 ## Full Length DAT Quantitative Reasoning Practice Test

If you want to prepare for the DAT Quantitative Reasoning Practice Test? It’s time to taking a Full-length DAT Quantitative Reasoning Practice Test. It is the best way to simulate test day. To challenge your skills and simulate the full length DAT Quantitative Reasoning Practice Test day experience, score your tests using the answer keys.

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A Quick Study Guide with Two Full-Length DAT Quantitative Reasoning Practice Tests

DAT Quantitative Reasoning
Practice Test 3

40 questions

Total time for this section: 45 Minutes

You may use a basic calculator on this test.

1-

How many tiles of $$5$$ cm$$^2$$ is needed to cover a floor of dimension $$5$$ cm by $$30$$ cm?

(A) $$25$$
(B) $$150$$
(C) $$35$$
(D) $$30$$
(E) $$40$$
2-

What is the value of $$y$$ in the following system of equation?
$$4 \ x \ + \ 6 \ y= 10$$
$$x \ + \ y= 3$$

(A) $$1$$
(B) $$- \ 1$$
(C) $$- \ 2$$
(D) $$2$$
(E) $$3$$
3-

The marked price of a computer is D dollar. Its price decreased by $$30\%$$ in January and later increased by $$15\%$$ in February. What is the final price of the computer in D dollar?

(A) $$0.60$$ D
(B) $$0.68$$ D
(C) $$0.69$$ D
(D) $$0.65$$ D
(E) $$0.45$$ D
4-

What is the area of a square whose diagonal is $$10$$ cm?

(A) $$50$$ cm$$^2$$
(B) $$\sqrt{50}$$ cm$$^2$$
(C) $$\sqrt{100}$$ cm$$^2$$
(D) $${10}$$ cm$$^2$$
(E) $$100$$ cm$$^2$$
5-

The number $$55.5$$ is $$1,000$$ times greater than which of the following numbers?

(A) $$0.555$$
(B) $$0.5550$$
(C) $$0.0555$$
(D) $$0.00555$$
(E) $$0.000555$$
6-

How long does a $$384–$$miles trip take moving at $$40$$ miles per hour (mph)?

(A) $$8$$ hours and $$36$$ minutes
(B) $$9$$ hours and $$30$$ minutes
(C) $$9$$ hours and $$35$$ minutes
(D) $$9$$ hours and $$36$$ minutes
(E) $$8$$ hours and $$26$$ minutes
7-

What is the value of $$x$$ in the following figure? (A) $$165$$
(B) $$160$$
(C) $$150$$
(D) $$15$$
(E) $$170$$
8- When $$30\%$$ of $$85$$ is added to $$15\%$$ of $$450$$, the resulting number is:
(A) $$88$$
(B) $$60$$
(C) $$28$$
(D) $$35$$
(E) $$32$$
9- In the following figure, ABCD is a rectangle, and E and F are points on AD and DC, respectively. The area of $$\triangle$$BED is $$25$$, and the area of $$\triangle$$BDF is $$12$$. What is the perimeter of the rectangle? (A) $$60$$
(B) $$40$$
(C) $$35$$
(D) $$38$$
(E) $$36$$
10- From the figure, which of the following must be true? (figure not drawn to scale) (A) $$2 \ y \ - \ x=𝑧$$
(B) $$2 \ y \ + \ x=𝑧$$
(C) $$- \ 2 \ y \ + \ x=𝑧$$
(D)  $$y \ + \ x=𝑧$$
(E) $$y \ - \ x=𝑧$$
11- Right triangle ABC is shown below. Which of the following is true for all possible values of angle A and B? (A) tan $$𝐴 =$$ tan $$B$$
(B) sin $$𝐴 =$$ cos$$B$$
(C) tan$$^2 𝐴 =$$ tan$$^2 B$$
(D) tan $$𝐴 =1$$
(E) cot $$𝐴 =$$ sin $$B$$
12- A chemical solution contains $$3\%$$ alcohol. If there is $$30$$ ml of alcohol, what is the volume of the solution?
(A) $$900$$ ml
(B) $$1,000$$ ml
(C) $$1,200$$ ml
(D) $$800$$ ml
(E) $$600$$ ml
13- A bag contains $$27$$ balls: three green,six  black, nine blue, five  brown, a red and one  white. If $$26$$ balls are removed from the bag at random, what is the probability that a red ball has been removed?
(A) $$\frac{1}{27}$$
(B) $$\frac{2}{27}$$
(C) $$\frac{25}{27}$$
(D) $$\frac{26}{27}$$
(E) $$\frac{5}{27}$$
14- If $$60\%$$ of a class are girls, and $$20\%$$ of girls play tennis, what percent of the class play tennis?
(A) $$44\%$$
(B) $$80\%$$
(C) $$12\%$$
(D) $$15\%$$
(E) $$60\%$$
15- Which of the following points lies on the line $$4 \ x \ + \ 6 \ y=4$$ ?
(A) $$( 2,1)$$
(B) $$( - \ 1 ,3)$$
(C) $$( - \ 2,2)$$
(D) $$(2,2)$$
(E) $$(2,8)$$
16- If a tree casts a $$30–$$foot shadow at the same time that a $$4$$ feet yardstick casts a $$3–$$foot shadow, what is the height of the tree? (A) $$38$$ ft
(B) $$36$$ ft
(C) $$40$$ ft
(D) $$42$$ ft
(E) $$44$$ ft
17- In five successive hours, a car travels $$30$$ km, $$62$$ km, $$47$$ km, $$70$$ km and $$50$$ km. In the next five hours, it travels with an average speed of $$65$$ km per hour. Find the total distance the car traveled in $$10$$ hours.
(A) $$580$$ km
(B) $$584$$ km
(C) $$585$$ km
(D) $$582$$ km
(E) $$581$$ km
18- If $$\frac{2 \ x}{12}=\frac{x \ + \ 1}{3}, \ x=$$
(A) $$2$$
(B) $$4$$
(C) $$3$$
(D) $$- \ 3$$
(E) $$- \ 2$$
19- What is the solution of the following inequality?
$$|x \ + \ 7 | \ ≤ \ 2$$
(A) $$9 \ ≤ \ x \ ≤ \ 5$$
(B) $$- \ 9 \ ≤ \ x \ ≤ \ 5$$
(C) $$- \ 9 \ ≤ \ x \ ≤ - \ 5$$
(D) $$- \ 9 \ ≤ \ x \ ≤ 9$$
(E) $$x \ ≤ 5$$
20- From last year, the price of gasoline has increased from $$1.35$$ per gallon to $$1.50$$ per gallon. The new price is what percent of the original price?
(A) $$95\%$$
(B) $$80\%$$
(C) $$85\%$$
(D) $$98\%$$
(E) $$90\%$$
21- If $$40\%$$ of $$x$$ equal to $$25\%$$ of $$32$$, then what is the value of $$(x \ - \ 7)^2$$?
(A) $$169$$
(B) $$196$$
(C) $$144$$
(D) $$225$$
(E) $$289$$
22- When point A $$(- \ 12 ,5)$$ is reflected over the $$y-$$axis to get the point B, what are the coordinates of point B?
(A) $$(- \ 12,- \ 5)$$
(B) $$( 12,- \ 5)$$
(C) $$( 12,- \ 6)$$
(D) $$(- \ 12,- \ 6$$
(E) $$(12,5)$$

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23- If tan $$\theta = \frac{8}{6}$$ and sin $$\theta \ > \ 0$$, then cos $$\theta =$$ ?
(A) $$\frac{8}{10}$$
(B) $$\frac{6}{10}$$
(C) $$\frac{6}{100}$$
(D) $$\frac{10}{8}$$
(E) $$\frac{10}{6}$$
24- A number is chosen at random from $$1$$ to $$45$$. Find the probability of not selecting a composite number.
(A) $$\frac{1}{2}$$
(B) $$\frac{1}{3}$$
(C) $$\frac{1}{45}$$
(D) $$\frac{14}{45}$$
(E) $$\frac{17}{45}$$
25- In the $$x \ y-$$plane, the point $$(4,6)$$ and $$(5,7)$$ are on line A. Which of the following equations of lines is parallel to line A?
(A) $$y= - \ x$$
(B) $$y=2 \ - \ x$$
(C) $$y=2 \ - \ 3 \ x$$
(D) $$y= x$$
(E) $$y= 2 \ x$$
26- If $$y=5 \ a \ b \ + \ b^4$$, what is $$y$$ when $$a=3$$ and $$b=4$$?
(A) $$310$$
(B) $$256$$
(C) $$300$$
(D) $$196$$
(E) $$316$$
27- If the area of trapezoid is $$192$$, what is the perimeter of the trapezoid? (A) $$69$$
(B) $$80$$
(C) $$65$$
(D) $$100$$
(E) $$60$$
28- If $$f(x)=- \ 8 \ + \ 3 \ x$$ and $$g(x)= 3 \ x^2 \ + \ 5 \ – \ 4 \ x$$, then find $$(g \ – \ f)(x)$$?
(A) $$3 \ x^2 \ + \ 7 \ x \ + \ 13$$
(B) $$3 \ x^2 \ - \ x \ + \ 13$$
(C) $$3 \ x^2 \ - \ x \ - \ 13$$
(D) $$3 \ x^2 \ – \ 7 \ x \ + \ 13$$
(E) $$3 \ x^2 \ + \ 7 \ x \ + \ 13$$
29- In the following equation when $$z$$ is multiplied  by $$3$$, what is the effect on $$x$$?
$$x=\frac{6 \ y \ + \ \frac{r}{r \ - \ 1}}{\frac{3}{z}}$$
(A) $$x$$ is multiplied by $$3$$
(B) $$x$$ is divided by $$3$$
(C) $$x$$ is divided by $$2$$
(D) $$x$$ does not change
(E) $$x$$ is multiplied by $$2$$
30- A rope weighs $$456$$ grams per meter of length. What is the weight in kilograms of $$10.5$$ meters of this rope? ($$1$$ kilograms $$= 1000$$ grams)
(A) $$47.88$$
(B) $$478.8$$
(C) $$0.4788$$
(D) $$0.04788$$
(E) $$4.788$$
31- If $$f(x)=3 \ x^4 \ - \ 2 \ x^3 \ + \ 5 \ x$$ and $$g(x)=- \ 3$$, what is the value of $$f(g(x))$$?
(A) $$280$$
(B) $$282$$
(C) $$- \ 282$$
(D) $$- \ 280$$
(E) $$290$$
32- Removing which of the following numbers will change the average of the numbers to $$11$$?
$$4, 7, 13, 15, 16, 20$$
(A) $$4$$
(B) $$13$$
(C) $$20$$
(D) $$16$$
(E) $$7$$
33- A boat sails $$50$$ miles south and then $$120$$ miles east. How far is the boat from its start point?
(A) $$135$$ miles
(B) $$120$$ miles
(C) $$140$$ miles
(D) $$130$$ miles
(E) $$150$$ miles
34- If cotangent of an angel $$β$$ is $$\frac{2}{3}$$, then the tangent of angle $$β$$ is:
(A) $$\frac{3}{2}$$
(B) $$\frac{3}{4}$$
(C) $$\frac{1}{4}$$
(D) $$\frac{1}{2}$$
(E) $$\frac{1}{3}$$
35- If a box contains red and blue balls in ratio of $$3 : 5$$, how many red balls are there if $$120$$ blue balls are in the box?
(A) $$115$$
(B) $$75$$
(C) $$72$$
(D) $$80$$
(E) $$85$$
36- $$2x$$ is $$y\%$$ of what number?
(A) $$\frac{200 \ x}{y}$$
(B) $$\frac{100 \ x}{y}$$
(C) $$\frac{100 \ y}{x}$$
(D) $$\frac{200 \ y}{x}$$
(E) $$\frac{20 \ y}{x}$$
37- $$5$$ liters of water are poured into an aquarium that's $$10$$ cm long, $$4$$ cm wide, and $$40$$ cm high. How many cm will the water level in the aquarium rise due to this added water? ($$1$$ liter of water $$= 1000$$ cm$$^3$$)
(A) $$120$$ cm
(B) $$130$$ cm
(C) $$125$$ cm
(D) $$115$$ cm
(E) $$110$$ cm
38- What is the surface area of the cylinder below? (A) $$110 \ π$$ in$$^2$$
(B) $$115 \ π$$ in$$^2$$
(C) $$125 \ π$$ in$$^2$$
(D) $$120 \ π$$ in$$^2$$
(E) $$130 \ π$$ in$$^2$$
39- A ladder leans against a wall forming a $$30^\circ$$ angle between the ground and the ladder. If the bottom of the ladder is $$40$$ feet away from the wall, how long is the ladder?
(A) $$40$$ feet
(B) $$60$$ feet
(C) $$80$$ feet
(D) $$100$$ feet
(E) $$120$$ feet
40- If $$|a| \ < \ 1$$, then which of the following is false ? $$(b>0)$$?
I. $$– \ b \ < \ b \ a \ < \ b$$
II. $$- \ a \ < \ a^2 \ < \ a$$ if $$a \ < \ 0$$
III. $$- \ 5 \ < \ 2 \ a \ - \ 3 \ < \ - \ 1$$
(A) II only
(B)  I and III only
(C) III only
(D) I only
(E) only
 1- Choice D is correct The correct answer is $$30$$The area of the floor is: $$5$$ cm $$× \ 30$$ cm $$= 150$$ cmThe number is tiles needed $$= 150\ ÷ \ 5=30$$ 2- Choice B is correct The correct answer is $$- \ 1$$Solving Systems of Equations by Elimination method.\cfrac{\begin{align} 4 \ x \ + \ 6 \ y \ = \ 10 \\ x \ + \ y \ = 3 \end{align}}{}Multiply the second equation by $$- \ 4$$, then add it to the first equation.\cfrac{\begin{align} 4 \ x \ + \ 6 \ y \ = 10 \\ - \ 4 \ ( x \ + \ y \ = 3) \end{align}}{} ⇒ \cfrac{ \begin{align} 4 \ x \ + \ 6 \ y \ = 10 \\ - \ 4 \ x \ - \ 4 \ y \ = 12 \end{align} }{\begin{align} 2\ y \ = - \ 2 \\ ⇒ y \ = - \ 1 \end{align}} 3- Choice C is correct The correct answer is $$0.69$$ DTo find the discount, multiply the number by ($$100\% \ –$$ rate of discount).Therefore, for the first discount we get: (D) $$(100\% \ – \ 30\%) =$$ (D) $$(0.60) = 0.60$$ DFor increase of $$10\%: \ (0.60$$ D) $$(100\% \ + \ 15\%) = (0.60$$ D)$$(1.15) = 0.69$$ D $$= 69\%$$ of D 4- Choice A is correct The correct answer is $$50$$ cm$$^2$$The diagonal of the square is $$10$$. Let $$x$$ be the side. Use Pythagorean Theorem: $$a^2 \ + \ b^2=c^2$$$$x^2 \ + \ x^2 = 10^2 ⇒ 2 \ x^2=10^2 ⇒ 2 \ x^2 = 100 ⇒ x^2 = 50 ⇒x= \sqrt{50}$$The area of the square is:$$\sqrt{50} \ × \ \sqrt{50}=50$$ 5- Choice C is correct The correct answer is $$0.0555$$$$1000$$ times the number is $$55.5$$. Let $$x$$ be the number, then:$$1000 \ x=55.5$$$$x=\frac{55.5}{1000}=0.0555$$ 6- Choice D is correct The correct answer is $$9$$ hours and $$36$$ minutesUse distance formula:Distance $$=$$ Rate $$×$$ time $$⇒ 384 = 40 \ ×$$ T, divide both sides by $$40$$.$$\frac{384}{40} =$$ T $$⇒$$ T $$= 9.6$$ hours.Change hours to minutes for the decimal part. $$0.6$$ hours $$= 0.6 \ × \ 60=36$$ minutes. 7- Choice A is correct The correct answer is $$165$$$$x=35 \ + \ 130=165$$ 8- Choice A is correct The correct answer is $$88$$$$35\%$$ of $$80$$ equals to: $$0.35 \ × \ 80=28$$$$12\%$$ of $$600$$ equals to: $$0.15\ × \ 400=60$$$$35\%$$ of $$80$$ is added to $$15\%$$ of $$400: \ 28 \ + \ 60=88$$ 9- Choice E is correct The correct answer is $$36$$The area of $$\triangle$$BED is $$25$$, then: $$\frac{5 \ × \ AB}{2}=25→5 \ ×$$ AB $$=50→$$ AB $$=10$$The area of $$\triangle$$BDF is $$18$$, then: $$\frac{3 \ × \ BC}{2}=12→3 \ ×$$ BC $$=24→$$ BC $$=8$$The perimeter of the rectangle is $$= 2 \ × \ (10 \ + \ 8)=36$$ 10- Choice B is correct The correct answer is $$2 \ y \ + \ x=𝑧$$$$y$$ and $$z$$ are colinear.$$x$$ and $$3 \ y$$ are colinear. Therefore,$$y \ + \ z= x \ + \ 3 \ y$$, subtract $$x$$ from both sides,then, $$z= 2 \ y \ + \ x$$ 11- Choice B is correct The correct answer is sin $$𝐴 =$$ cos $$B$$By definition, the sine of any acute angle is equal to the cosine of its complement.Since, angle A and B are complementary angles, therefore:sin $$A =$$ cos $$B$$ 12- Choice B is correct The correct answer is $$1,000$$ ml$$3\%$$ of the volume of the solution is alcohol.Let $$x$$ be the volume of the solution. Then: $$3\%$$ of $$x=30$$ ml $$⇒ 0.03 \ x=30 ⇒ x=30 \ ÷ \ 0.03=1,000$$ 13- Choice D is correct The correct answer is $$\frac{26}{27}$$If $$26$$ balls are removed from the bag at random, there will be one ball in the bag.The probability of choosing a red ball is $$1$$ out of $$27$$.Therefore, the probability of not choosing a red ball is $$26$$ out of $$27$$ and the probability of having not a red ball after removing $$26$$ balls is the same. 14- Choice C is correct The correct answer is $$12\%$$The percent of girls playing tennis is: $$60\% \ × \ 20\%=0.60 \ × \ 0.20=0.12=12\%$$ 15- Choice C is correct The correct answer is $$(– \ 2,2)$$Plug in each pair of number in the equation:A. $$(2,1)$$:         $$4 \ (2) \ + \ 6 \ (1)=15$$ Nope!B. $$(– \ 1,3)$$:     $$4 \ (– \ 1) \ + \ 6 \ (3)=14$$ Nope!C. $$(– \ 2,2)$$:     $$4 \ (– \ 2) \ + \ 6 \ (2)=4$$ Bingo!D. $$(2,2)$$:        $$4 \ (2) \ + \ 6 \ (2)=20$$ Nope!E. $$(2,8)$$:        $$4 \ (2) \ + \ 6 \ (8)=56$$ Nope! 16- Choice C is correct The correct answer is $$40$$ ftWrite a proportion and solve for $$x$$.$$\frac{4}{3}=\frac{x}{30} ⇒ 3 \ x=4 \ × \ 30 ⇒ x=40$$ ft 17- Choice B is correct The correct answer is $$584$$ kmAdd the first $$5$$ numbers.$$30 \ + \ 62 \ + \ 47 \ + \ 70 \ + \ 50=259$$To find the distance traveled in the next $$5$$ hours, multiply the average by number of hours.Distance $$=$$ Average $$×$$ Rate $$=65 \ × \ 5=325$$Add both numbers. $$259 \ + \ 325=584$$ 18- Choice E is correct The correct answer is $$- \ 2$$Solve for $$x$$.$$\frac{2 \ x}{12}=\frac{x \ + \ 1}{3}$$Multiply the second fraction by $$4$$.$$\frac{2 \ x}{12}=\frac{4 \ (x \ +\ 1)}{3 \ × \ 4}$$Tow denominators are equal. Therefore, the numerators must be equal.$$2 \ x=4 \ x \ + \ 4$$$$- \ 2 \ x = 4$$$$x= - \ 2$$ 19- Choice B is correct The correct answer is $$- \ 9 \ ≤ \ x \ ≤ \ 5$$$$|x \ + \ 7 | \ ≤ \ 2→$$$$- \ 2 \ ≤ \ x \ + \ 7 \ ≤ \ 2→$$$$- \ 2 \ - \ 7 \ ≤ \ x \ + \ 7 \ - \ 7 \ ≤ \ 2 \ - \ 7→$$$$-9 \ ≤ \ x \ ≤ \ 5$$ 20- Choice E is correct The correct answer is $$90\%$$The question is this: $$1.50$$ is what percent of $$1.35$$?Use percent formula:part $$=\frac{percent}{100} \ ×$$ whole $$1.50 = \frac{percent}{100} \ × \ 1.35 ⇒$$$$1.50=\frac{percent \ × \ 1.35}{100} ⇒$$$$150=$$ percent $$× \ 1.35 ⇒$$ percent $$=\frac{150}{1.35}= 90$$ 21- Choice A is correct The correct answer is $$169$$$$0.4 \ x=(0.25) \ × \ 32→x=20→(x \ - \ 7)^2=(13)^2=169$$ 22- Choice E is correct The correct answer is $$(12,5)$$When points are reflected over $$y-$$axis, the value of $$y$$ in the coordinates doesn’t change and the sign of $$x$$ changes.Therefore, the coordinates of point B is $$(12,5)$$. 23- Choice A is correct The correct answer is $$\frac{8}{10}$$tan $$θ=\frac{opposite}{adjacent}$$tan $$θ=\frac{8}{6}⇒$$ we have the following right triangle.Then:$$c=\sqrt{8^2 \ + \ 6^2 }=\sqrt{64 \ + \ 36}=\sqrt{100}=10$$cos $$θ=\frac{adjacent}{hypotenuse}=\frac{8}{10}$$ 24- Choice B is correct The correct answer is $$\frac{1}{3}$$Set of number that are not composite between $$1$$ and $$45$$:A $$= \left\{1, 2, 3, 5, 7, 11, 13, 17, 19, 23 , 29 , 31 ,37 ,41 ,43 \right\}$$Probability $$= \frac{number \ of \ desired \ outomes}{number \ of \ total \ outcomes} =\frac{15}{45}=\frac{1}{3}$$ 25- Choice D is correct The correct answer is $$y= x$$The slop of line A is: $$m=\frac{y_{2} \ - \ y_{1}}{x_{2} \ - \ x_{1}}=\frac{7 \ - \ 6}{5 \ - \ 4}=1$$Parallel lines have the same slope and only choice  D $$(y=x)$$ has slope of $$1$$. 26- Choice E is correct The correct answer is $$316$$$$y = 5 \ a \ b \ + \ b^4$$Plug in the values of $$a$$ and $$b$$ in the equation: $$a=3$$ and $$b=4$$$$y = 5 \ (3) \ (4) \ + \ (4)^4 = 60 \ + \ (256) = 316$$ 27- Choice A is correct The correct answer is $$69$$The area of trapezoid is: $$(\frac{30 \ + \ 12}{2}) \ × \ x=192→24 \ x=192→x=8$$$$y=\sqrt{12^2 \ + \ 5^2}=13$$Perimeter is: $$18 \ + \ 30 \ + \ 8 \ + \ 13=69$$ 28- Choice D is correct The correct answer is $$3 \ x^2 \ – \ 7 \ x \ + \ 13$$$$(g \ – \ f)(x)=g(x) \ – \ f(x)=(3 \ x^2 \ + \ 5 \ – \ 4 \ x) \ – \ (- \ 8 \ + \ 3 \ x)$$$$3 \ x^2 \ + \ 5 \ – \ 4 \ x \ + \ 8 \ – \ 3 \ x = \ 3 \ x^2 \ - \ 7 \ x \ + \ 13$$ 29- Choice A is correct The correct answer is $$x$$ is multiplied by $$3$$Plug in $$z\times 3$$ for $$z$$ and simplify.$$x_{1}=\frac{8 \ y \ + \ \frac{r}{r \ + \ 1}}{\frac{6}{z \times 3 }}=\frac{8 \ y \ + \ \frac{r}{r \ + \ 1}}{\frac{1}{3}\times \frac{ 6}{z }}=$$$$\frac{8 \ y \ + \ \frac{r}{r \ + \ 1}}{\frac{6}{z}}={3} \ × \ \frac{8 \ y \ + \ \frac{r}{r \ + \ 1}}{\frac{6}{z}}=x \times 3$$ 30- Choice E is correct The correct answer is $$4.788$$The weight of $$10.5$$ meters of this rope is: $$10.5 \ × \ 456$$ g $$=4788$$ g$$1$$ kg $$=1000$$ g, therefore, $$4788$$ g $$÷ \ 1000=4.788$$ kg 31- Choice B is correct The correct answer is $$282$$$$g(x)=- \ 3$$, then $$f(g(x))= f(- \ 3)=3 \ (- \ 3)^4 \ - \ 2 \ (- \ 3)^3 \ + \ 5 \ (- \ 3)= 243 \ + \ 54 \ - \ 15=282$$ 32- Choice C is correct The correct answer is $$20$$Check each option provided:A. $$4 \ \ \ \ \frac{7\ + \ 13 \ + \ 15 \ + \ 16 \ + \ 20}{5}=\frac{71}{5}=14.2$$B. $$13 \ \ \ \ \frac{4 \ + \ 7 \ + \ 15 \ + \ 16 \ + \ 20}{5}=\frac{62}{5}=12.4$$C. $$20 \ \ \ \ \frac{4 \ + \ 7 \ + \ 13 \ + \ 15 \ + \ 16}{5}=\frac{55}{5}=11$$D. $$16\ \ \frac{4 \ + \ 7 \ + \ 13 \ + \ 15 \ + \ 20}{5}=\frac{59}{5}=11.8$$E. $$7 \ \ \frac{4 \ + \ 13 \ + \ 15 \ + \ 16 \ + \ 20}{5}=\frac{68}{5}=13.6$$ 33- Choice D is correct The correct answer is $$130$$ milesUse the information provided in the question to draw the shape.Use Pythagorean Theorem: $$a^2 \ + \ b^2=c^2$$$$50^2 \ + \ 120^2=c^2 ⇒$$$$2500 \ + \ 14400= c^2⇒$$$$16,900=c^2⇒ c=130$$ 34- Choice A is correct The correct answer is $$\frac{3}{2}$$tangent $$\beta= \frac{1}{cotangent \ \beta}=\frac{3}{2}$$ 35- Choice C is correct The correct answer is $$72$$$$\frac{3}{5} \ × \ 120=72$$ 36- Choice A is correct The correct answer is $$\frac{200 \ x}{y}$$Let the number be A. Then: $$2 \ x=y\% \ ×$$ ASolve for A. $$2 \ x=\frac{y}{100} \ ×$$ AMultiply both sides by $$\frac{100}{y}$$:$$2 \ x \ × \ \frac{100}{y}=\frac{y}{100} \ × \ \frac{100}{y} \ ×$$ AA $$=\frac{200 \ x}{y}$$ 37- Choice C is correct The correct answer is $$125$$ cmOne liter $$= 1000$$ cm$$^3→ 5$$ liters $$= 5000$$ cm$$^3$$$$5000=10 \ × \ 4 \ × \ h→h=\frac{5000}{40}=125$$ cm 38- Choice A is correct The correct answer is $$110 \ π$$ in$$^2$$Surface Area of a cylinder $$= 2 \ π \ r \ (r \ + \ h)$$,The radius of the cylinder is $$5 \ (10 \ ÷ \ 2)$$ inches and its height is $$8$$ inches. Therefore, Surface Area of a cylinder $$=2 \ π \ (5) \ (5 \ + \ 6)=110 \ π$$  in$$^2$$ 39- Choice C is correct The correct answer is $$80$$ feetThe 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 $$60^\circ$$ angle is half of the hypotenuse. Draw the shape of this question: The latter is the hypotenuse. Therefore, the latter is $$80$$ ft. 40- Choice A is correct The correct answer is II onlyI. $$|a| \ < \ 1→- \ 1 \ < \ a \ < \ 1$$Multiply all sides by $$b$$.Since, $$b \ > \ 0→- \ b \ < \ b \ a \ < \ b$$ (it is true!)II. Since, $$- \ 1 \ < \ a \ < \ 1$$,and $$a \ < \ 0→- \ a \ > \ a^2 \ > \ a$$ (plug in $$- \ \frac{1}{2}$$, and check!) (It’s false)III. $$- \ 1 \ < \ a \ < \ 1$$, multiply all sdes by $$2$$, then: $$- \ 2 \ < \ 2 \ a \ < \ 2$$Subtract $$3$$ from all sides. Then:$$- \ 2 \ - \ 3 \ < \ 2 \ a \ - \ 3 \ < \ 2 \ - \ 3→- \ 5 \ < \ 2 \ a \ - \ 3 \ < \ - \ 1$$ (It is true!)

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