Full Length ISEE Middle Level Practice Test

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ISEE Middle Level
Practice Test 3
Quantitative Reasoning

• 37 questions
• Total time for this section: 35 Minutes
• Calculators are not allowed at the test.
1- Solve. $$\frac{- \ 45 \ × \ 0.2}{5}$$
(A) $$- \ \frac{9}{5}$$
(B) $$- \ \frac{7}{5}$$
(C) $$\frac{4}{5}$$
(D) $$- \ 2$$
2- Jim purchased a table for $$10\%$$ off and saved $$25$$. What was the original price of the table?
(A) $$250$$
(B) $$240$$
(C) $$220$$
(D) $$230$$
3- The area of a circle is $$49 \ π$$ in$$^2$$. What is the circumference of the circle?
(A) $$16 \ π$$
(B) $$12 \ π$$
(C) $$14 \ π$$
(D) $$18 \ π$$
4- What is the value of $$x$$ in the following equation? $$9^x=729$$
(A) $$2$$
(B) $$3$$
(C) $$4$$
(D) $$5$$
5- A $$40$$ shirt now selling for $$30$$ is discounted by what percent?
(A) $$25\%$$
(B) $$30\%$$
(C) $$35\%$$
(D) $$20\%$$
6- Which of the following shows the numbers in descending order?
(A) $$\frac{3}{8}, \frac{1}{8}, \frac{2}{5}, \frac{1}{2}$$
(B) $$\frac{1}{8}, \frac{3}{8}, \frac{2}{5}, \frac{1}{2}$$
(C) $$\frac{1}{2}, \frac{3}{8}, \frac{2}{5}, \frac{1}{8}$$
(D) $$\frac{2}{5}, \frac{3}{8}, \frac{1}{8}, \frac{1}{2}$$
7- The score of Emma was half as that of Ava and the score of Mia was twice that of Ava. If the score of Mia was $$30$$, what is the score of Emma?
(A) $$5$$
(B) $$15$$
(C) $$10$$
(D) $$20$$
8- If $$f=2 \ x \ - \ 6 \ y$$ and $$g=x \ + \ 2 \ y$$, what is $$2 \ f \ + \ g$$?
(A) $$5 \ x \ + \ 20 \ y$$
(B) $$2 \ x \ + \ 10 \ y$$
(C) $$5 \ x \ - \ 10 \ y$$
(D) $$- \ 5 \ x \ + \ 10 \ y$$
9- $$712,232,691 \ × \ 0.001$$?
(A) $$71,223.2691$$
(B) $$7,122,326.91$$
(C) $$712,232.691$$
(D) $$7,122.32691$$
10- one third of $$12$$ is equal to $$\frac{1}{4}$$ of what number?
(A) $$16$$
(B) $$12$$
(C) $$8$$
(D) $$24$$
11- What is the mean in the following set of numbers?
$$7,15,26,32,48,63,100,121$$
(A) $$51$$
(B) $$51.5$$
(C) $$54.5$$
(D) $$54$$
12- Round off the result of $$1.18 \ × \ 6.3$$ to the nearest tenth?
(A) $$7.40$$
(B) $$7.43$$
(C) $$7.44$$
(D) $$7.41$$
13- Find $$\frac{1}{3}$$ of $$\frac{5}{6}$$ of $$360$$?
(A) $$150$$
(B) $$200$$
(C) $$250$$
(D) $$100$$
14- What is the value of $$x$$ in the following equation?
$$3 \ (x \ + \ 5) = 2 \ (x \ − \ 1) \ + \ 15$$
(A) $$- \ 2$$
(B) $$2$$
(C) $$5$$
(D) $$3$$
15- What is the value of $$x$$ in the following figure?
(A) $$16^\circ$$
(B) $$132^\circ$$
(C) $$164^\circ$$
(D) $$150^\circ$$
16- What is the value of $$x$$ in the following figure?
(A) $$148^\circ$$
(B) $$152^\circ$$
(C) $$140^\circ$$
(D) $$125^\circ$$
17- The ratio of boys and girls in a class is $$2:5$$. If there are $$49$$ students in the class, how many more boys should be enrolled to make the ratio $$1:1$$?
(A) $$24$$
(B) $$21$$
(C) $$35$$
(D) $$18$$
18- In five successive hours, a car travels $$38$$ km, $$40$$ km, $$54$$ km, $$32$$ km and $$61$$ km. In the next five hours, it travels with an average speed of $$54$$ km per hour. Find the total distance the car traveled in $$10$$ hours.
(A) $$475$$ km
(B) $$425$$ km
(C) $$495$$ km
(D) $$455$$ km
19- The price of a laptop is decreased by $$12\%$$ to $$280$$. What is its original price?
(A) $$200$$
(B) $$400$$
(C) $$300$$
(D) $$500$$
20- A company pays its employee $$5,000$$ plus $$5\%$$ of all sales profit. If $$x$$ is all sold profit, which of the following represents the employee’s revenue?
(A) $$0.5 \ x \ - \ 5,000$$
(B) $$- \ 0.05 \ x \ - \ 5,000$$
(C) $$0.05 \ x \ + \ 500$$
(D) $$0.05 \ x \ + \ 5,000$$
21- The perimeter of the trapezoid below is $$45$$. What is its area?
(A) $$88$$ cm$$^2$$
(B) $$82$$ cm$$^2$$
(C) $$93$$ cm$$^2$$
(D) $$79$$ cm$$^2$$
22- What is value of $$- \ 22 \ - \ (- \ 71)$$?
(A) $$29$$
(B) $$39$$
(C) $$49$$
(D) $$59$$
23- Which of the following is a correct statement?
(A) $$\frac{3}{2} \ > \ 2.8$$
(B) $$10\%=\frac{1}{5}$$
(C) $$4 \ < \ \frac{3}{6}$$
(D) $$\frac{2}{5} \ > \ 0.3$$
24- What is the area of a square whose diagonal is $$6$$?
(A) $$36$$
(B) $$30$$
(C) $$32$$
(D) $$38$$
25- Car A use $$10-$$liter petrol per $$100$$ kilometers; car B use $$6-$$liter petrol per $$100$$ kilometers. If both cars drive $$350$$ kilometers, how much more petrol does car A use?
(A) $$28$$
(B) $$14$$
(C) $$24$$
(D) $$12$$
26- Using the information provided below, compare the quantity in column A to the quantity in Column B.
$$x^2 \ + \ 15 \ =\ 64$$
$$124 \ - \ 15 \ y\ =\ 49$$
 Quantity A Quantity  B $$x$$ $$y$$
(A) The relationship cannot be determined from the information given
(B) The two quantities are equal
(C) The quantity in Column A is greater
(D) The quantity in Column B is greater
27- Using the information provided below, compare the quantity in column A to the quantity in Column B.
$$\frac{3}{4} \lt x \lt \frac{3}{2}$$
 Quantity A Quantity  B $$x$$ $$\frac{4}{3}$$
(A) The relationship cannot be determined from the information given
(B) The quantity in Column A is greater
(C) The quantity in Column B is greater
(D) The two quantities are equal
28- $$a$$ and $$b$$ are real numbers. $$a \lt b$$
 Quantity A Quantity  B $$|a \ - \ b|$$ $$|b \ - \ a|$$
(A) The two quantities are equal
(B) The quantity in Column A is greater
(C) The quantity in Column B is greater
(D) The relationship cannot be determined from the information given
29- Using the information provided below, compare the quantity in column A to the quantity in Column B.
 Quantity A Quantity  B $$\frac{x^5}{5}$$ $$(\frac{x}{5})^5$$
(A) The two quantities are equal
(B) The quantity in Column B is greater
(C) The quantity in Column A is greater
(D) The relationship cannot be determined from the information given
30- Using the information provided below, compare the quantity in column A to the quantity in Column B.
 Column A Column B $$6 \ + \ 2 \times 7 \ + \ 5$$ $$4 \ + \ 4 \times 7 \ - \ 3$$
(A) The quantity in Column B is greater
(B) The quantity in Column A is greater
(C) The two quantities are equal
(D) The relationship cannot be determined from the information given
31- Using the information provided below, compare the quantity in column A to the quantity in Column B.
 Column A Column B $$\sqrt{49} \ +\ \sqrt{64}$$ $$\sqrt{81}$$
(A) The two quantities are equal
(B) The quantity in Column A is greater
(C) The quantity in Column B is greater
(D) The relationship cannot be determined from the information given
32- Using the information provided below, compare the quantity in column A to the quantity in Column B.
 Column A Column B $$\sqrt{121\ - \ 57}$$ $$\sqrt{121}\ -\ \sqrt{57}$$
(A) The relationship cannot be determined from the information given
(B) The two quantities are equal
(C) The quantity in Column A is greater
(D) The quantity in Column B is greater
33- The average age of Joe, Michelle, and Nicole is $$24$$.
 Column A Column B The average age of Joe and Michelle The average age of Michelle and Nicole
(A) The quantity in Column A is greater
(B) The quantity in Column B is greater
(C) The two quantities are equal
(D) The relationship cannot be determined from the information given
34- Using the information provided below, compare the quantity in column A to the quantity in Column B.
$$\ y\ = \ - \ 5 \ x \ - \ 12$$
 Column A Column B The value of $$x$$ when $$y=8$$ $$- \ 9$$
(A) The relationship cannot be determined from the information given
(B) The quantity in Column A is greater
(C) The quantity in Column B is greater
(D) The two quantities are equal
35- A right cylinder with radius $$4$$ inches has volume $$36 \ π$$ cubic inches.
 Quantity A Quantity  B The height of the cylinder $$4$$ inches
36- The average of $$5, 7$$, and $$x$$ is $$2$$.
 Quantity A Quantity  B $$x$$ average of $$\ x\ ,\ x\ -\ 2 \ ,\ x\ + \ 6\ ,\ 4 \ x\$$
(A) The relationship cannot be determined from the information given
(B) The quantity in Column A is greater
(C) The quantity in Column B is greater
(D) The two quantities are equal
37- $$x$$ is an integer greater than zero.
 Quantity A Quantity  B $$\frac{3}{x}\ + \ 2 \ x$$ $$7$$
(A) The quantity in Column A is greater
(B) The quantity in Column B is greater
(C) The two quantities are equal
(D) The relationship cannot be determined from the information given

ISEE Middle Level

Practice Test 3

Mathematics Achievement

• 47 questions
• Total time for this section: 40 Minutes
• Calculators are not allowed at the test.
38- In a bundle of $$60$$ pencils, $$27$$ are red and the rest are blue. About what percent of the bundle is composed of blue pencils?
(A) $$55\%$$
(B) $$50\%$$
(C) $$60\%$$
(D) $$63\%$$
39- Solving the equation: $$10\ x\ -\ 12.5\ =- \ 42$$?
(A) $$-\ 2.95$$
(B) $$-\ 3.18$$
(C) $$-\ 2.54$$
(D) $$3.43$$
40- What is the value of $$x$$ in the following equation?
$$(x \ - \ 2)^3=125$$
(A) $$5$$
(B) $$7$$
(C) $$- \ 2$$
(D) $$- \ 5$$
41- The price of a car was $$24,000$$ in $$2014, \ 18,000$$ in $$2015$$ and $$12,500$$ in $$2016$$. What is the rate of depreciation of the price of car per year?
(A) $$15\%$$
(B) $$20\%$$
(C) $$25\%$$
(D) $$30\%$$
42- $$2 \ (\frac{1}{2} \ - \ \frac{1}{6})\ + \ 7$$?
(A) $$12$$
(B) $$10$$
(C) $$8$$
(D) $$6$$
43- $$36$$ is equal to?
(A) $$2 \ + \ (3 \ × \ 10) \ + \ (2 \ × \ 30)$$
(B) $$(\frac{9}{3} \ × \ 2) \ + \ (\frac{30}{2} \ × \ 2)$$
(C) $$((\frac{3}{2} \ + \ 3) \ × \ \frac{18}{3}) \ + \ 63$$
(D) $$(2 \ × \ 15) \ + \ (50 \ × \ 2) \ - \ 46$$
44- What number is $$7$$ less than $$40\%$$ of $$24$$?
(A) $$2.6$$
(B) $$4.2$$
(C) $$5.8$$
(D) $$3.6$$
45- 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) $$59$$
(B) $$64$$
(C) $$81$$
(D) $$72$$
46- If $$\frac{2 \ x}{5}=40$$, then $$\frac{2 \ x}{6} =$$?
(A) $$20$$
(B) $$24$$
(C) $$12$$
(D) $$18$$
47- What is the difference in perimeter between a $$6$$ cm by $$5$$ cm rectangle and a circle with diameter of $$12$$ cm? $$(π=3)$$
(A) $$16$$ cm
(B) $$12$$ cm
(C) $$10$$ cm
(D) $$24$$ cm

ISEE Middle Level Math Prep 2020

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A Comprehensive Review and Step-By-Step Guide to Preparing for the ISEE Middle Level Math Test

48- What number is $$10$$ more than $$12\%$$ of $$230$$?
(A) $$42$$
(B) $$39.6$$
(C) $$28.9$$
(D) $$30$$
49- If $$170\%$$ of a number is $$68$$, then what is the $$80\%$$ of that number?
(A) $$25$$
(B) $$28$$
(C) $$32$$
(D) $$36$$
50- When a number is subtracted from $$18$$ and the difference is divided by that number, the result is $$3$$. What is the value of the number?
(A) $$3$$
(B) $$5$$
(C) $$6$$
(D) $$9$$
51- Calculate the approximate area of the following circle.
(A) $$81.2$$
(B) $$78.5$$
(C) $$69.3$$
(D) $$72.1$$
52- When a gas tank can hold $$24$$ gallons, how many gallons does it contain when it is $$\frac{3}{4}$$ full?
(A) $$24$$
(B) $$20$$
(C) $$18$$
(D) $$15$$
53- From last year, the price of gasoline has increased from $$1.25$$ per gallon to $$1.75$$ per gallon. The new price is what percent of the original price?
(A) $$120\%$$
(B) $$160\%$$
(C) $$100\%$$
(D) $$140\%$$
54- Which of the following angles can represent the three angles of an isosceles right triangle?
(A) $$45^\circ, 45^\circ, 90^\circ$$
(B) $$10^\circ, 80^\circ, 90^\circ$$
(C) $$50^\circ, 50^\circ, 80^\circ$$
(D) $$60^\circ, 60^\circ, 60^\circ$$
55- If a gas tank can hold $$42$$ gallons, how many gallons does it contain when it is $$\frac{5}{7}$$ full?
(A) $$30$$
(B) $$38$$
(C) $$42$$
(D) $$47$$
56- Which of the following is the greatest number?
(A) $$\frac{1}{2}$$
(B) $$\frac{5}{8}$$
(C) $$54\%$$
(D) $$\sqrt{0.36}$$
57- A football team had $$21,000$$ to spend on supplies. The team spent $$12,000$$ on new balls. New sport shoes cost $$120$$ each. Which of the following inequalities represent how many new shoes the team can purchase?
(A) $$120 \ x \ + \ 9,000 \ ≤ \ 21,000$$
(B) $$120 \ x \ + \ 12,000 \ \geq \ 21,000$$
(C) $$120 \ x \ + \ 12,000 \ ≤ \ 21,000$$
(D) $$12,000 \ x \ + \ 120\ ≤ \ 21,000$$
58- In following rectangle which statement is true?
(A) Length of AB equal to length DC.
(B)  AB is parallel to BC.
(C) The sum of all the angles equals $$180^\circ$$.
(D) AB is perpendicular to DC.
59- What is the missing term in the given numbers?
$$2, 3, 5, 8, 12, 17,$$ ___, $$30$$
(A) $$36$$
(B) $$30$$
(C) $$25$$
(D) $$23$$
60- The capacity of a red box is $$18\%$$ greater than a blue box. If the capacity of the red box is $$59$$ books, how many books can be put in the blue box?
(A) $$60$$
(B) $$68$$
(C) $$58$$
(D) $$50$$
61- What is the perimeter of a square that has an area of $$49$$ square inches?
(A) $$36$$ inches
(B) $$28$$ inches
(C) $$14$$ inches
(D) $$30$$ inches
62- $$[3 \times (–\ 18) \ +\ 6]\ – \ (– \ 8) \ + \ [2 \times 7] \div 2 = ?$$
(A) $$- \ 33$$
(B) $$- \ 36$$
(C) $$26$$
(D) $$40$$
63- $$183$$ minutes $$=$$ …?
(A) $$2.85$$ hours
(B) $$3.25$$ hours
(C) $$3.05$$ hours
(D) $$2.65$$ hours
64- Two-kilograms apple and two-kilograms orange cost $$27.3$$ If one-kilogram apple costs $$3.2$$ how much does one-kilogram orange cost?
(A) $$12.50$$
(B) $$15.25$$
(C) $$10.45$$
(D) $$8.45$$
65- Jason is $$12$$ miles ahead of Joe running at $$4.5$$ miles per hour and Joe is running at the speed of $$6$$ miles per hour. How long does it take Joe to catch Jason?
(A) $$10$$ hours
(B) $$12$$ hours
(C) $$6$$ hours
(D) $$8$$ hours
66- In a class, there are twice as many girls as boys. If the total number of students in the class is $$69$$, how many girls are in the class?
(A) $$28$$
(B) $$36$$
(C) $$23$$
(D) $$25$$
67- Jason left a $$15.00$$ tip on a lunch that cost $$50.00$$, approximately what percentage was the tip?
(A) $$30\%$$
(B) $$0.3\%$$
(C) $$27\%$$
(D) $$2.7\%$$
68- At a Zoo, the ratio of lions to tigers is $$2$$ to $$5$$. Which of the following could NOT be the total number of lions and tigers in the zoo?
(A) $$56$$
(B) $$72$$
(C) $$99$$
(D) $$96$$
69- Which of the following is not a prime number?
(A) $$103$$
(B) $$101$$
(C) $$97$$
(D) $$58$$
70- $$(((- \ 15) \ +\ 24)\ ×\ 2)\ +\ (- \ 21)?$$
(A) $$- \ 1$$
(B) $$2$$
(C) $$- \ 3$$
(D) $$3$$
71- If $$50\%$$ of a class are girls, and $$36\%$$ of girls play tennis, what percent of the class play tennis?
(A) $$18\%$$
(B) $$12\%$$
(C) $$24\%$$
(D) $$33\%$$
72- A shaft rotates $$200$$ times in $$5$$ seconds. How many times does it rotate in$$15$$ seconds?
(A) $$600$$
(B) $$400$$
(C) $$540$$
(D) $$620$$
73- The price of a sofa is decreased by $$30\%$$ to $$420$$. What was its original price?
(A) $$600$$
(B) $$560$$
(C) $$500$$
(D) $$480$$
74- The width of a rectangle is $$2 \ x$$ and its length is $$5 \ x$$. The perimeter of the rectangle is $$42$$. What is the value of $$x$$?
(A) $$3$$
(B) $$5$$
(C) $$7$$
(D) $$9$$
75- What is the area of the trapezoid?
(A) $$50$$
(B) $$40$$
(C) $$30$$
(D) $$20$$
76- Ella bought a pair of gloves for $$12.49$$. She gave the clerk $$18.00$$. How much change should she get back?
(A) $$5.51$$
(B) $$6.23$$
(C) $$8.78$$
(D) $$4.98$$
77- $$\frac{7\times12}{80}$$ is closest estimate to:
(A) $$1.1$$
(B) $$6.1$$
(C) $$3.4$$
(D) $$2.9$$
78- $$\frac{3}{4}\ +\ \frac{\frac{-\ 2}{5}} {\frac{4}{10}}=$$?
79- What is the value of in the following equation?
$$10\ +\ 4\ (\ x\ +\ 5\ -\ 5\ x\ )=30$$
(A) $$0$$
(B) $$2$$
(C) $$8$$
(D) $$5$$
80- 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) $$8$$ feet
(B) $$4$$ feet
(C) $$9$$ feet
(D) $$3$$ feet
81- If $$60\%$$ of A is $$20\%$$ of B, then B is what percent of A?
(A) $$300\%$$
(B) $$200\%$$
(C) $$250\%$$
(D) $$350\%$$
82- $$12.124\div0.002= ?$$
(A) $$6,062$$
(B) $$6,132$$
(C) $$9,278$$
(D) $$7,342$$
83- 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) $$\frac{ 1}{4}$$
(B) $$\frac{ 1}{3}$$
(C) $$\frac{2}{3}$$
(D) $$\frac{5}{6}$$
84- Solve the following equation?
$$6^x=1,296$$
(A) $$4$$
(B) $$10$$
(C) $$12$$
(D) $$7$$
 1- Choice A is correct The correct answer is $$- \ \frac{9}{5}$$$$\frac{- \ 45 \ × \ 0.2}{5}=\frac{- \ 45 \ × \ \frac{2}{10}}{5}\Rightarrow$$$$\frac{\frac{- \ 45 \ × \ 2 }{10}}{5} = \frac{- \ 90}{50}\Rightarrow$$$$- \ \frac{9}{5}$$ 2- Choice A is correct The correct answer is $$250$$$$10\%$$ off equals $$25$$. Let $$x$$ be the original price of the table.Then: $$10\%$$ of $$x=25→0.10 \ x=25→x=\frac{25}{0.10}=250$$ 3- Choice C is correct The correct answer is $$14 \ π$$Use the formula of areas of circles.Area of circle $$= \pi \ r^2 ⇒ 49 \ π = π^2 ⇒ 49 = π^2 ⇒ π = 7$$Radius of the circle is $$7$$. Now, use the circumference formula:Circumference $$= 2\ π \ r = 2 \ π (7) = 14 \ π$$ 4- Choice B is correct The correct answer is $$3$$Method 1: $$9=3^2→9^x=(3^2)^x=3^{2 \ x}$$ $$729=3^6→3^{2 \ x}=3^6→2 \ x=6→x=3$$Method 2: $$9 \ x=729$$Let’s review the choices provided:A. $$2 \ \ \ 9^x=729→9^2=81$$B. $$3 \ \ \ 9^x=729→9^3=729$$C. $$4 \ \ \ 9^x=729→9^4=6,561$$D. $$5 \ \ \ 9^x=729→9^5=59,049$$ 5- Choice A is correct The correct answer is $$25\%$$Use the formula for Percent of Change:$$\frac{ New \ Value \ − \ Old Value}{old \ value} \ × \ 100\%$$$$\frac{30 \ − \ 40}{40} \ × \ 100\% = \ – \ 25\%$$ (negative sign here means that the new price is less than old price) 6- Choice B is correct The correct answer is $$\frac{1}{8}, \frac{3}{8}, \frac{2}{5}, \frac{1}{2}$$$$\frac{1}{8}=0.125$$$$\frac{1}{2}=0.5$$$$\frac{2}{5}=0.4$$$$\frac{3}{8}=0.375$$ 7- Choice C is correct The correct answer is $$10$$If the score of Mia was $$40$$, therefore the score of Ava is $$20$$.Since, the score of Emma was half as that of Ava, therefore, the score of Emma is $$10$$. 8- Choice C is correct The correct amswer is $$5 \ x \ - \ 10 \ y$$$$2 \ π=2 \ × \ (2 \ x \ - \ 6 \ y)=4 \ x \ − \ 12 \ y$$$$2 \ π \ + \ π=4 \ x \ − \ 12 \ y \ + \ x \ + \ 2 \ y$$$$2 \ π \ + \ π=5 \ x \ - \ 10 \ y$$ 9- Choice C is correct The correct answer is $$712,232.691$$$$712,232,691 \ × \ 0.001 =712,232,691\ × \frac{1}{1000}=712,232.691$$ 10- Choice A is correct The correct answer is $$16$$Let $$x$$ be the number.Write the equation and solve for $$x$$.$$\frac{1}{3 } \ × \ 12=\frac{1}{4} \times x ⇒$$$$\frac{1 \ × \ 12}{3}= \frac{1 \ x}{4}$$ , use cross multiplication to solve for $$x$$.$$4 \ × \ 12=3 \ x \ × \ 1 ⇒48=3 \ x ⇒ x=16$$ 11- Choice B is correct The correct answer is $$51.5$$Mean $$= \frac{7 \ + \ 15 \ + \ 26 \ + \ 32 \ + \ 48 \ + \ 63 \ + \ 100 \ + \ 121}{8}=\frac{412}{8}=51.5$$ 12- Choice A is correct The correct answer is $$7.40$$$$1.18=\frac{118}{100}$$ and $$6.3=\frac{63}{10}$$ $$→1.18 \ × \ 6.3=\frac{118}{100} \ × \ \frac{63}{10}=\frac{7,434}{1000}=7.434≅7.40$$ 13- Choice D is correct The correct answer is $$100$$$$\frac{5}{6}$$ of $$360=\frac{5}{6} \ × \ 360=300$$$$\frac{1}{3}$$ of $$300=\frac{1}{3} \ × \ 300=100$$ 14- Choice A is correct The correct answer is $$- \ 2$$Simplify: $$3 \ (x \ + \ 5) = 2 \ (x \ − \ 1) \ + \ 15$$$$3 \ x \ + \ 15 = 2 \ x \ − \ 2 \ + \ 15$$$$3 \ x \ + \ 15 = 2 \ x \ + \ 13$$ Subtract $$2 \ x$$ from both sides:$$x \ + \ 15 = 13$$ Add $$- \ 15$$ to both sides: $$x = - \ 2$$ 15- Choice C is correct The correct answer is $$164^\circ$$$$x=30 \ + \ 134=164^\circ$$ 16- Choice A is correct The correct answer is $$148^\circ$$Supplementary angles sum up to $$180$$ degrees.$$x$$ and $$32$$ degrees are supplementary angles.Then: $$x=180^\circ \ − \ 32^\circ=148^\circ$$ 17- Choice B is correct The correct answer is $$21$$The ratio of boy to girls is $$2:5$$.Therefore, there are $$2$$ boys out of $$7$$ students.To find the answer, first divide the total number of students by $$7$$, then multiply the result by $$2$$.$$49 \ ÷ \ 7 = 7 ⇒ 2 \ × \ 7 = 14$$There are $$14$$ boys and $$35 \ (49 \ – \ 14)$$ girls. So, $$21$$ more boys should be enrolled to make the ratio $$1:1$$ 18- Choice C is correct The correct answer is $$495$$ kmAdd the first $$5$$ numbers. $$38 \ + \ 40 \ + \ 54 \ + \ 32 \ + \ 61 = 225$$To find the distance traveled in the next $$5$$ hours, multiply the average by number of hours.Distance $$=$$ Average $$×$$ Rate $$= 54 \ × \ 5 = 270$$Add both numbers.$$270 \ + \ 225 = 495$$ km 19- Choice C is correct The correct answer is $$300$$Let $$x$$ be the original price. If the price of a laptop is decreased by $$20\%$$ to $$280$$, then: $$80\%$$ of $$x=280⇒ 0.80 \ x=240 ⇒ x=240 \ ÷ \ 0.80=300$$ 20- Choice D is correct The correct answer is $$0.05 \ x \ + \ 5,000$$Let $$x$$ be the sales profit.Then, $$5\%$$ of sales profit is $$0.05 \ x$$. Employee’s revenue: $$0.05 \ x \ + \ 5,000$$ 21- Choice A is correct The correct answer is $$88$$ cm$$^2$$The perimeter of the trapezoid is $$45$$.Therefore, the missing side (height) is $$=45 \ – \ 15 \ – \ 12 \ – \ 10 = 8$$Area of the trapezoid:$$A = \frac{1}{2} \ h \ (b1 \ + \ b2) = \frac{1}{2} \ (8) \ (12 \ + \ 10) = 88$$ cm$$^2$$ 22- Choice C is correct The correct answer is $$49$$$$− \ 22 \ − \ (− \ 71)=− \ 22 \ + \ 71=71 \ − \ 22=49$$ 23- Choice D is correct The correct answer is $$\frac{2}{5} \ > \ 0.3$$Let’s review the choices:A. $$\frac{3}{2} \ > \ 2.8$$ This is not a correct statement.Because $$\frac{3}{2}=1.5$$ and it’s less than $$0.8$$.B. $$10\%=\frac{1}{5}$$ This is not a correct statement. Because $$10\% = 0.1$$ and $$\frac{1}{5}=0.2$$C. $$4 \ < \ \frac{3}{6}$$ This is not a correct statement. Because $$\frac{3}{6}=0.6$$ and it’s less than $$4$$.D. $$\frac{2}{5} \> \ 0.3$$ This is a correct statement. 24- Choice A is correct The correct answer is $$36$$The diagonal of the square is $$6$$. Let $$x$$ be the side.Use Pythagorean Theorem:$$a^2 \ + \ b^2 = c^2$$$$x^2 \ + \ x^2= 6^2 ⇒ 2 \ x^2 = 6^2 ⇒$$$$2 \ x^2= 36 ⇒ x^2= 36 ⇒x= \sqrt{36} =6$$The area of the square is:$$6 \ × \ 6= 36$$ 25- Choice B is correct The correct answer is $$14$$Petrol of car A in $$350$$ km $$=\frac{10 \ × \ 350}{100}=35$$Petrol of car A in $$350$$ km $$=\frac{6 \ × \ 350}{100}=21$$$$35 \ − \ 24.5=14$$ 26- Choice C is correct The correct answer is if the quantity in Column A is greater$$x^2 \ + \ 15=64 \to x^2=64 \ - \ 15=49\to x^2=49 \to x=7$$$$124 \ - \ 15 \ y\ =49 \to - \ 15 \ y=49 \ - \ 124=- \ 75\to y=\frac{- \ 75}{-\ 15}=5$$ 27- Choice A is correct The correct answer is if the relationship cannot be determined from the information givenSimply change the fractions to decimals.$$\frac{3}{4}=0.75$$$$\frac{3}{2}=1.5$$$$\frac{4}{3}=1.3333$$...As you can see, $$x$$ lies between $$0.75$$ and $$1.5$$ and it can be $$0.76$$ or $$1.4$$.The first one is less than $$1.5$$ and the second one is greater than $$0.75$$ .The relationship cannot be determined from the information given. 28- Choice A is correct The correct answer is the two quantities are equalChoose different values for a and b and find the values of quantity A and quantity B.$$a=2$$ and $$b=3$$, then:Quantity A: $$|2\ -\ 3|=|-\ 1|=1$$Quantity B: $$|3\ -\ 2|=|1|=1$$The two quantities are equal. $$a=-3$$ and $$b=2$$, then:Quantity A: $$|-3\ -\ 2|=|-\ 5|=5$$Quantity B:$$|2\ -\ (-\ 3)|=|2\ +\ 3|=5$$The two quantities are equal.Any other values of a and b provide the same answer. 29- Choice C is correct The correct answer is if the quantity in Column A is greaterSimplify quantity B. Quantity B:$$(\frac{x}{5})^5=\frac{x^5}{5^5}$$Since, the two quantities have the same numerator ($$x^5$$) and the denominator in quantity B is bigger ($${5^5}\gt 5$$), then the quantity A is greater. 30- Choice A is correct The correct answer is "The quantity in Column B is greater"Column A: Use order of operation to calculate the result. $$6 \ + \ 2 \ × \ 7 \ + \ 5=6 \ + \ 14 \ + \ 5=25$$Column B: $$4 \ + \ 4 \ × \ 7 \ − \ 3→4 \ + \ 28 \ − \ 3=29$$ 31- Choice B is correct The correct answer is "The quantity in Column A is greater"Column A: Simplify. $$\sqrt{49} \ + \ \sqrt{64} = 7 \ + \ 8 = 15$$$$15$$ is greater than $$\sqrt{81} \ (\sqrt{225} = 15)$$ 32- Choice C is correct The correct answer is if the quantity in Column A is greaterColumn A: Simplify.$$\sqrt{121 \ − \ 49} = \sqrt{72}$$Column B:$$\sqrt{121} \ −\ \sqrt{49} = 11 \ − \ 7 = 4 , \sqrt{72}$$ is bigger than $$4. (\sqrt{16} = 4)$$ 33- Choice D is correct The correct answer is the relationship cannot be determined from the information givenColumn A: Based on information provided, we cannot find the average age of Joe and Michelleor average age of Michelle and Nicole. 34- Choice B is correct The correct answer is "The quantity in Column A is greater"Column A: The value of $$x$$ when $$y=8$$: $$y=− \ 5 \ x \ − \ 12→8=− \ 5 \ x \ − \ 12→− \ 5 \ x=20→x=− \ 4$$Column B: $$− \ 9$$$$− \ 4$$ is greater than $$− \ 9$$. 34- Choice B is correct The correct answer is "The quantity in Column A is greater"Column A: The value of $$x$$ when $$y=8$$: $$y=− \ 5 \ x \ − \ 12→8=− \ 5 \ x \ − \ 12→− \ 5 \ x=20→x=− \ 4$$Column B: $$− \ 9$$$$− \ 4$$ is greater than $$− \ 9$$. 36- Choice B is correct The quantity in Column A is greaterQuantity A is: $$\frac{5 \ +\ 7 \ +\ x}{3}=2\to x=- \ 6$$Quantity B is: $$\frac{- \ 6\ + \ (- \ 6 \ - \ 2) \ + \ (- \ 6 \ + \ 6)\ + \ (4 \ × \ (- \ 6))}{4}=- \ 9.5$$ 37- Choice D is correct The correct answer is the relationship cannot be determined from the information givenChoose different values for $$x$$ and find the value of quantity A.$$x=1$$, then:Quantity A: $$\frac{3}{x}\ + \ 2 \ x= \frac{3}{1}\ + \ 2=5$$Quantity B is greater$$x=0.1$$, then: Quantity A: $$\frac{3}{0.1}\ + \ 2 \ x= \frac{ 1}{0.1} \ + \ 0.2=30 \ + \ 0.2=30.2$$Quantity A is greaterThe relationship cannot be determined from the information given. 37- Choice D is correct The correct answer is the relationship cannot be determined from the information givenChoose different values for $$x$$ and find the value of quantity A.$$x=1$$, then:Quantity A: $$\frac{3}{x}\ + \ 2 \ x= \frac{3}{1}\ + \ 2=5$$Quantity B is greater$$x=0.1$$, then: Quantity A: $$\frac{3}{0.1}\ + \ 2 \ x= \frac{ 1}{0.1} \ + \ 0.2=30 \ + \ 0.2=30.2$$Quantity A is greaterThe relationship cannot be determined from the information given. 38- Choice A is correct The correct answer is $$55\%$$Number of pencils are blue $$=60 \ − \ 27=33$$Percent of blue pencils is: $$\frac{33}{60} \ × \ 100=55\%$$ 39- Choice A is correct The correct answer is $$-\ 2.95$$$$10 \ x=-\ 42 \ +\ 12.5=-\ 29.5 \to x=\frac{-\ 29.5}{10}=-\ 2.95$$ 40- Choice B is correct The correct answer is $$7$$$$(x \ - \ 2)^3=125→x \ - \ 2=\sqrt[3]{125}→x \ - \ 2=\sqrt[3]{5^3}→x \ - \ 2=5→x=7$$ 41- Choice B is correct The correct answer is $$20\%$$Use this formula: Percent of Change $$= \frac{New \ Value \ − \ Old Value}{Old \ Value} \ × \ 100\%$$$$\frac{16000 \ − \ 20000}{20000} \ × \ 100\% = 20\%$$ and $$\frac{12800 \ − \ 16000}{16000 } \ × \ 100\% = 20\%$$ 42- Choice C is correct The correct answer is $$8$$$$3 \ (\frac{1}{2} \ - \ \frac{1}{6}) \ + \ 7=$$$$3 \ (\frac{3 \ - \ 1 }{6} \ + \ 7 =$$$$3 \ (\frac{2}{6}) \ + \ 7 =$$$$3 \ (\frac{1}{3}) \ + \ 7 =$$$$1 \ + \ 7 =8$$ 43- Choice B is correct The correct answer is $$(\frac{9}{3} \ × \ 2) \ + \ (\frac{30}{2} \ × \ 2)$$$$(\frac{9}{3} \ × \ 2) \ + \ (\frac{30}{2} \ × \ 2) = (3 \ × \ 2) \ + \ ( 15 \ × \ 2) = 6 \ + \ 30 =36$$ 44- Choice A is correct The correct answer is $$2.6$$$$40\%$$ of $$24$$ is: $$\frac{40}{100} \ × \ 24=9.6$$Let $$x$$ be the number then: $$x=9.6 \ − \ 7=2.6$$ 45- Choice D is correct The correct answer is $$72$$$$\frac{3}{5} \ × \ 120=72$$ 46- Choice A is correct The correct answer is $$20$$If $$\frac{2 \ x}{5}=40$$, then $$\frac{2 \ x}{10}:$$$$2 \ x = 40 \times 5→2 \ x = 200 → x =100$$$$\frac{2 \ x}{10}=\frac{2 \ × \ 100}{10}=\frac{200}{10}=20$$ 47- Choice A is correct The correct answer is $$16$$ cmThe perimeter of rectangle is: $$2 \ × \ (6 \ + \ 5)=2 \ × \ 11=22$$The perimeter of circle is: $$2 \ \pi \ r=2 \ × \ 3 \ × \ \frac{12}{2}=36$$, Difference in perimeter is: $$36 \ − \ 22=16$$ cm 48- Choice B is correct The correct answer is $$39.6$$$$12\%$$ of $$230 =\frac{12}{100}\times {230}={27.6}$$Let $$x$$ be the number then, $$\ x\ =\ 27.6 \ +\ 12\ =\ 39.6$$ 49- Choice C is correct The correct answer is $$32$$First, find the number.Let $$x$$ be the number.Write the equation and solve for $$x$$.$$170%$$ of a number is $$68$$, then: $$1.7 \ × \ x=68 ⇒68 \ ÷ \ 1.7=40$$$$80\%$$ of $$40$$ is: $$0.8 \ × \ 40 =32$$ 50- Choice C is correct The correct answer is $$6$$Let $$x$$ be the number.Write the equation and solve for $$x$$.$$(18 \ – \ x) \ ÷ \ x = 3$$Multiply both sides by $$x$$.$$(18 \ – \ x) = 3 \ x$$, then add $$x$$ both sides.$$18 = 3 \ x$$, now divide both sides by $$3$$.$$x = 6$$ 51- Choice B is correct The correct answer is $$78.5$$Area $$=\pi \ r^2=\pi \ × \ (\frac{10}{2})^2=25 \ \pi=25 \ × \ 3.14=78.5$$ 52- Choice C is correct The correct answer is $$18$$$$\frac{3}{4} \ × \ 24=\frac{72}{4}=18$$ 53- Choice D is correct The correct answer is $$140\%$$The question is this:$$1.84$$ is what percent of $$1.25$$?Use percent formula:Part $$= \frac{percent}{100 } \ ×$$ whole, $$1.75 = \frac{percent}{100 } \ × \ 1.25 ⇒$$$$1.75=\frac{ percent \ × \ 1.25}{100} ⇒$$$$175 =$$ percent $$× \ 1.25 ⇒$$percent $$= \frac{175}{1.25} =140$$ 54- Choice A is correct The correct answer is $$45^\circ, 45^\circ, 90^\circ$$All angles in a triangle sum up to $$180$$ degrees. Then: $$2 \ \alpha \ + \ 90^\circ=180^\circ→2 \ \alpha=90→πΌ=45^\circ$$ 55- Choice A is correct The correct answer is $$30$$$$\frac{5}{7}\times 42=\frac{210}{7}=30$$ 56- Choice B is correct The correct answer is $$\frac{5}{8}$$$$\frac{1}{2}=0.5$$$$\frac{5}{8}=0.625$$$$54\%=0.54$$$$\sqrt{0.36}=0.6$$ 57- Choice C is correct The correct answer is $$120 \ x \ + \ 12,000 \ ≤ \ 21,000$$Let $$x$$ be the number of shoes the team can purchase.Therefore, the team can purchase $$120 \ x$$.The team had $$21,000$$ and spent $$12000$$.Now the team can spend on new shoes $$9000$$ at most.Now, write the inequality: $$120 \ x \ + \ 12,000 \ ≤ \ 21,000$$ 58- Choice A is correct The correct answer is Length of AB equal to length DC.In rectangle sides that face to face each other is equal. 59- Choice D is correct The correct answer is $$23$$Find the difference of each pairs of numbers:$$2, 3, 5, 8, 12, 17,$$ ___,$$30$$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 $$5$$ and next number should be $$6$$. The number is $$17 \ + \ 6 = 23$$ 60- Choice D is correct The correct answer is $$50$$The capacity of a red box is $$18\%$$ greater than a blue box. Let $$x$$ be the capacity of the blue box.Then: $$x \ + \ 18\%$$ of $$x=59→1.18x=59→x=\frac{59}{1.18}=50$$ 61- Choice B is correct The correct answer is $$28$$ inchesThe area of the square is $$49$$ inches.Therefore, the side of the square is square root of the area. $$\sqrt{49}=7$$ inchesFour times the side of the square is the perimeter: $$4 \times 7 = 28$$ inches 62- Choice A is correct The correct answer is $$- \ 33$$Use PEMDAS (order of operation):$$[3 \times (–\ 18) \ +\ 6] \ – \ (– \ 8) \ +\ [2 \times 7] \div 2 =$$$$[–\ 54 \ +\ 6]\ –\ (–\ 8) \ +\ [14] \div 2 =$$$$[–\ 54 \ +\ 6]\ –\ (–\ 8) \ +\ 7 =$$$$[–\ 48] \ –\ (\ –\ 8) \ +\ 7 =$$$$[–\ 48] \ + \ 8 \ + \ 7 = \ – \ 33$$ 63- Choice C is correct The correct answer is $$3.05$$ hours$$60$$ minutes $$= 1$$ Hours $$\to \frac{183}{60}=3.05$$ Hours 64- Choice C is correct The correct answer is $$10.45$$Let $$x$$ be one-kilogram orange cost, then:$$2 \ x \ +\ (2 \ ×\ 3.2)=27.3 \to$$$$2 \ x\ +\ 6.4=27.3\to$$$$2 \ x\ =27.3 \ - \ 6.4 \to$$$$2 \ x\ =20.9 \to$$$$x=\frac{20.9}{2}=10.45$$ 65- Choice D is correct The correct answer is $$8$$ hoursThe distance between Jason and Joe is $$12$$ miles.Jason running at $$4.5$$ miles per hour and Joe is running at the speed of $$6$$ miles per hour.Therefore, every hour the distance is $$1.5$$ miles less. $$12 \div 1.5 = 8$$ 66- Choice C is correct The correct answer is $$23$$There are twice as many girls as boys.Let $$x$$ be the number of girls in the class. Then: $$x\ +\ 2\ x\ =\ 69\ \to$$$$3\ x\ =\ 69\ \to \ x\ =\ 23$$ 67- Choice A is correct The correct answer is $$30\%$$$$15$$ is what percent of $$50$$?$$15 \div 50 = 0.3 = 30\%$$ 68- Choice C is correct The correct answer is $$99$$The ratio of lions to tigers is $$2$$ to$$5$$ at the zoo.Therefore, total number of lions and tigers must be divisible by $$7. \ 2 \ +\ 5=7$$From the numbers provided, only $$99$$ is not divisible by $$8$$. 69- Choice D is correct The correct answer is $$58$$$$58$$ is not prime number, it is divisible by $$2$$. 70- Choice C is correct The correct answer is $$- \ 3$$$$(((- \ 15) \ +\ 24)\ ×\ 2)\ +\ (- \ 21)=((9) \times 2)\ - \ 21=18 \ - \ 21=- \ 3$$ 71- Choice A is correct The correct answer is $$18\%$$The percent of girls playing tennis is:$$50\% \times 36\% = 0.50 \times 0.36= 0.18 = 18\%$$ 72- Choice A is correct The correct answer is $$600$$Number of rotates in $$15$$ second $$=\frac{(200\ \times\ 15)}{5}=600$$ 73- Choice A is correct The correct answer is $$600$$Let $$x$$ be the original price. If the price of the sofa is decreased by $$30\%$$ to $$420$$, then:$$70\%$$ of $$x=420 \Rightarrow 0.70 \ x=420 \Rightarrow x=420\div 0.70=600$$ 74- Choice A is correct The correct answer is $$3$$The width of a rectangle is $$2 \ x$$ and its length is $$5 \ x$$.Therefore, the perimeter of the rectangle is $$14\ x$$. Perimeter of a rectangle $$=2$$ (width $$+$$ length)$$=2\ (2 \ x\ + \ 5 \ x)=2 \ (7 \ x)=14 \ x$$The perimeter of the rectangle is $$42$$. Then: $$14 \ x=42 \to x=3$$ 75- Choice B is correct The correct answer is $$40$$The area of trapezoid is: $$(\frac{8 \ +\ 12}{2}) \times 4=40$$ 76- Choice A is correct The correct answer is $$5.51$$$$18\ -\ 12.49=5.51$$ 77- Choice A is correct The correct answer is $$1.1$$$$\frac{7\times12}{80}=\frac{84}{80}=1.05\cong 1.1$$ 77- Choice A is correct The correct answer is $$1.1$$$$\frac{7\times12}{80}=\frac{84}{80}=1.05\cong 1.1$$ 79- Choice A is correct The correct answer is $$0$$$$10\ +\ 4\ (x\ +\ 5\ -\ 5\ x)=10\ +\ 4\ (-\ 4\ x\ +\ 5)=30\to 10\ -\ 16\ x\ +\ 20=30\to -\ 16\ x\ +\ 30=30\to -\ 16\ x=0\to x=0$$ 80- Choice A is correct The correct answer is $$8$$ feet Use formula of rectangle prism volume.$$V =$$ (length) (width) (height) $$\Rightarrow 2000 = (25) \ (10)$$ (height) $$\Rightarrow$$ height $$= 2000 \div 250 = 8$$ 81- Choice A is correct The correct answer is $$300\%$$Write the equation and solve for B:$$0.60$$A $$=0.20$$B , divide both sides by $$0.20$$, then you will have $$\frac{0.60}{0.20}$$ A $$=$$ B, therefore: B $$=3$$ A , and B is $$3$$ times of A or it’s $$300\%$$ of A . 82- Choice A is correct The correct answer is $$6,062$$$$12.124\div 0.002=\frac{\frac{12124}{1000}}{\frac{2}{1000}}=\frac{12,124}{2}=6,062$$ 83- Choice A is correct The correct answer is $$\frac{ 1}{4}$$The probability of choosing a Hearts is $$\frac{13}{52} =\frac{ 1}{4}$$ 84- Choice A is correct The correct answer is $$4$$$$1269=6^4\to 6^x=6^4\to x=4$$

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