In two successive years, the population of a town is increased by $$15\%$$ and $$20\%$$.
What percent of the population is increased after two years?
(A) $$32\%$$
(B) $$35\%$$
(C) $$38\%$$
(D) $$68\%$$
45- Last week $$24,000$$ fans attended a football match.
This week three times as many bought tickets, but one-sixth of them canceled their tickets.
How many are attending this week?
(A) $$48,000$$
(B) $$54,000$$
(C) $$60,000$$
(D) $$72,000$$
46- What is the perimeter of a square in centimeters that has an area of $$595.36\ cm^2$$?
(A) 97.6
(B) 97.6
(C) 97.6
(D) 97.6

 1- Choice D is correct The correct answer is $$–\ 122$$Use PEMDAS (order of operation):$$[6\ ×\ (–\ 24)\ +\ 8]\ –\ (–\ 4)\ +\ [4\ ×\ 5]\ ÷\ 2 = [–\ 144\ +\ 8]\ –\ (–\ 4)\ +\ [20]\ ÷\ 2 =$$ $$[–\ 144\ +\ 8]\ –\ (–\ 4)\ +\ 10 =$$ $$[–\ 136]\ –\ (–\ 4) \ +\ 10 = [–\ 136]\ +\ 4\ +\ 10 = \ –\ 122$$ 2- Choice D is correct The correct answer is $$4\ x^2\ +\ 2\ x\ y \ - \ 2 \ y^2$$Use FOIL method.$$(2\ x\ +\ 2\ y)\ (2\ x\ -\ y) = 4\ x^2\ -\ 2\ x\ y\ +\ 4\ x\ y\ -\ 2\ y^2=4\ x^2\ +\ 2\ x\ y\ -\ 2\ y^2$$ 3- Choice D is correct The correct answer is $$91$$To solve absolute values equations, write two equations. $$x\ -\ 10$$ could be positive $$3$$, or negative $$3$$. Therefore, $$x\ -\ 10=3 ⇒ x=13$$$$x\ -\ 10=-\ 3 ⇒ x=7$$Find the product of solutions: $$7\ ×\ 13 = 91$$ 4- Choice B is correct The correct answer is $$-\frac{1}{2}$$The equation of a line in slope intercept form is: $$y=m\ x\ +\ b$$Solve for $$y$$.$$4\ x\ -\ 2\ y=12 ⇒ -\ 2\ y=12\ -\ 4\ x ⇒ y=(12\ -\ 4\ x)\ ÷\ (-\ 2)$$ ⇒$$y=2\ x\ -\ 6$$The slope of this line is $$2$$.The product of the slopes of two perpendicular lines is $$-\ 1$$. Therefore, the slope of a line that is perpendicular to this line is:$$m_1\ ×\ m_2 = -\ 1 ⇒ 2\ ×\ m_2 = -\ 1 ⇒ m_2 = \ -\frac{1}{2}$$ 5- Choice C is correct The correct answer is $$36$$Plug in the value of$$x$$ and $$y$$. $$x=3$$ and $$y=-\ 2$$$$5\ (x\ -\ 2\ y)\ +\ (2\ -\ x)^2= 5\ (3\ -\ 2\ (-\ 2))\ +\ (2\ -\ 3)^2=5\ (3\ +\ 4)\ +\ (-\ 1)^2 =36$$ 6- Choice C is correct The correct answer is $$10$$Let $$x$$ be the number. Write the equation and solve for $$x$$. $$40\%$$ of $$x=4⇒ 0.40\ x=4 ⇒ x=4\ ÷\ 0.40=10$$ 7- Choice A is correct The correct answer is $$3$$$$A$$ is $$4$$ times of $$B$$, then: $$A$$ = $$4\ B$$ ⇒ $$(A = 12)\ 12 = 4\ ×\ B ⇒ B = 12\ ÷\ 4 = 3$$ 8- Choice C is correct The correct answer is $$6$$ hoursThe distance between Jason and Joe is $$9$$ miles. Jason running at $$5.5$$ miles per hour and Joe is running at the speed of $$7$$ miles per hour. Therefore, every hour the distance is $$1.5$$ miles less. $$9\ ÷\ 1.5 = 6$$ 9- Choice D is correct The correct answer is $$80\%$$ The failing rate is $$11$$ out of $$55 = \frac{11}{55}$$Change the fraction to percent:$$\frac{11}{55} ×\ 100\%=20\%$$$$20$$ percent of students failed. Therefore, $$80$$ percent of students passed the exam. 10- Choice D is correct The correct answer is $$729$$ $$3^6 = 3\ ×\ 3\ ×\ 3\ ×\ 3\ ×\ 3\ ×\ 3 = 729$$ 11- Choice D is correct Solve for $$x$$.$$-\ 2\ ≤\ 2\ x\ -\ 4\ <\ 8$$ ⇒ (add $$4$$ all sides) $$-\ 2\ +\ 4\ ≤\ 2\ x\ -\ 4\ +\ 4\ <\ 8\ +\ 4$$ ⇒ $$2\ ≤\ 2\ x\ <\ 12$$ ⇒ (divide all sides by $$2$$) $$1\ ≤\ x\ <\ 6$$$$x$$ is between $$1$$ and $$6$$ 12- Choice D is correct The correct answer is $$28$$Let $$x$$ be the width of the rectangle. Use Pythagorean Theorem: $$a^2\ +\ b^2 = c^2$$$$x^2\ +\ 8^2 = 10^2 ⇒ x^2\ +\ 64 = 100 ⇒ x^2 = 100\ –\ 64 = 36 ⇒ x = 6$$Perimeter of the rectangle $$= 2$$ (length $$+$$ width) $$= 2\ (8\ +\ 6) = 2\ (14) = 28$$ 13- Choice B is correct The correct answer is $$70$$ cm$$^2$$ The perimeter of the trapezoid is $$36$$ cm.Therefore, the missing side (height) is $$= 36\ –\ 8\ –\ 12\ –\ 6 = 10$$Area of a trapezoid: A = $$\frac{1}{2}\ h\ (b_1\ +\ b_2) = \frac{1}{2}\ (10)\ (6\ +\ 8) = 70$$ 14- Choice B is correct The correct answer is $$\frac{1}{4}$$The probability of choosing a Hearts is $$\frac{13}{52} =\frac{1}{4}$$ 15- Choice D is correct The correct answer is $$\frac{2}{3} ,\ 67\%,\ 0.68,\ \frac{4}{5}$$$$\frac{2}{3} = 0.666…$$$$0.68$$ $$67\% = 0.67$$$$\frac{4}{5} = 0.80$$Therefore$$\frac{2}{3}\ <\ 67\%\ <\ 0.68\ <\ \frac{4}{5}$$ 16- Choice C is correct The correct answer is $$87.5$$average (mean) $$=\frac{sum\ of\ terms}{number\ of\ terms} ⇒ 88 =\frac{sum\ of\ terms}{50} ⇒ sum = 88\ ×\ 50 = 4400$$The difference of $$94$$ and $$69$$ is $$25$$. Therefore, $$25$$ should be subtracted from the sum.$$4400\ –\ 25 = 4375$$mean $$=\frac{sum\ of\ terms}{number\ of\ terms}$$ ⇒ mean =$$\frac{4375}{50} = 87.5$$ 17- Choice D is correct The correct answer is $$\frac{5}{36}$$To get a sum of $$6$$ for two dice, we should get $$3$$ and $$3$$, or $$2$$ and $$4$$, or $$4$$ and $$2$$, or $$1$$ and $$5$$, or $$5$$ and $$1$$. Therefore, there are $$5$$ options. Since, we have $$6\ ×\ 6 = 36$$ total options, the probability of getting a sum of $$6$$ is $$5$$ out of $$36$$ or $$\frac{5}{36}$$. 18- Choice D is correct The correct answer is $$8$$Use formula of rectangle prism volume.V $$=$$ (length) (width) (height) ⇒ $$2000 = (25)\ (10)$$ (height) ⇒ height $$= 2000\ ÷\ 250 = 8$$ 19- Choice C is correct The correct answer is $$60$$To find the number of possible outfit combinations, multiply the number of options for each factor:$$3\ ×\ 5\ ×\ 4 = 60$$ 20- Choice D is correct The correct answer is $$24$$$$4\ ÷\ \frac{1}{6} = 24$$ 21- Choice B is correct The correct answer is $$32$$The diagonal of the square is $$8$$. Let $$x$$ be the side. Use Pythagorean Theorem: $$a^2\ +\ b^2 = c^2$$$$x^2\ +\ x^2 = 8^2 ⇒ 2\ x^2 = 8^2 ⇒ 2\ x^2 = 64 ⇒x^2 = 32 ⇒\ x= \sqrt{32}$$The area of the square is:$$\sqrt{32}\ ×\ \sqrt{32} = 32$$ 22- Choice B is correct The correct answer is $$\frac{1}{4}$$Probability $$=\frac{number \ of\ desired\ outcomes}{number \ of\ total\ outcomes} = \frac{18}{12\ +\ 18\ +\ 18\ +\ 24} = \frac{18}{72} = \frac{1}{4}$$ 23- Choice D is correct The correct answer is $$30$$Find the difference of each pairs of numbers: $$2,\ 3,\ 5,\ 8,\ 12,\ 17,\ 23,$$ ___$$,\ 38$$The difference of $$2$$ and $$3$$ is $$1,\ 3$$ and $$5$$ is $$2,\ 5$$ and $$8$$ is $$3,\ 8$$ and $$12$$ is $$4,\ 12$$ and $$17$$ is $$5,\ 17$$ and $$23$$ is $$6,\ 23$$ and next number should be $$7$$. The number is $$23\ +\ 7 = 30$$ 24- Choice A is correct The correct answer is $$10$$ metersThe 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) $$= 2\ (2\ x\ +\ x)=60 ⇒ 6\ x=60 ⇒ x=10$$The length of the rectangle is $$10$$ meters. 25- Choice D is correct The correct answer is $$16$$average $$=\frac{sum\ of\ terms}{number\ of\ terms}$$ ⇒ (average of $$6$$ numbers) $$12 = \frac{sum\ of\ numbers}{6}$$ ⇒sum of $$6$$ numbers is $$12\ ×\ 6 = 72$$(average of $$4$$ numbers) $$10 =\frac{sum\ of\ numbers}{4}$$ ⇒sum of $$4$$ numbers is $$10\ ×\ 4 = 40$$sum of $$6$$ numbers $$–$$ sum of $$4$$ numbers $$=$$ sum of $$2$$ numbers$$72\ –\ 40 = 32$$average of $$2$$ numbers $$=\frac{32}{2} = 16$$ 26- Choice C is correct The correct answer is $$-\ 2$$Solving Systems of Equations by EliminationMultiply the first equation by $$(–2)$$, then add it to the second equation.\cfrac{\begin{align}-\ 2\ (2\ x\ +\ 5\ y= 11) \\ \ 4\ x\ -\ 2\ y=-\ 14 \end{align}}{} $$⇒-\ 4\ x\ -\ 10\ y= -\ 22\\4\ x\ -\ 2\ y=-\ 14 ⇒ -\ 12\ y= -\ 36 ⇒ y= 3$$Plug in the value of $$y$$ into one of the equations and solve for $$x$$.$$2\ x\ +\ 5\ (3)= 11 ⇒ 2\ x\ +\ 15= 11 ⇒ 2\ x= -\ 4 ⇒ x= -\ 2$$ 27- Choice C is correct The correct answer is $$27$$Solve for the sum of five numbers. average $$=\frac{sum\ of\ terms}{number\ of\ terms} ⇒ 24 = \frac{sum\ of\ 5\ numbers}{5}$$ ⇒ sum of $$5$$ numbers $$= 24\ ×\ 5 = 120$$The sum of $$5$$ numbers is $$120$$. If a sixth number $$42$$ is added, then the sum of $$6$$ numbers is $$120\ +\ 42 = 162$$average $$=\frac{sum\ of\ terms}{number\ of\ terms} =\frac{162}{6} = 27$$ 28- Choice C is correct The correct answer is $$12$$The ratio of boys to girls is $$4:7$$. Therefore, there are $$4$$ boys out of $$11$$ students. To find the answer, first, divide the total number of students by $$11$$, then multiply the result by $$4$$. $$44\ ÷\ 11 = 4 ⇒ 4\ ×\ 4 = 16$$There are $$16$$ boys and $$28\ (44\ –\ 16)$$ girls. So, $$12$$ more boys should be enrolled to make the ratio $$1:1$$ 29- Choice A is correct The correct answer is $$\frac{1}{22}$$$$2,500$$ out of $$55,000$$ equals to $$\frac{2500}{55000} =\frac{25}{550} =\frac{1}{22}$$ 30- Choice A is correct The correct answer is $$120\ x\ +\ 14,000\ ≤\ 20,000$$Let $$x$$ be the number of new shoes the team can purchase. Therefore, the team can purchase $$120\ x$$.The team had $$20,000$$ and spent $$14000$$. Now the team can spend on new shoes $$6000$$ at most. Now, write the inequality:$$120\ x\ +\ 14,000\ ≤\ 20,000$$ 31- Choice D is correct The correct answer is $$60$$Jason needs an $$75\%$$ average to pass for five exams. Therefore, the sum of $$5$$ exams must be at lease $$5\ ×\ 75 = 375$$The sum of $$4$$ exams is:$$68\ +\ 72\ +\ 85\ +\ 90 = 315$$.The minimum score Jason can earn on his fifth and final test to pass is:$$375\ –\ 315 = 60$$ 32- Choice D is correct The correct answer is $$\frac{1}{4}$$Isolate and solve for $$x$$.$$\frac{2}{3}\ x\ +\ \frac{1}{6}= \frac{1}{3} ⇒ \frac{2}{3}\ x= \frac{1}{3}\ -\frac{1}{6} =\frac{1}{6} ⇒ \frac{2}{3}\ x=\frac{1}{6}$$ Multiply both sides by the reciprocal of the coefficient of $$x$$.$$(\frac{3}{2})\ \frac{2}{3}\ x= \frac{1}{6}\ (\frac{3}{2}) ⇒ x= \frac{3}{12}=\frac{1}{4}$$ 33- Choice B is correct The correct answer is $$840$$Use simple interest formula:$$I=$$prt$$(I =$$ interest, $$p =$$ principal, $$r =$$ rate, $$t =$$ time)$$I=(12000)\ (0.035)\ (2)=840$$ 34- Choice D is correct The correct answer is $$48\ x^8\ y^6$$Simplify. $$6\ x^2\ y^3\ (2\ x^2\ y)^3= 6\ x^2\ y^3\ (8\ x^6\ y^3 ) = 48\ x^8\ y^6$$ 35- Choice C is correct The correct answer is $$66\ π\ i n^2$$Surface Area of a cylinder $$= 2\ π\ r\ (r\ +\ h)$$,The radius of the cylinder is $$3\ (6\ ÷\ 2)$$ inches and its height is $$8$$ inches. Therefore, Surface Area of a cylinder $$= 2\ π\ (3)\ (3\ +\ 8) = 66\ π$$ 36- Choice C is correct The correct answer is $$\frac{125}{512}$$The square of a number is $$\frac{25}{64}$$, then the number is the square root of $$\frac{25}{64}$$$$\sqrt{\frac{25}{64}}=\frac{5}{8}$$The cube of the number is:$$(\frac{5}{8})^3 =\frac{125}{512}$$ 37- Choice B is correct The correct answer is $$28$$Write the numbers in order:$$2,\ 19,\ 27,\ 28,\ 35,\ 44,\ 67$$The Median is the number in the middle. So, the median is $$28$$. 38- Choice D is correct The correct answer is $$170$$Use the information provided in the question to draw the shape.Use Pythagorean Theorem: $$a^2\ +\ b^2 = c^2$$$$80^2\ +\ 150^2 = c^2 ⇒ 6400\ +\ 22500 = c^2 ⇒ 28900 = c^2 ⇒ c = 170$$ 39- Choice B is correct The correct answer is $$40$$Plug in $$104$$ for F and then solve for $$C$$.$$C = \frac{5}{9}\ (F\ –\ 32) ⇒ C = \frac{5}{9}\ (104\ –\ 32) ⇒ C = \frac{5}{9}\ (72) = 40$$ 40- Choice A is correct The correct answer is $$45$$First, find the number.Let $$x$$ be the number. Write the equation and solve for $$x$$. $$150\%$$ of a number is $$75$$, then:$$1.5\ ×\ x=75 ⇒ x=75\ ÷\ 1.5=50$$$$90\%$$ of $$50$$ is:$$0.9\ × \ 50 = 45$$ 41- Choice D is correct The correct answer is $$2$$Solve for $$y$$.$$4\ x\ -\ 2\ y=6 ⇒ -\ 2\ y=6\ -\ 4\ x ⇒ y=2\ x\ -\ 3$$ The slope of the line is $$2$$. 42- Choice D is correct The correct answer is $$120$$ cm$$^3$$Volume of a box = length $$×$$ width $$×$$ height $$= 4\ ×\ 5\ ×\ 6 = 120$$ 43- Choice A is correct The correct answer is $$4\ x^4\ +\ 4\ x^3\ -\ 12\ x^2$$$$(6\ x^3\ -\ 8\ x^2\ +\ 2\ x^4 )\ -\ (4\ x^2\ -\ 2\ x^4\ +\ 2\ x^3 ) ⇒ (6\ x^3\ -\ 8\ x^2\ +\ 2\ x^4 )\ -\ 4\ x^2\ +\ 2\ x^4\ -\ 2\ x^3 ⇒ 4\ x^4\ +\ 4\ x^3\ -\ 12\ x^2$$ 44- Choice C is correct The correct answer is $$38\%$$the population is increased by $$15\%$$ and $$20\%$$. $$15\%$$ increase changes the population to $$115\%$$ of original population. For the second increase, multiply the result by $$120\%$$.$$(1.15)\ ×\ (1.20) = 1.38 = 138\%$$$$38$$ percent of the population is increased after two years. 45- Choice C is correct The correct answer is $$60,000$$Three times of $$24,000$$ is $$72,000$$. One-sixth of them canceled their tickets.One-sixth of $$72,000$$ equals $$12,000\ (\frac{1}{6}\ ×\ 72000 = 12000)$$. $$60,000\ (72000\ –\ 12000 = 60000)$$ fans are attending this week 46- Choice D is correct The correct answer is $$97.6$$The area of the square is $$595.36$$. Therefore, the side of the square is the square root of the area.$$\sqrt{595.36}=24.4$$Four times the side of the square is the perimeter:$$4\ × \ 24.4 = 97.6$$

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