## Full Length TASC Mathematics Practice Test

The best way to prepare for the TASC math test is by taking a practice test. Not only will this simulate what it would be like on exam day, but this will help you feel more confident and measure your readiness to take the actual exam.

In order to get the most out of this practice test and prepare your mind, body, and spirit for the actual TASC Math test (which is also a realistic resource), we recommend you treat it as if it were an actual one. Clear away any distractions with scratch paper in hand, pencil ready to go, timer ticking down every second as well as calculator on standby. Take this in one sitting so you can quickly assess your score at the end!

Take this practice test to simulate the experience of taking a full-length TASC Math Test Day. After you've finished, use the answer keys to score your tests. Best of luck!

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TASC Mathematics
Practice Test 3

Section 1

(Calculator)

40 questions

Total time for this section: 50 Minutes

You may use a calculator on this Section.

1- If $$50\%$$ of A is $$25%$$ of B, then B is what percent of A?
(A) $$200\%$$
(B) $$250\%$$
(C) $$150\%$$
(D) $$180\%$$
2- Find the average of the following numbers: $$17, 13, 7, 21, 22$$
(A) $$17$$
(B) $$16$$
(C) $$22$$
(D) $$25$$
3- John traveled $$180$$ km in $$3$$ hours and Alice traveled $$270$$ km in $$9$$ hours. What is the ratio of the average speed of John to average speed of Alice?
(A) $$2 : 1$$
(B) $$2 : 3$$
(C) $$1 : 3$$
(D) $$1 : 5$$
4- The width of a box is one third of its length. The height of the box is one third of its width. If the length of the box is $$36$$ cm, what is the volume of the box?
(A) $$1,728$$ cm$$^3$$
(B) $$1,490$$ cm$$^3$$
(C) $$1,569$$ cm$$^3$$
(D) $$1,289$$ cm$$^3$$
5- When a number is subtracted from $$25$$ and the difference is divided by that number, the result is $$4$$. What is the value of the number?
(A) $$4$$
(B) $$10$$
(C) $$8$$
(D) $$5$$
6- What is the value of $$7^4$$?
(A) $$2,809$$
(B) $$1,979$$
(C) $$2,379$$
(D) $$2,401$$
7- $$27$$ is What percent of $$30$$?
(A) $$90\%$$
(B) $$99\%$$
(C) $$85\%$$
(D) $$78\%$$
8- Right triangle ABC has two legs of lengths $$5$$ cm (AB) and $$12$$ cm (AC). What is the length of the third side (BC)?
(A) $$18$$ cm
(B) $$12$$ cm
(C) $$21$$ cm
(D) $$13$$ cm
9- An angle is equal to one eighth of its supplement. What is the measure of that angle?
(A) $$20^\circ$$
(B) $$22^\circ$$
(C) $$32^\circ$$
(D) $$18^\circ$$
10- In five successive hours, a car travels $$35$$ km, $$40$$ km, $$45$$ km, $$25$$ km and $$50$$ km. In the next five hours, it travels with an average speed of $$45$$ km per hour. Find the total distance the car traveled in $$10$$ hours.
(A) $$401$$
(B) $$391$$
(C) $$430$$
(D) $$420$$
11- A taxi driver earns $$12$$ per $$1-$$hour work. If he works $$8$$ hours a day and in $$1$$ hour he uses $$2-$$liters petrol with price $$1$$ for $$1-$$liter. How much money does he earn in one day?
(A) $$75$$
(B) $$80$$
(C) $$86$$
(D) $$92$$
12- How long does a $$380–$$miles trip take moving at $$40$$ miles per hour (mph)?
(A) $$8$$ hours and $$30$$ minutes
(B) $$8$$ hours and $$25$$ minutes
(C) $$10$$ hours and $$25$$ minutes
(D) $$9$$ hours and $$30$$ minutes
13- A $$50$$ shirt now selling for $$25$$ is discounted by what percent?
(A) $$50\%$$
(B) $$29\%$$
(C) $$64\%$$
(D) $$25\%$$
14- The ratio of boys and girls in a class is $$3:8$$. If there are $$55$$ students in the class, how many more boys should be enrolled to make the ratio $$1:1$$?
(A) $$15$$
(B) $$12$$
(C) $$18$$
(D) $$10$$
15- A rope weighs $$700$$ grams per meter of length. What is the weight in kilograms of $$13.2$$ meters of this rope? ($$1$$ kilograms $$= 1000$$ grams)
(A) $$9.350$$ kg
(B) $$9.240$$ kg
(C) $$10.210$$ kg
(D) $$10.250$$ kg
16- The average weight of $$15$$ girls in a class is $$60$$ kg and the average weight of $$30$$ boys in the same class is $$66$$ kg. What is the average weight of all the $$75$$ students in that class?
(A) $$69$$ kg
(B) $$72$$ kg
(C) $$64$$ kg
(D) $$59$$ kg
17- Which of the following could be the product of two consecutive prime numbers?
(A) $$2$$
(B) $$10$$
(C) $$14$$
(D) $$15$$
18- The price of a car was $$20,000$$ in $$2016$$, $$18,000$$ in $$2018$$ and $$16,200$$ in $$2019$$. What is the rate of depreciation of the price of car per year?
(A) $$10\%$$
(B) $$20\%$$
(C) $$25\%$$
(D) $$15\%$$
19- Sophia purchased a sofa for $$560.50$$. The sofa is regularly priced at $$1,121$$. What was the percent discount Sophia received on the sofa?
(A) $$50\%$$
(B) $$40\%$$
(C) $$60\%$$
(D) $$65\%$$
20- The price of a sofa is decreased by $$15\%$$ to $$748$$. What was its original price?
(A) $$820$$
(B) $$950$$
(C) $$790$$
(D) $$880$$
21- The score of Emma was one third that of Ava and the score of Mia was twice that of Ava. If the score of Mia was $$90$$, what is the score of Emma?
(A) $$12$$
(B) $$18$$
(C) $$15$$
(D) $$25$$
22- The average of five consecutive numbers is $$32$$. What is the smallest number?
(A) $$36$$
(B) $$30$$
(C) $$25$$
(D) $$15$$
23- The price of a laptop is decreased by $$10\%$$ to $$378$$. What is its original price?
(A) $$449$$
(B) $$378$$
(C) $$420$$
(D) $$398$$
24- What is the median of these numbers? $$4, 9, 13, 8, 15, 18, 5$$
(A) $$9$$
(B) $$18$$
(C) $$15$$
(D) $$13$$
25- If $$35\%$$ of a class are girls, and $$20\%$$ of girls play tennis, what percent of the class play tennis?
(A) $$7\%$$
(B) $$13\%$$
(C) $$9\%$$
(D) $$19\%$$
26- One third of $$12$$ is equal to $$\frac{2}{3}$$ of what number?
(A) $$9$$
(B) $$12$$
(C) $$6$$
(D) $$7$$
27- How many tiles of $$10$$ cm$$^2$$ is needed to cover a floor of dimension $$8$$ cm by $$35$$ cm?
(A) $$28$$
(B) $$24$$
(C) $$32$$
(D) $$36$$
28- Which of the following values for $$x$$ and $$y$$ satisfy the following system of equations?
$$\begin{cases}x \ + \ 2 \ y = 12\\3 \ x \ + \ 5 \ y= 18\end{cases}$$
(A) $$x=24, \ y=15$$
(B) $$x=24, \ y=- \ 18$$
(C) $$x=- \ 24, \ y=18$$
(D) $$x=- \ 18, \ y=24$$
29- A chemical solution contains $$5\%$$ alcohol. If there is $$30$$ ml of alcohol, what is the volume of the solution?
(A) $$450$$ ml
(B) $$550$$ ml
(C) $$700$$ ml
(D) $$600$$ ml

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30- The surface area of a cylinder is $$150 \ π$$ cm$$^2$$. If its height is $$10$$ cm, what is the radius of the cylinder?
(A) $$15$$ cm
(B) $$- \ 15$$ cm
(C) $$5$$ cm
(D) $$10$$ cm
31- In $$2000$$, the average worker's income increased $$4,000$$ per year starting from $$21,000$$ annual salary. Which equation represents income greater than average? ($$I =$$ income, $$x =$$ number of years after $$2000$$)
(A) $$I \ \leq \ 4000 \ x \ - \ 21000$$
(B) $$I \ \geq \ - \ 4000 \ x \ + \ 21000$$
(C) $$I \ > \ 4000 \ + \ 21000 \ x$$
(D) $$I \ > \ 4000 \ x \ + \ 21000$$
32- A bank is offering $$4\%$$ simple interest on a savings account. If you deposit $$7,000$$, how much interest will you earn in three years?
(A) $$868$$
(B) $$820$$
(C) $$834$$
(D) $$840$$
33- A boat sails $$40$$ miles south and then $$30$$ miles east. How far is the boat from its start point?
(A) $$50$$ miles
(B) $$36$$ miles
(C) $$49$$ miles
(D) $$60$$ miles
34- A bag contains $$18$$ balls: two green, five black, eight blue, a brown, a red and one white. If $$17$$ balls are removed from the bag at random, what is the probability that a brown ball has been removed?
(A) $$\frac{17}{18}$$
(B) $$\frac{18}{17}$$
(C) $$\frac{1}{17}$$
(D) $$\frac{1}{18}$$
35- The area of a circle is less than $$49 \ π$$. Which of the following can be the circumference of the circle? (Select one or more answer choices)
(A) $$12 \ \pi$$
(B) $$15 \ \pi$$
(C) $$18 \ \pi$$
(D) $$20 \ \pi$$
36- Which of the following lists shows the fractions in order from least to greatest?
$$\frac{3}{4}, \frac{ 2}{7}, \frac{3}{8}, \frac{ 5}{11}$$
(A) $$\frac{2}{7}, \frac{3}{8}, \frac{5}{11}, \frac{3}{4}$$
(B) $$\frac{3}{4}, \frac{2}{7}, \frac{5}{11}, \frac{3}{8}$$
(C) $$\frac{3}{8}, \frac{2}{7}, \frac{3}{4}, \frac{5}{11}$$
(D) $$\frac{5}{11}, \frac{3}{4}, \frac{2}{7}, \frac{3}{8}$$
37- The marked price of a computer is D dollar. Its price decreased by (20\%\) in January and later increased by $$10\%$$ in February. What is the final price of the computer in D dollar?
(A) $$0.80$$ D
(B) $$0.88$$ D
(C) $$80$$ D
(D) $$88$$ D
38- How many possible outfit combinations come from seven shirts, two slacks, and five ties?
(A) $$64$$
(B) $$75$$
(C) $$85$$
(D) $$70$$
39- In the $$x \ y-$$plane, the point $$(5,3)$$ and $$(6,4)$$ are on line A. Which of the following points could also be on line A? (Select one or more answer choices)
(A) $$(- \ 1, 2)$$
(B) $$(5, 7)$$
(C) $$(3, 4)$$
(D) $$(- \ 1, - \ 2)$$
40- If the area of trapezoid is $$126$$ cm, what is the perimeter of the trapezoid?
(A) $$65$$ cm
(B) $$38$$ cm
(C) $$46$$ cm
(D) $$40$$ cm

TASC Mathematics
Practice Test 3

Section 2

(No Calculator)

12 questions

Total time for this section: 55 Minutes

You may NOT use a calculator on this Section.

41- If $$2 \ x \ - \ 6=10.5$$, What is the value of $$3 \ x \ + \ 2$$?
(A) 26.75
(B) 26.75
(C) 26+0.75
(D) 26 +0.75
(E) 26 + 0.75
(F) 26+3/4
(G) 26+(3/4)
(H) 26 +(3/4)
(I) 26 + (3/4)
42- $$- \ 16 \ + \ 6 \ × \ (– \ 5) \ – \ [6 \ + \ 22 \ × \ (- \ 4)] \ ÷ \ 2 \ + \ 5=$$?
(A) -2
(B) - 2
(C) - 2
43- What is the value of $$f(3)$$ for the following function $$f$$?
$$f(x)=x^2 \ + \ 4 \ x$$
(A) 21
(B) 21.0
(C) 21
44- The perimeter of the trapezoid below is $$58$$. What is its area?
(A) 220
(B) 220
(C) 220.0
45- If $$\frac{x \ + \ 2}{3}=N$$ and $$N=5$$, what is the value of $$x$$?
(A) 13
(B) 13.0
(C) 13
46- The volume of cube A is $$\frac{1}{4}$$ of its surface area. What is the length of an edge of cube A?
(A) 3/2
(B) 3/2
(C) 1.5
(D) 1+0.5
(E) 1 +0.5
(F) 1 + 0.5
47- What is the area of an isosceles right triangle that has one leg that measures $$4$$?
(A) 8
(B) 8
(C) 8.0
48- The average of $$13, 16, 24$$ and $$x$$ is $$15$$. What is the value of $$x$$?
(A) 7
(B) 7.0
(C) 7.0
49- A ladder leans against a wall forming a $$60^\circ$$ angle between the ground and the ladder. If the bottom of the ladder is $$45$$ feet away from the wall, how many feet is the ladder?
(A) 90
(B) 90 degrees
(C) 90
50- From last year, the price of gasoline has increased from $$1.30$$ per gallon to $$1.75$$ per gallon. The new price is what percent of the original price?
(A) 150
(B) 150.0
(C) 150
51- If the ratio of $$3 \ a$$ to $$4 \ b$$ is $$\frac{1}{10}$$, what is the ratio of $$a$$ to $$b$$?
(A) 0.2
(B) 0.2
(C) 1/5
(D) 1/5
(E) 0.20
52- A construction company is building a wall. The company can build $$50$$ cm of the wall per minute. After $$45$$ minutes $$\frac{2}{3}$$ of the wall is completed. How many meters is the wall?
(A) 33.75
(B) 33.75
(C) 33+3/4
(D) 33+(3/4)
(E) 33 + (3/4)
 1- Choice A is correct The correct answer is $$200\%$$Write the equation and solve for B:$$0.50$$ A $$= 0.25$$ B, divide both sides by $$0.25$$, then:$$0.65/0.25$$ A $$=$$ B, therefore: B $$=2$$ A, and B is $$2$$ times of A or it’s $$200\%$$ of A. 2- Choice B is correct The correct answer is $$16$$average $$= \frac{sum \ of \ terms}{ number \ of \ terms}=\frac{17 \ + \ 13 \ + \ 7 \ + \ 21 \ + \ 22}{5} = 805 = 16$$ 3- Choice A is correct The correct answer is $$2 : 1$$The average speed of john is: $$180 \ ÷ \ 3=60$$ km$$/$$hThe average speed of Alice is: $$270 \ ÷ \ 9=30$$ km$$/$$hWrite the ratio and simplify.$$60 : 30 ⇒ 2 : 1$$ 4- Choice A is correct The correct answer is $$1728$$ cm$$^3$$ If the length of the box is $$36$$, then the width of the box is one third of it, $$12$$, and the height of the box is $$4$$ (one third of the width).The volume of the box is:V $$=$$ lwh $$= (36) \ (12) \ (4) = 1728$$ 5- Choice D is correct The correct answer is $$5$$Let $$x$$ be the number.Write the equation and solve for $$x$$.$$(25 \ – \ x) \ ÷ \ x = 4$$Multiply both sides by $$x$$.$$(25 \ – \ x) = 4 \ x$$, then add both sides.$$25 = 5 \ x$$, now divide both sides by 5. $$x = 5$$ 6- Choice D is correct The correct answer is $$2,401$$$$7^4=7 \ × \ 7 \ × \ 7 \ × \ 7=2,401$$ 7- Choice A is correct The correct answer is $$90\%$$Use percent formula: part $$=\frac{ percent}{100} \ ×$$ whole$$27=\frac{percent}{100} \ × \ 30 ⇒$$$$27=\frac{ percent \ × \ 30}{100} ⇒$$$$27=\frac{percent \ × \ 3}{10}$$, multiply both sides by $$10$$.$$270=$$ percent $$× \ 3$$, divide both sides by $$3$$. $$90=$$ percent 8- Choice D is correct The correct answer is $$13$$ cmUse Pythagorean Theorem: $$a^2 \ + \ b^2=c^2$$$$5^2 \ + \ 12^2 = c^2 ⇒$$$$25 \ + \ 144=c^2 ⇒$$$$169=c^2⇒$$$$c=13$$ cm 9- Choice A is correct The correct answer is $$20^\circ$$The sum of supplement angles is $$180$$. Let $$x$$ be that angle.Therefore, $$x \ + \ 8\ x = 180$$$$9 \ x = 180$$, divide both sides by $$9: \ x = 20^\circ$$ 10- Choice D is correct The correct answer is $$420$$Add the first $$5$$ numbers.$$35 \ + \ 40 \ + \ 45 \ + \ 25 \ + \ 50 = 195$$To find the distance traveled in the next $$5$$ hours, multiply the average by number of hours.Distance $$=$$ Average $$×$$ Rate $$= 45 \ × \ 5 = 225$$Add both numbers.$$225 \ + \ 195 = 420$$ 11- Choice B is correct The correct answer is $$80$$$$12×8=96$$, Petrol use: $$8 \ × \ 2=16$$ litersPetrol cost: $$16 \ × \ 1=16$$Money earned: $$96 \ − \ 16=80$$ 12- Choice D is correct The correct answer is $$9$$ hours and $$30$$ minutesUse distance formula: Distance $$=$$ Rate $$×$$ time $$⇒ 380 = 40 \ ×$$ T, divide both sides by $$40$$.$$380 / 40 =$$ T $$⇒$$ T $$= 9.5$$ hours.Change hours to minutes for the decimal part.$$0.5$$ hours $$= 0.5 \ × \ 60 = 30$$ minutes. 13- Choice A is correct The correct answer is $$50\%$$Use the formula for Percent of Change $$\frac{New \ Value \ − \ Old \ Value}{old \ value} \ × \ 100\%$$$$\frac{25−50}{50} \ × \ 100\%= \ – \ 50\%$$ (Negative sign here means that the new price is less than old price). 14- Choice A is correct The correct answer is $$15$$The ratio of boy to girls is $$3:8$$. Therefore, there are $$3$$ boys out of $$11$$ students.To find the answer, first divide the total number of students by $$11$$, then multiply the result by $$3$$.$$55 \ ÷ \ 11=5 ⇒ 5 \ × \ 3=15$$There are $$15$$ boys and $$30 \ (55 \ – \ 15)$$ girls.So, $$15$$ more boys should be enrolled to make the ratio $$1:1$$ 15- Choice B is correct The correct answer is $$9.240$$ kgThe weight of $$13.2$$ meters of this rope is: $$13.3 \ × \ 700$$ g $$=9,240$$ g$$1$$ kg $$= 1,000$$ g, therefore, $$9,240$$ g $$÷ \ 1000=9.24$$ kg 16- Choice C is correct The correct answer is $$64$$ kgaverage $$=\frac{sum \ of \ terms}{ number \ of \ terms}$$The sum of the weight of all girls is: $$15 \ × \ 60=900$$ kgThe sum of the weight of all boys is: $$30 \ × \ 66=1,980$$ kgThe sum of the weight of all students is: $$900 \ + \ 1,980=2,880$$ kgaverage $$=\frac{2,880}{45}=64$$ 17- Choice D is correct The correct answer is $$15$$Some of prime numbers are: $$2, 3, 5, 7, 11, 13$$Find the product of two consecutive prime numbers:$$2 \ × \ 3 = 6$$ (not in the options)$$3 \ × \ 5 = 15$$ (bingo!)$$5 \ × \ 7 = 35$$ (not in the options)$$7 \ × \ 11 = 77$$ (not in the options) 18- Choice A is correct The correct answer is $$10\%$$Use this formula: Percent of Change $$\frac{New \ Value \ − \ Old Value}{pld \ value} \ × \ 100\%$$$$\frac{18,000 \ − \ 20,000 }{20,000} \ × \ 100\%=10\%$$ and$$\frac{16,200 \ − \ 18,000}{18000} \ × \ 100\%=10\%$$ 19- Choice A is correct The correct answer is $$50\%$$The question is this: $$560.50$$ is what percent of $$1,121$$?Use percent formula:part $$=\frac{percent}{100} \ ×$$ whole$$560.50= \frac{percent}{100} × \ 1,121 ⇒ 560.50=\frac{ percent \ × \ 1,121}{100 }⇒$$$$56050 =$$ percent $$× \ 1.121 ⇒$$percent $$=\frac{56050}{1,121}=50$$$$560.50$$ is $$50\%$$ of $$1,121$$.Therefore, the discount is: $$100\% \ – \ 50\%=50\%$$ 20- Choice D is correct The correct answer is $$880$$Let $$x$$ be the original price.If the price of the sofa is decreased by $$15\%$$ to $$748$$, then:$$85\%$$ of $$x=748 ⇒ 0.85 \ x =748 ⇒$$$$x=748 \ ÷ \ 0.85=880$$ 21- Choice C is correct The correct answer is $$15$$If the score of Mia was $$90$$, therefore the score of Ava is $$45$$. Since, the score of Emma was one third as that of Ava, therefore, the score of Emma is $$15$$. 22- Choice B is correct The correct answer is $$30$$Let $$x$$ be the smallest number.Then, these are the numbers:$$x, x \ + \ 1, x \ + \ 2, x \ + \ 3, x \ +\ 4$$average $$= \frac{sum \ of \ terms}{ number \ of \ terms} ⇒ 32=\frac{x \ + \ (x \ + \ 1) \ + \ (x \ + \ 2) \ + \ (x \ + \ 3) \ + \ (x \ + \ 4)}{5}⇒32=\frac{5 \ x \ +10}{5 }⇒ 160=5 \ x \ + \ 10 ⇒ 150=5 \ x ⇒ x=30$$ 23- Choice C is correct The correct answer is $$420$$Let $$x$$ be the original price.If the price of a laptop is decreased by $$10\%$$ to $$378$$, then:$$90\%$$ of $$x=378 ⇒ 0.90 \ x=378 ⇒ x=378 \ ÷ \ 0.90=420$$ 24- Choice A is correct The correct answer is $$9$$Write the numbers in order:$$4, 5, 8, 9, 13, 15, 18$$Since we have $$7$$ numbers ($$7$$ is odd), then the median is the number in the middle, which is $$9$$. 25- Choice A is correct The correct answer is $$7\%$$The percent of girls playing tennis is:$$35\% \ × \ 20\% = 0.35 \ × \ 0.20 = 0.07 = 7\%$$ 26- Choice C is correct The correct answer is $$6$$Let $$x$$ be the number.Write the equation and solve for $$x$$.$$\frac{1}{3} \ × \ 12= \frac{2}{3} \ x$$. $$x ⇒ \frac{1 \ × \ 12}{3}= \frac{2 \ x}{3}$$ , use cross multiplication to solve for $$x$$.$$3 \ × \ 12=2 \ x \ × \ 3 ⇒36=6 \ x ⇒ x=6$$ 27- Choice A is correct The correct answer is $$28$$The area of the floor is: $$8$$ cm $$× \ 35$$ cm $$= 280$$ cm$$^2$$The number of tiles needed $$= 288 \ ÷ \ 10 = 28$$ 28- Choice C is correct The correct answer is $$x=- \ 24, \ y=18$$$$\begin{cases}x \ + \ 2 \ y = 12\\3 \ x \ + \ 5 \ y= 18\end{cases} →$$ Multiply the top equation by $$- \ 3$$ then,$$\begin{cases}- \ 3 \ x \ - \ 6 \ y = - \ 36\\3 \ x \ + \ 5 \ y= 18\end{cases} →$$ Add two equations$$- \ y = - \ 18→y=18$$ plug in the value of $$y$$ into the first equation$$x \ + \ 2 \ y = 12 → x \ + \ 2 \ (18) = 12→ x \ + \ 36 = 12$$Subtract $$36$$ from both sides of the equation. Then: $$x \ + \ 36=12→x=- \ 24$$ 29- Choice D is correct The correct answer is $$600$$ ml$$5\%$$ of the volume of the solution is alcohol. Let $$x$$ be the volume of the solution.Then: $$5\%$$ of $$x=30$$ ml $$⇒ 0.05 \ x =30 ⇒ x=30÷0.05=600$$ 30- Choice C is correct The correct answer is $$5$$ cmFormula for the Surface area of a cylinder is:$$SA=2 \ \pi \ r^2 \ + \ 2 \ \pi \ r \ h →150 \ π=2 \ \pi \ r^2 \ + \ 2 \ \pi \ r \ (10)→r^2 \ + \ 10 \ π \ − \ 75=0 \ (r \ + \ 15) \ (π \ − \ 5)=0→π=5$$ or $$π= \ − \ 15$$ (unacceptable) 31- Choice D is correct The correct answer is $$I \ > \ 4000 \ x \ + \ 21000$$Let $$x$$ be the number of years. Therefore, $$2,000$$ per year equals $$2000 \ x$$.starting from $$24,000$$ annual salary means you should add that amount to $$2000 \ x$$.Income more than that is:$$I \ > \ 4000 \ x \ + \ 21000$$ 32- Choice D is correct The correct answer is $$840$$Use simple interest formula: $$I=prt$$($$I=$$ interest, $$p=$$ principal, $$r=$$ rate,$$t=$$ time) $$I=(7,000) \ (0.04) \ (3)=840$$ 33- Choice A is correct The correct answer is $$50$$ milesUse the information provided in the question to draw the shape.$$40$$ milesUse Pythagorean Theorem: $$a^2 \ + \ b^2 = c^2$$$$40^2+ 30^2=c^2 ⇒ 1600 \ + \ 900= c^2 ⇒ 2500=c^2 ⇒ c=50$$ 34- Choice A is correct The correct answer is $$\frac{17}{18}$$If $$17$$ balls are removed from the bag at random, there will be one ball in the bag.The probability of choosing a brown ball is $$1$$ out of $$18$$.Therefore, the probability of not choosing a brown ball is $$17$$ out of $$18$$ and the probability of having not a brown ball after removing $$17$$ balls is the same. 35- Choice A is correct The correct answer is $$12 \ \pi$$Area of the circle is less than $$49 \ π$$.Use the formula of areas of circles.Area $$= \pi \ r^2 ⇒ 49 \ \pi \ > \ \pi \ r^2⇒$$$$49 > r^2⇒ r \ < \ 7$$Radius of the circle is less than $$7$$.Let’s put $$7$$ for the radius.Now, use the circumference formula:Circumference $$=2 \ \pi \ r =2 \ \pi \ (7)=14 \ \pi$$Since the radius of the circle is less than $$7$$.Then, the circumference of the circle must be less than $$14 \ \pi$$.Only choice A is less than $$14 \ \pi$$. 36- Choice A is correct The correct answer is $$\frac{2}{7}, \frac{3}{8}, \frac{5}{11}, \frac{3}{4}$$Let’s compare each fraction:$$\frac{2}{7} \ < \ \frac{3}{8} \ < \ \frac{5}{11} \ < \ \frac{3}{4}$$Only choice A provides the right order. 37- Choice B is correct The correct answer is $$0.88$$ DTo find the discount, multiply the number by ($$100\% \ –$$ rate of discount).Therefore, for the first discount we get: (D) ($$100\% \ – \ 20\%) =$$ (D) $$(0.80) = 0.80$$ DFor increase of $$10\%: (0.85$$ D) $$(100\% \ + \ 10\%) = (0.85$$ D) $$(1.10) = 0.88$$ D $$= 88\%$$ of D 38- Choice D is correct The correct answer is $$70$$To find the number of possible outfit combinations, multiply number of options for each factor: $$7 \ × \ 2 \ × \ 5=70$$ 39- Choice B is correct The correct answer is $$(5, 7)$$The equation of a line is in the form of $$y=m \ x \ + \ b$$, where $$m$$ is the slope of the line and $$b$$ is the $$y−$$intercept of the line.Two points $$(5, 3)$$ and $$(6, 4)$$ are on line A.Therefore, the slope of the line A is:slope of line $$A=\frac{y_{2} \ − \ y_{1}}{x_{2} \ − \ x_{1}}= \frac{4 \ − \ 3}{6 \ − \ 5}=\frac{1}{1}=1$$The slope of line A is $$1$$.Thus, the formula of the line A is:$$y=x \ + \ π$$, choose a point and plug in the values of $$x$$ and $$y$$ in the equation to solve for .Let’s choose point $$(5, 3)$$.Then: $$y=x \ + \ b→5=3 \ + \ b→b=5 \ − \ 3= 2$$The equation of line A is: $$y=x \ + \ 2$$Now, let’s review the choices provided:A. $$(− \ 1, 2) \ \ y=x \ + \ 2→2=− \ 1 \ + \ 2=1$$ This is not true.B. $$(5, 7) \ \ y=x \ + \ 2→7=5 \ + \ 2=7$$ This is true!C. $$(3, 4) \ \ y=x \ + \ 2→4=3 \ + \ 2=5$$ This is not true.D. $$(− \ 1, − \ 2) \ \ y=x \ + \ 2→− \ 2=− \ 1 \ + \ 2=1$$ This is not true. 40- Choice C is correct The correct answer is $$46$$ cmThe area of the trapezoid is: Area $$=\frac{1}{2} \ h \ (b1 \ + \ b2)=\frac{1}{2} \ (x)(13+8)=126→10.5 \ x=126→x=12$$$$y=\sqrt{5^2 \ + \ 12^2}=\sqrt{25 \ + \ 144}=\sqrt{169}=13$$The perimeter of the trapezoid is: $$12 \ + \ 13 \ + \ 8 \ + \ 13=46$$ 40- Choice C is correct The correct answer is $$46$$ cmThe area of the trapezoid is: Area $$=\frac{1}{2} \ h \ (b1 \ + \ b2)=\frac{1}{2} \ (x)(13+8)=126→10.5 \ x=126→x=12$$$$y=\sqrt{5^2 \ + \ 12^2}=\sqrt{25 \ + \ 144}=\sqrt{169}=13$$The perimeter of the trapezoid is: $$12 \ + \ 13 \ + \ 8 \ + \ 13=46$$ 41- Choice I is correct The correct answer is $$26.75$$$$2 \ x \ - \ 6=10.5→2 \ x=10.5+6=16.5→x=\frac{16.5}{2}=8.25$$Then; $$3 \ x \ + \ 2=3 (8.25) \ + \ 2=24.75 \ + \ 2=26.75$$ 42- Choice C is correct The correct answer is $$- \ 2$$Use PEMDAS (order of operation):$$- \ 16 \ + \ 6 \ × \ (– \ 5) \ – \ [ \ 6 \ + \ 22 \ × \ (- \ 4) \ ] \ ÷ \ 2 \ + \ 5=$$$$− \ 16 \ − \ 30 \ − \ [ \ 6 \ − \ 88 \ ] \ ÷ \ 2 \ + \ 5=$$$$− \ 43 \ − \ [ \ − \ 82 \ ] \ ÷ \ 2 \ + \ 5=$$$$− \ 48 \ +\ 82 \ ÷ \ 2 \ + \ 5=$$$$− \ 48 \ + \ 41 \ + \ 5= \ - \ 2$$ 43- Choice C is correct The correct answer is $$21$$The input value is $$3$$. Then: $$x=3, \ π(x)=x^2 \ + \ 4 \ x→$$$$f(3)=9 \ + \ 4 \ (3)=9 \ + 12=21$$ 44- Choice C is correct The correct answer is $$220$$The perimeter of the trapezoid is $$58$$.Therefore, the missing side (height) is $$= 58 \ – \ 16 \ – \ 12 \ – \ 10= 20$$Area of a trapezoid: A $$= \frac{1}{2} \ h \ (b1 \ + \ b2) = \frac{1}{2} \ (20) \ (10 \ + \ 12) = 220$$ 45- Choice C is correct The correct answer is $$13$$Since $$π=5$$, substitute $$5$$ for $$N$$ in the equation $$\frac{x \ + \ 2}{3}=N$$, which gives $$\frac{x \ + \ 2}{3}=5$$.Multiplying both sides of $$\frac{x \ + \ 2}{3}=5$$ by $$3$$ gives $$x \ + \ 2=15$$ and then adding $$- \ 2$$ to both sides of$$x \ + \ 2=15$$ then, $$x=13$$. 46- Choice F is correct The correct answer is $$\frac{3}{2}$$Let $$x$$ be the length of an edge of cube, then the volume of a cube is: $$π=x^3$$The surface area of cube is: $$ππ΄=6 \ x^2$$The volume of cube A is $$\frac{1}{4}$$ of its surface area. Then:$$x^3=\frac{6 \ x^2}{4}→x^3=\frac{3}{2} \ x^2$$, divide both side of the equation by $$x^2$$.Then: $$\frac{x^3}{x^2}=\frac{3 \ x^2}{2 \ x^2}→x=\frac{3}{2}$$ 47- Choice C is correct The correct answer is $$8$$First draw an isosceles triangle.Remember that two sides of the triangle are equal.Let put $$a$$ for the legs. Then:$$π=4⇒$$ area of the triangle is $$=\frac{1}{2}(4 \ × \ 4)=\frac{16}{2}=8$$ 48- Choice C is correct The correct answer is $$7$$average $$=\frac{sum \ of \ terms}{ number \ of \ terms} ⇒$$$$15=\frac{13 \ + \ 16 \ + \ 24 \ + \ x}{4}⇒$$$$60=53 \ + \ x⇒x=7$$ 49- Choice C is correct The correct answer is $$90^\circ$$The relationship among all sides of special right triangle$$30^\circ \ − \ 60^\circ \ − \ 90^\circ$$ is provided in this triangle:In this triangle, the opposite side of $$30^\circ$$ angle is half of the hypotenuse.Draw the shape of this question.The latter is the hypotenuse.Therefore, the latter is $$90$$ feet. 50- Choice C is correct The correct answer is $$150$$The question is this: $$1.95$$ is what percent of $$1.30$$?Use percent formula:part $$= \frac{percent}{100 } \ ×$$ whole$$1.95 = \frac{percent}{100} \ × \ 1.30 ⇒ 1.95 =\frac{ percent \ × \ 1.30}{100} ⇒195 =$$ percent $$× \ 1.30 ⇒$$ percent $$= \frac{195}{1.30} = 150$$ 51- Choice E is correct The correct answer is $$\frac{1}{5}$$ or $$0.2$$Write the ratio of $$3 \ π$$ to $$4 \ b$$. $$\frac{3 \ a}{6 \ b}=\frac{1}{10}$$Use cross multiplication and then simplify.$$3 \ a × 10= 6 \ b × 1 → 30 \ a = 6 \ b → a = \frac{6 \ b}{30} = \frac{ b}{5}$$Now, find the ratio of $$a$$ to $$b$$. $$\frac{a}{b} = \frac{\frac{ b}{5}}{b} →\frac{ b}{5} ÷ b =\frac{ b}{5} × \frac{1}{b} = \frac{b }{5 \ b} = \frac{1}{5} =0.2$$ 52- Choice E is correct The correct answer is $$33.75$$ mThe rate of construction company $$=\frac{50 \ cm}{1 \ min}=50$$ cm$$/$$minHeight of the wall after $$45$$ minutes $$=\frac{ 50 \ cm}{1 \ min}× \ 45$$ min $$=2,250$$ cmLet $$x$$ be the height of wall, then $$\frac{2}{3} \ x=2,250$$ cm $$→x=\frac{3 \ × \ 2,250}{2}→x=3,375$$ cm $$= 33.75$$ m

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