## 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.

### Prepare for the DAT Quantitative Reasoning Test in 7 Days

$16.99$11.99
29% Off*

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

DAT Quantitative Reasoning
Practice Test 4

40 questions

Total time for this section: 45 Minutes

You may use a basic calculator on this test.

1-

If the interior angles of a quadrilateral are in the ratio $$1:2:3:6$$, what is the measure of the largest angle?

(A) $$72^\circ$$
(B) $$180^\circ$$
(C) $$30^\circ$$
(D) $$90^\circ$$
(E) $$60^\circ$$
2-

A bank is offering $$2.7\%$$ simple interest on a savings account. If you deposit $$18,000$$, how much interest will you earn in three years?

(A) $$1,450$$
(B) $$1,458$$
(C) $$1,456$$
(D) $$1,445$$
(E) $$1,440$$
3-

If $$f(x) = 6 \ x \ + \ 3$$ and $$g(x) = 2 \ x^2 \ + \ 2 \ x$$, then find $$(\frac{f}{g})(x)$$.

(A) $$\frac{6 \ x \ + \ 3}{2 \ x^2 \ + \ 2 \ x}$$
(B) $$\frac{6 \ x \ - \ 3}{2 \ x^2 \ + \ 2 \ x}$$
(C) $$\frac{3 \ x \ - \ 3}{ x^2 \ + \ 2 \ x}$$
(D) $$\frac{3 \ x \ + \ 3}{ x^2 \ + \ 2 \ x}$$
(E) $$\frac{3 \ x \ + \ 3}{ x^2 \ - \ 2 \ x}$$
4-

If the area of a circle is $$36$$ square meters, what is its diameter?

(A) $$\frac{6 \ \sqrt{π}}{6}$$
(B) $$\frac{ \sqrt{6 \ π}}{π}$$
(C) $$\frac{6 \ \sqrt{π}}{π}$$
(D) $${6\ π}$$
(E) $${6}$$
5-

If the ratio of home fans to visiting fans in a crowd is $$6:4$$ and all $$30,000$$ seats in a stadium are filled, how many visiting fans are in attendance?

(A) $$12,000$$
(B) $$10,000$$
(C) $$14,000$$
(D) $$11,000$$
(E) $$16,000$$
6-

In the standard $$(x,y)$$ coordinate plane, which of the following lines contains the points $$(2, - \ 6)$$ and $$(5, 18)$$?

(A) $$y=8 \ x \ + \ 22$$
(B) $$y=8 \ x \ + \ 10$$
(C) $$y=8 \ x \ − \ 22$$
(D) $$y=8 \ x \ − \ 10$$
(E) $$y=4 \ x \ − \ 10$$
7-

In the figure below, line A is parallel to line B. What is the value of angle $$x$$?

(A) $$125$$ degree
(B) $$135$$ degree
(C) $$60$$ degree
(D) $$120$$ degree
(E) $$130$$ degree
8-

If sin $$A =\frac{6}{4}$$ in a right triangle and the angle $$A$$ is an acute angle, then what is cos $$A$$?

(A) $$\frac{\sqrt{20}}{6}$$
(B) $$\frac{\sqrt{20}}{4}$$
(C) $$\frac{\sqrt{6}}{4}$$
(D) $$\frac{\sqrt{4}}{6}$$
(E) $$\frac{{20}}{6}$$
9-

The length of a rectangle is $$\frac{3}{2}$$ times its width. If the width is $$18$$, what is the perimeter of this rectangle?

(A) $${95}$$
(B) $${80}$$
(C) $${92}$$
(D) $${72}$$
(E) $$90$$
10- If $$120\%$$ of a number is $$60$$, then what is $$80\%$$ of that number?
(A) $$45$$
(B) $$40$$
(C) $$60$$
(D) $$65$$
(E) $$44$$
11-

Last week $$32,000$$ fans attended a football match. This week four times as many bought tickets, but one Fourth of them cancelled their tickets. How many are attending this week?

(A) $$96,000$$
(B) $$128,000$$
(C) $$32,000$$
(D) $$98,000$$
(E) $$90,000$$
12- The width of a box is one Fourth of its length. The height of the box is one Fourth of its width. If the length of the box is $$32$$ cm, what is the volume of the box?
(A) $$510$$ cm$$^3$$
(B) $$515$$ cm$$^3$$
(C) $$520$$ cm$$^3$$
(D) $$512$$ cm$$^3$$
(E) $$514$$ cm$$^3$$
13- If tan⁡$$x=\frac{5}{12}$$, then sin ⁡$$x=$$
(A) $$\frac{12}{13}$$
(B) $$\frac{13}{5}$$
(C) $$\frac{13}{12}$$
(D) $$\frac{5}{13}$$
(E) $$\frac{12}{5}$$
14- Convert $$860,000$$ to scientific notation.
(A) $$86 \ × \ 10^5$$
(B) $$8.6 \ × \ 10^4$$
(C) $$8.6 \ × \ 10^5$$
(D) $$8.6 \ × \ 10^6$$
(E) $$8.6 \ × \ 10^7$$
15- If $$(x \ - \ 3)^2 \ + \ 2 \ > \ 4 \ x \ - \ 5$$, then $$x$$ can equal which of the following?
(A) $$1$$
(B) $$6$$
(C) $$8$$
(D) $$3$$
(E) $$4$$
16- What is the solution of the following inequality?
$$|x \ + \ 4| \ ≥ \ 7$$
(A) $$x \ ≥ - \ 3 \ ∪ \ x \ ≤ − \ 11$$
(B) Set of real numbers
(C) $$x \ ≥ \ 3 \ ∪ \ x \ ≤ − \ 11$$
(D) $$x \ ≥ \ 3$$
(E) $$x \ ≤ − \ 11$$
17- In the following figure, ABCD is a rectangle. If $$a=\sqrt{5}$$, and $$b=3 \ a$$, find the area of the shaded region. (the shaded region is a trapezoid)
(A) $$\sqrt{5}$$
(B) $$5 \ \sqrt{5}$$
(C) $$4 \ \sqrt{5}$$
(D) $${5}$$
(E) $${4}$$
18- In two successive years, the population of a town is increased by $$30\%$$ and $$40\%$$. What percent of the population is increased after two years?
(A) $$182\%$$
(B) $$85\%$$
(C) $$82\%$$
(D) $$80\%$$
(E) $$88\%$$
19- Which of the following is one solution of this equation?
$$x^2\ -\ 2\ x\ -\ 4=0$$
(A) $$1 \ - \ \sqrt{4}$$
(B) $$1 \ + \ \sqrt{4}$$
(C) $$1 \ - \ \sqrt{5}$$
(D) $$- \ \sqrt{5}$$
(E) $$\sqrt{5}$$
20- $$(x^2)^{\frac{6}{9}}$$ equal to?
(A) $$x^{\frac{6}{9}}$$
(B) $$x^{\frac{12}{9}}$$
(C) $$x^{\frac{2}{9}}$$
(D) $$x^{\frac{12}{6}}$$
(E) $$x^{\frac{9}{6}}$$
21- three-kilograms apple and four -kilograms orange cost $$30$$. If one$$-$$kilogram apple costs $$6$$ how much does one-kilogram orange cost?
(A) $$9$$
(B) $$8$$
(C) $$6$$
(D) $$4$$
(E) $$3$$
22- In the following figure, what is the perimeter of $$\triangle$$ABC if the area of $$\triangle$$ADC is $$30$$?
(A) $$35$$
(B) $$15$$
(C) $$45$$
(D) $$40$$
(E) $$30$$

### DAT Quantitative Reasoning Preparation 2020 – 2021

$18.99$13.99
26% Off*

DAT Math Workbook + 2 Full-Length DAT Quantitative Reasoning Practice Tests

23- Which of the following expressions is equal to $$\sqrt{\frac{x^2}{5} \ - \ \frac{x^2}{25}}$$?
(A) $$\frac{4 \ x}{5}$$
(B) $$\frac{2 \ x}{5}$$
(C) $$\frac{5\ x}{2}$$
(D) $$\frac{ 6 \ x}{2}$$
(E) $$\frac{ 3 \ x}{2}$$
24- If $$5 \sqrt{ \ x}=\sqrt{y}$$, then $$x=$$
(A) $$\frac{y}{5}$$
(B) $$\frac{25}{y}$$
(C) $$\frac{5}{y}$$
(D) $$\frac{y}{25}$$
(E) $$- \ \frac{y}{25}$$
25- A card is drawn at random from a standard $$72–$$card deck, what is the probability that the card is of Hearts? (The deck includes $$16$$ of each suit clubs, diamonds, hearts, and spades)
(A) $$\frac{2}{9}$$
(B) $$\frac{4}{9}$$
(C) $$\frac{16}{9}$$
(D) $$\frac{9}{2}$$
(E) $$\frac{12}{9}$$
26- The average weight of $$23$$ girls in a class is $$50$$ kg and the average weight of $$25$$ boys in the same class is $$65$$ kg. What is the average weight of all the $$45$$ students in that class?
(A) $$57.82$$
(B) $$57.83$$
(C) $$57.81$$
(D) $$57.80$$
(E) $$57.84$$
27- A football team had $$35,000$$ to spend on supplies. The team spent $$18,000$$ on new balls. New sport shoes cost $$135$$ each. Which of the following inequalities represent how many new shoes the team can purchase?
(A) $$135 \ x \ - \ 18,000 \ ≤ \ 35,000$$
(B) $$135 \ x \ - \ 18,000 \ \geq \ 35,000$$
(C) $$135 \ x \ +\ 18,000 \ \geq \ 35,000$$
(D) $$135 \ x \ + \ 18,000 \ ≤ \ 35,000$$
(E) $$135 \ x \ + \ 18,000 \ ≤ - \ 35,000$$
28- What is the value of the expression $$4 \ (x \ + \ 3 \ y) \ - \ (3 \ + \ x)^2$$ when $$x=4$$ and $$y= 2$$?
(A) $$8 9$$
(B) $$9$$
(C) $$- \ 9$$
(D) $$- \ 89$$
(E) $$49$$
29- The average of five consecutive numbers is $$25$$. What is the smallest number?
(A) $$25$$
(B) $$27$$
(C) $$32$$
(D) $$30$$
(E) $$26$$
30- If $$y=(- \ 4 \ x^3)^2$$, which of the following expressions is equal to $$y$$?
(A) $$16 \ x^3$$
(B) $$64 \ x^3$$
(C) $$- \ 16 \ x^6$$
(D) $$- \ 64 \ x^6$$
(E) $$16 \ x^6$$
31- The surface area of a cylinder is $$192 \ π$$ cm$$^2$$. If its height is $$4$$ cm, what is the radius of the cylinder?
(A) $$- \ 8$$ cm
(B) $$8$$ cm
(C) $$12$$ cm
(D) $$- \ 12$$ cm
(E) $$96$$ cm
32- Mia purchased a sofa for $$616.85$$. The sofa is regularly priced at $$845$$. What was the percent discount Mia received on the sofa?
(A) $$73\%$$
(B) $$75\%$$
(C) $$25\%$$
(D) $$27\%$$
(E) $$20\%$$
33- What is the difference in area between a $$6$$ cm by $$3$$ cm rectangle and a circle with diameter of $$8$$ cm? $$(π=3)$$
(A) $$35$$
(B) $$18$$
(C) $$48$$
(D) $$66$$
(E) $$30$$
34- A cruise line ship left Port $$A$$ and traveled $$50$$ miles due west and then $$120$$ miles due north. At this point, what is the shortest distance from the cruise to port $$A$$?
(A) $$140$$ miles
(B) $$130$$ miles
(C) $$120$$ miles
(D) $$110$$ miles
(E) $$170$$ miles
35- What is the slope of a line that is perpendicular to the line?
$$9 \ x \ - \ 3 \ y=24$$?
(A) $$\frac{1}{3}$$
(B) $$\frac{1}{2}$$
(C) $$− \ \frac{1}{3}$$
(D) $$− \ \frac{1}{2}$$
(E) $$− \ \frac{1}{9}$$
36- If $$f(x)=4 \ x^3 \ - \ 5$$ and $$(x)=\frac{x}{6}$$, what is the value of $$f(g(x))$$?
(A) $$\frac{ x^3}{54} \ + \ 5$$
(B) $$\frac{ x^3}{54} \ - \ 5$$
(C) $$\frac{ x^3}{216} \ - \ 5$$
(D) $$\frac{ x^3}{216} \ + \ 5$$
(E) $$\frac{ x^3}{216}$$
37- The ratio of boys to girls in a school is $$1:5$$. If there are $$750$$ students in a school, how many boys are in the school.
(A) $$133$$
(B) $$120$$
(C) $$135$$
(D) $$140$$
(E) $$125$$
38- If the ratio of $$7 \ a$$ to $$4 \ b$$ is $$\frac{1}{8}$$, what is the ratio of $$a$$ to $$b$$?
(A) $$\frac{1}{16}$$
(B) $$\frac{1}{15}$$
(C) $$\frac{1}{14}$$
(D) $$\frac{1}{13}$$
(E) $$\frac{1}{12}$$
39- If one angle of a right triangle measures $$30^\circ$$, what is the sine of the other acute angle?
(A) $$\frac{\sqrt{3}}{2}$$
(B) $$\frac{\sqrt{2}}{3}$$
(C) $$\frac{\sqrt{3}}{3}$$
(D) $$\frac{\sqrt{2}}{2}$$
(E) $$1$$
40- If $$x=8$$, what is the value of $$y$$ in the following equation?
$$4 \ y =\frac{4 \ x^2}{2} \ - \ 4$$
(A) $$30$$
(B) $$35$$
(C) $$34$$
(D) $$31$$
(E) $$33$$
 1- Choice B is correct The correct answer is $$180^\circ$$The sum of all angles in a quadrilateral is $$360$$ degrees. Let $$x$$ be the smallest angle in the quadrilateral.Then the angles are:$$x, 2 \ x, 3 \ x, 6 \ x$$$$x \ + \ 2 \ x \ + \ 3 \ x \ + \ 6 \ x=360→12 \ x=360→x=30$$The angles in the quadrilateral are: $$30^\circ, 60^\circ, 90^\circ$$, and $$180^\circ$$ 2- Choice B is correct The correct answer is $$1,458$$Use simple interest formula:$$I=prt$$($$I =$$ interest, $$p =$$ principal, $$r =$$ rate, $$t =$$ time)$$I=(18000) \ (0.027) \ (3)=1458$$ 3- Choice A is correct The correct answer is $$\frac{6 \ x \ + \ 3}{2 \ x^2 \ + \ 2 \ x}$$$$(\frac{f}{g})(x) = \frac{f(x)}{g(x)}=\frac{6 \ x \ + \ 3}{2 \ x^2 \ + \ 2\ x}$$ 4- Choice C is correct The correct answer is $$\frac{6 \ \sqrt{π}}{π}$$Formula for the area of a circle is:A $$=π \ r^2$$Using $$36$$ for the area of the circle we have:$$36=π \ r^2$$Let’s solve for the radius $$(r)$$.$$\frac{36}{π}=r^2→r=\sqrt{\frac{36}{π}}=\frac{6}{\sqrt{π}}=\frac{6}{\sqrt{π}} \ × \ \frac{\sqrt{π}}{\sqrt{π}}=\frac{6\ \sqrt{π}}{π}$$ 5- Choice A is correct The correct answer is $$12,000$$Number of visiting fans: $$\frac{4 \ × \ 30000}{10}=12,000$$ 6- Choice C is correct The correct answer is $$y=8 \ x \ − \ 22$$The equation of a line is: $$y=m \ x \ + \ b$$, where m is the slope and is the $$y-$$intercept.First find the slope:$$m=\frac{y_{2} \ - \ y_{1}}{x_{2} \ - \ x_{1}}=\frac{18 \ -\ (- \ 6)}{5 \ - \ 2}=\frac{24}{3}=8$$Then, we have: $$y=8 \ x \ + \ b$$Choose one point and plug in the values of $$x$$ and $$y$$ in the equation to solve for $$b$$.Let’s choose the point $$(2, - \ 6)$$$$y=8 \ x \ + \ b→- \ 6=8 \ (2) \ + \ b→- \ 6=16 \ + \ b→b=- \ 22$$The equation of the line is: $$y=8 \ x \ - \ 22$$ 7- Choice D is correct The correct answer is $$120$$ degreeThe angle $$x$$ and $$35$$ are complementary angles.Therefore:$$x \ + \ 60=180$$$$180^\circ \ - \ 60^\circ=120^\circ$$ 8- Choice B is correct The correct answer is $$\frac{\sqrt{20}}{4}$$sin $$A=\frac{6}{4}⇒$$ Since sin $$θ=\frac{opposite}{hypotenuse}$$, we have the following right triangle. Then:$$c=\sqrt{6^2 \ - \ 4^2 }=\sqrt{36 \ - \ 16}=\sqrt{20}$$cos $$=\frac{\sqrt{20}}{4}$$ 9- Choice E is correct The correct answer is $$90$$Length of the rectangle is: $$\frac{3}{2} \ × \ 18=27$$perimeter of rectangle is: $$2 \ × \ (27 \ + \ 18)=90$$ 10- Choice B is correct The correct answer is $$40$$First, find the number.Let $$x$$ be the number.Write the equation and solve for $$x$$. $$120\%$$ of a number is $$60$$, then:$$1.2 \ × \ x=60 ⇒ x=60 \ ÷ \ 1.2=50$$$$80\%$$ of $$50$$ is:$$0.9 \ × \ 50=40$$ 11- Choice A is correct The correct answer is $$96,000$$Three times of $$32,000$$ is $$128,000$$.One sixth of them cancelled their tickets.One sixth of $$128,000$$ equals $$32,000 \ (\frac{1}{4} \ × \ 128000=32000)$$. $$96,000 \ (128000 \ – \ 32000=96000)$$ fans are attending this week 12- Choice D is correct The correct answer is $$512$$ cm$$^3$$If the length of the box is $$32$$, then the width of the box is one Fourth of it, $$8$$, and the height of the box is $$2$$ (one Fourth of the width). The volume of the box is:V $$=$$ (length) $$×$$ (wdth) $$×$$ (height) $$=(32) \ × \ (8) \ × \ (2)=512$$ cm$$^3$$ 13- Choice D is correct The correct answer is $$\frac{5}{13}$$tan⁡$$=\frac{opposite}{adjacet}$$, and tan⁡$$x=\frac{5}{12}$$, therefore, the opposite side of the angle $$x$$ is $$5$$ and the adjacent side is $$12$$.Let’s draw the triangle.Using Pythagorean theorem, we have:$$a^2 \ + \ b^2=c^2→5^2 \ + \ 12^2=c^2→25 \ + \ 144=c^2→c=13$$sin $$x⁡=\frac{opposite}{hypotenuse}=\frac{5}{13}$$ 14- Choice C is correct The correct answer is $$8.6 \ × \ 10^5$$$$860000=8.6 \ × \ 10^5$$ 15- Choice A is correct The correct answer is $$1$$Plug in the value of each option in the inequality.A. $$1 \ \ \ (1 \ - \ 3)^2 \ + \ 2 \ > \ 4 \ (1) \ - \ 5→6 \ > - \ 1$$    Bingo!B. $$6 \ \ \ (6 \ - \ 3)^2 \ + \ 2 \ > \ 4 \ (6) \ - \ 5→11 \ > \ 19$$ No!C. $$8 \ \ \ (8 \ - \ 3)^2 \ + \ 2 \ > \ 4 \ (8) \ - \ 5→27 \ > \ 27$$ No!D. $$3 \ \ \ (3 \ - \ 3)^2 \ + \ 2 \ > \ 4 \ (3) \ - \ 5→2 \ > \ 7$$    No!E. $$4 \ \ \ (4 \ - \ 3)^2 \ + \ 3 \ > \ 4 \ (4) \ - \ 5→4 \ > \ 11$$   No! 16- Choice C is correct The correct answer is $$x \ ≥ \ 3 \ ∪ \ x \ ≤ − \ 11$$$$x \ + \ 4 \ ≥ \ 7→x \ ≥ \ 7 \ - \ 4→x \ ≥ \ 3$$Or$$x \ + \ 4 \ ≤ \ - \ 7→x \ ≤ \ - \ 7 \ - \ 4→x \ ≤ \ - \ 11$$Then, solution is: $$x \ ≥ \ 3 \ ∪ \ x \ ≤ \ − \ 11$$ 17- Choice B is correct The correct answer is $$5 \ \sqrt{5}$$Based on triangle similarity theorem: $$\frac{a}{a \ + \ b}=\frac{c}{4}→c=\frac{4 \ a}{a \ + \ b}=\frac{4 \ \sqrt{5}}{4 \ \sqrt{5}}=1→$$area of shaded region is: $$(\frac{c \ + \ 4}{2}) \ (b)=\frac{5}{2} \ × \ 2 \ \sqrt{5}=5 \ \sqrt{5}$$ 18- Choice C is correct The correct answer is $$82\%$$the population is increased by $$30\%$$ and $$40\%$$. $$15\%$$ increase changes the population to $$130\%$$ of original population. For the second increase, multiply the result by $$140\%$$.$$(1.30) \ × \ (1.40)=1.82=182\%$$$$82$$ percent of the population is increased after two years. 19- Choice C is correct The correct answer is $$1 \ - \ \sqrt{5}$$$$x_{1,2} = \frac{- \ b \pm \sqrt{b^2 \ - \ 4 \ a \ c}}{2 \ a }$$$$a \ x^2 \ + \ b \ x \ + \ c=0$$$$2 \ x^2 \ - \ 4 \ x \ – \ 8=0 ⇒$$ then: $$a=1, \ b=- \ 2$$ and $$c= – \ 4$$ $$x =\frac{ 2 \ + \ \sqrt{- \ 2 ^2 \ - \ (4) .(1) .(- \ 4)} }{2 .1}=1 \ - \ \sqrt{5 }$$$$x =\frac{2 \ - \ \sqrt{- \ 2^2 \ - \ (4) .(1) .(- \ 4)} }{2 .1}= 1 \ + \ \sqrt{5 }$$ 20- Choice B is correct The correct answer is $$x^{\frac{12}{9}}$$$$(x^2)^{\frac{6}{9}} = x^{2 \ × \ \frac{6}{9}} = x^{ \frac{12}{6}} =$$ 21- Choice E is correct The correct answer is $$3$$Let $$x$$ be the cost of one-kilogram orange, then:$$4\ x \ + \ (3 \ × \ 6)=30→$$$$4 \ x \ + \ 18= 30→$$$$4 \ x=30 \ - \ 18→$$$$4 \ x=12→x=\frac{12}{4}=3$$ 22- Choice D is correct The correct answer is $$40$$Let $$x$$ be the length of AB, then:$$30=\frac{x \ × \ 2}{2}→x=15$$The length of AC $$=\sqrt{15^2 \ + \ 8^2}=\sqrt{289}=17$$The perimeter of $$\triangle$$ABC $$=15 \ + \ 8 \ + \ 17=40$$ 23- Choice B is correct The correct answer is $$\frac{2 \ x}{5}$$Simplify the expression.$$\sqrt{\frac{x^2}{5} \ - \ \frac{x^2}{25}}=\sqrt{\frac{5 \ x^2}{25} \ - \ \frac{x^2}{25}}=\sqrt{\frac{4 \ x^2}{25}}=\sqrt{\frac{4}{25} \ x^2}=$$$$\sqrt{\frac{4}{25}} \ × \ \sqrt{x^2}=\frac{2}{5} \ × \ x=\frac{2 \ x}{5}$$ 24- Choice D is correct The correct answer is $$\frac{y}{25}$$Solve for $$x$$.$$5 \ \sqrt{ x}=\sqrt{y}$$Square both sides of the equation:$$( 5\ \sqrt{ x})^2=(\sqrt{y})^2$$$$25 \ x=y$$$$x=\frac{y}{25}$$ 25- Choice A is correct The correct answer is $$\frac{2}{9}$$The probability of choosing a Hearts is $$\frac{16}{72} = \frac{2}{9}$$ 26- Choice C is correct The correct answer is $$57.81$$average $$= \frac{sum \ of \ terms }{number \ of \ terms}$$The sum of the weight of all girls is: $$23 \ × \ 50=1150$$ kgThe sum of the weight of all boys is: $$25 \ × \ 65=1625$$ kgThe sum of the weight of all students is: $$1150 \ + \ 1625=2775$$ kgaverage $$= \frac{2775}{48}=57.81$$ 27- Choice D is correct The correct answer is $$135 \ x \ + \ 18,000 \ ≤ \ 35,000$$Let $$x$$ be the number of shoes the team can purchase. Therefore, the team can purchase $$120 \ x$$.The team had $$35,000$$ and spent $$18000$$.Now the team can spend on new shoes $$17000$$ at most. Now, write the inequality:$$135 \ x \ + \ 18,000 \ ≤ \ 35,000$$ 28- Choice C is correct The correct answer is $$- \ 9$$Plug in the value of $$x$$ and, $$x=4$$ and $$y= 2$$$$4 \ (x \ + \ 3 \ y) \ - \ (3 \ + \ x)^2=$$$$4 \ (4 \ + \ 3 \ ( 2)) \ - \ (3 \ + \ 4)^2=$$$$4 \ (4 \ + \ 6) \ - \ (7)^2 = 40 \ - \ 49=- \ 9$$ 29- Choice A is correct The correct answer is $$25$$Let $$x$$ be the smallest number.Then, these are the numbers:$$x, x \ + \ 1, x \ + \ 2, x \ + \ 3, x \ + \ 4$$average $$= \frac{sum \ of \ terms}{number \ of \ terms} ⇒$$$$27= \frac{x \ + \ (x \ + \ 1) \ + \ (x \ + \ 2) \ + \ (x \ + \ 3) \ + \ (x \ + \ 4)}{5}⇒$$$$27=\frac{5 \ x \ + \ 10}{5} ⇒$$$$135 = 5 \ x \ + \ 10 ⇒$$$$125 = 5 \ x ⇒ x=25$$ 30- Choice E is correct The correct answer is $$16 \ x^6$$$$y=(- \ 4 \ x^3)^2=(- \ 4)^2 \ (x^3)^2=16 \ x^6$$ 31- Choice B is correct The correct answer is $$8$$ cmFormula for the Surface area of a cylinder is:SA $$=2 \ π \ r^2 \ + \ 2 \ π \ h→192 \ π=2 \ π \ r^2 \ + \ 2 \ π \ r \ (4)→r^2 \ + \ 4 \ r \ - \ 96=0$$Factorize and solve for $$r$$.$$(r \ + \ 12) \ (r \ - \ 8)=0→r=8$$ or $$= - \ 12$$ (unacceptable) 32- Choice D is correct The correct answer is $$27\%$$The question is this: $$616.85$$ is what percent of $$845$$?Use percent formula:part $$= \frac{percent}{100} \ ×$$ whole $$616.85 = \frac{percent}{100} \ × \ 845 ⇒$$$$616.85=\frac{percent \ × \ 845}{100} ⇒$$$$61685=$$ percent $$× \ 845 ⇒$$ percent $$= \frac{61685}{845} =73$$$$616.85$$ is $$73\%$$ of $$845$$.Therefore, the discount is: $$100\% \ – \ 73\%=27\%$$ 33- Choice E is correct The correct answer is $$30$$The area of rectangle is: $$6 \ × \ 3=18$$ cm$$^2$$The area of circle is: $$π \ r^2=π \ × \ (\frac{8}{2})^2=3 \ × \ 16=48$$ cm$$^2$$Difference of areas is: $$48 \ - \ 18=30$$ 34- Choice B is correct The correct answer is $$130$$ milesUse the information provided in the question to draw the shape.Use Pythagorean Theorem: $$a^2 \ + \ b^2=c^2$$$$50^2 \ + \ 120^2=c^2⇒$$$$2500 \ + \ 14400 = c^2⇒$$$$16900 = c^2⇒ c = 130$$ 35- Choice C is correct The correct answer is $$− \ \frac{1}{3}$$The equation of a line in slope intercept form is: $$y=m \ x \ + \ b$$Solve for $$y$$.$$9 \ x \ - \ 3 \ y=24 ⇒$$$$- \ 3 \ y=24 \ - \ 9 \ x ⇒$$$$y=(24 \ - \ 9 \ x) \ ÷ \ (- \ 3) ⇒$$$$y=3\ x \ - \ 8$$The slope is $$3$$.The slope of the line perpendicular to this line is:$$m_{1} \ × \ m_{2} = - \ 1 ⇒$$$$3 \ × \ m_{2} = - \ 1 ⇒$$$$m_{2} = - \ \frac{1}{3}$$ 36- Choice B is correct The correct answer is $$\frac{ x^3}{54} \ - \ 5$$$$f(g(x))=4 \ × \ (\frac{x}{6})^3 \ - \ 5=\frac{4 \ x^3}{216} \ - \ 5 = \frac{x^3 }{54} \ - \ 5$$ 37- Choice E is correct The correct answer is $$125$$The ratio of boy to girls is $$1:5$$.Therefore, there are $$1$$ boys out of $$6$$ students.To find the answer, first divide the total number of students by $$6$$, then multiply the result by $$1$$. $$750 \ ÷ \ 6=125 ⇒ 125 \ × \ 1=125$$ 38- Choice C is correct The correct answer is $$\frac{1}{14}$$Write the ratio of $$7\ a$$ to $$4 \ b$$.$$\frac{7 \ a}{4 \ b}=\frac{1}{8}$$Use cross multiplication and then simplify.$$7 \ a \ × \ 8=4 \ b \ × \ 1→56 \ a=4 \ b→a=\frac{4 \ b}{56}=\frac{b}{14}$$Now, find the ratio of $$a$$ to $$b$$.$$\frac{a}{b}=\frac{\frac{b}{14}}{b}→\frac{b}{14} \ ÷ \ b=\frac{b}{14} \ × \ \frac{1}{b}=\frac{b}{14 \ b}=\frac{1}{14}$$ 39- Choice A is correct The correct answer is $$\frac{\sqrt{3}}{2}$$The relationship among all sides of right triangle $$30^\circ \ - \ 60^\circ \ - \ 90^\circ$$ is provided in the following triangle: Sine of $$60^\circ$$ equals to:$$\frac{opposite}{hypotenuse}=\frac{x\sqrt{3}}{2 \ x}=\frac{\sqrt{3}}{2}$$ 40- Choice D is correct The correct answer is $$31$$Plug in the value of $$x$$ in the equation and solve for $$y$$.$$4 \ y=\frac{4 \ x^2}{2} \ - \ 4→$$$$4 \ y = \frac{ 4 \ (8)^2}{2} \ - \ 4→$$$$4 \ y= \frac{4 \ (64)}{2} \ - \ 4→$$$$4 \ y= 128 \ - \ 4=124$$$$4 \ y = 124→y=31$$

### Prepare for the DAT Quantitative Reasoning Test in 7 Days

$16.99$11.99
29% Off*

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

### 5 Full Length SSAT Lower Level Math Practice Tests

$16.99$11.99

### GED Math Practice Workbook 2022

$27.99$13.99

### 5 Full-Length STAAR Grade 7 Math Practice Tests

$16.99$11.99

### SSAT Middle Level Mathematics Workbook

$16.99$11.99