# Full-Length ISEE Middle Level Math Practice Test-Answers and Explanations

Did you take the ISEE Middle Level Math Practice Test? If so, then it’s time to review your results to see where you went wrong and what areas you need to improve.

## ISEE Middle Level Math Practice Test Answers and Explanations

#### ISEE Middle Level Practice TestQuantitative Reasoning

1- Choice D is correct
$$15\%$$ off equals $$18$$. Let x be the original price of the table. Then:
$$15\%$$ of $$x=18→0.15x=18→x=\frac{18}{0.15}=120$$

2- Choice B is correct
$$981,364,454×\frac{1}{10,000,000}=98.1364454$$

3- Choice C is correct
$$\frac{1}{8}≅0.125, \frac{1}{3}≅0.33, \frac{1}{2}=0.5, \frac{3}{5}=0.6$$

4- Choice C is correct
Method 1: $$5×5×5×5=625$$, Method 2: $$8^x=512$$
Let’s review the choices provided:
A. $$2$$ →$$5^x=625→5^2=25$$
B. $$3$$ →$$5^x=625→5^3=125$$
C. $$4$$ →$$5^x=625→5^4=625$$
D. $$5$$ →$$5^x=625→5^5=3125$$
Choice C is correct.

5- Choice C is correct
$$2g=2×(-2x-2y)=-4x-4y$$
$$f-2g=4x-y-(-4x-4y)=8x+3y$$

6- Choice A is correct
$$\frac{-45 × 0.8}{4}=-\frac{45×\frac{8}{10}}{4}=-\frac{\frac{360}{10}}{4}=-\frac{360}{40}=-9$$

7- Choice A is correct
Use the formula for Percent of Change: $$\frac{New \space Value\space-\space Old \space Value}{Old \space Value}× 100 \%$$
$$\frac{43.2-54}{54}× 100\% = –20\%$$ (negative sign here means that the new price is less than old price)

8- Choice A is correct
Supplementary angles sum up to 180 degrees. x and 33 degrees are supplementary angles. Then: $$x=180^\circ -33^\circ=147^\circ$$

9- Choice C is correct
Use the formula of areas of circles.
Area of a circe $$= πr^2 ⇒ 36 π = r^2 ⇒ 36 = r^2 ⇒ r = 6$$
Radius of the circle is 6. Now, use the circumference formula:
Circumference $$= 2πr = 2π(6) = 12π$$

10- Choice D is correct
$$2.21=\frac{221}{100}$$ and $$6.5=\frac{65}{10} →2.21×6.5=\frac{221}{100}×\frac{65}{10}=\frac{14365}{1000}=14.365≅14.4$$

11- Choice C is correct
If the score of Mia was 80, therefore the score of Ava is 40. Since, the score of Emma was half as that of Ava, therefore, the score of Emma is 20.

12- Choice A is correct
The perimeter of the trapezoid is 60.
Therefore, the missing side (height) is $$= 60 – 10 – 20 – 12 = 18$$
Area of the trapezoid: A $$= \frac{1}{2} h (b_1 + b_2) = \frac{1}{2}(18) (10 + 12) = 198$$

13- Choice C is correct
Add the first 4 numbers. $$50 + 48 + 42 + 52 = 192$$
To find the distance traveled in the next 4 hours, multiply the average by number of hours.
Distance = Average $$×$$ Rate$$= 50 × 4 = 200$$, Add both numbers.$$200 + 192 = 392$$

14- Choice D is correct
Mean$$=\frac{12+22+34+46+52+68+72+86}{8}=\frac{392}{8}=49$$

15- Choice D is correct
Let $$x$$ be the number. Write the equation and solve for $$x$$.
$$\frac{2}{3}×36=\frac{4}{9}$$. $$x ⇒ \frac{2×36}{3}= \frac{4x}{9}$$, use cross multiplication to solve for $$x$$.
$$9×72=4x×3 ⇒648=12x ⇒ x=54$$

16-Choice B is correct
Simplify: $$-2(2x+3)=3(4-2x), -4x-6=12-6x$$, Add $$4x$$ from both sides: $$-6=-2x+12$$, subtract 12 to both sides: $$-18 = -2x, 9 = x$$

17Choice B is correct
$$\frac{3}{4}$$ of $$240=\frac{3}{4}×240=180$$, $$\frac{1}{3}$$ of $$180=\frac{1}{3}×180=60$$

18Choice C is correct
The ratio of boy to girls is 6:8. Therefore, there are 6 boys out of 14 students. To find the answer, first divide the total number of students by 14, then multiply the result by 6.
$$70 ÷ 14 = 5 ⇒ 5× 6 = 30$$
There are 30 boys and 40 ($$70 – 30$$) girls. So, 10 more boys should be enrolled to make the ratio 1:1

19Choice D is correct
Let $$x$$ be the original price. If the price of a laptop is decreased by $$20\%$$ to $420, then: $$0.8\%$$ of $$x=420⇒ 0.8x=420 ⇒ x=420÷0.8=525$$ 20-Choice C is correct Let $$x$$ be the sales profit. Then, $$2\%$$ of sales profit is $$0.03x$$. Employee’s revenue: $$0.03x+6,500$$ 21-Choice C is correct Petrol of car A in 300km=$$\frac{7×300}{100}=21$$, Petrol of car B in 300km = $$\frac{9×300}{100}=27, 27-21=6$$ 22-Choice B is correct $$x=105+35=140$$ 23-Choice D is correct The diagonal of the square is 10. Let $$x$$ be the side. Use Pythagorean Theorem:$$a^2 + b^2 = c^2$$ $$x^2 + x^2 = 102 ⇒ 2x^2 = 102 ⇒ 2x^2 = 100 ⇒x^2 = 50 ⇒x= \sqrt{50}$$ The area of the square is: $$\sqrt{50} × \sqrt{50} = 50$$ 24-Choice A is correct $$-42-(-73)=-42+73=73-42=31$$ 25-Choice D is correct Choice B is correct Simplify: $$-2(2x+3)=3(4-2x), -4x-6=12-6x$$, Add $$4x$$ from both sides: $$-6=-2x+12$$, subtract 12 to both sides: $$-18 = -2x, 9 = x$$ Let’s review the choices: A. $$4/5>0.8$$ This is not a correct statement. Because $$\frac{4}{5}=0.8$$ and it’s less than 0.8. B. $$12\%=\frac{1}{5}$$ This is not a correct statement. Because $$12\% = 0.12$$ and $$\frac{1}{5}=0.2$$ C. $$4<\frac{6}{2}$$ This is not a correct statement. Because $$\frac{6}{2}=3$$ and it’s less than 4. D. $$\frac{8}{9}>0.8$$ This is a correct statement. $$\frac{8}{9}=0.88→0.8<\frac{8}{9}$$ ## The Absolute Best Book to Ace the ISEE Middle LevelMath Test 26-Choice A is correct Column A: Use order of operation to calculate the result. $$5+5×7-4=5+35-4=36$$ Column B: $$4+6×6-6→4+36-6=34$$ 27-Choice A is correct Column A: The value of $$x$$ when $$y=9$$ : $$y=3x+18→9=3x+18→3x=-9→x=-3$$ Column B: $$-4$$, $$-3$$ is greater than $$-4$$. 28-Choice C is correct Column A: Simplify. $$\sqrt{25}+\sqrt{25}=5+5=10, 10$$ is equal to $$\sqrt{100}(\sqrt{100}=10)$$ 29-Choice D is correct Column A: Based on information provided, we cannot find the average age of Joe and Michelle or average age of Michelle and Nicole. 30-Choice A is correct Column A: Simplify. $$\sqrt{144-12}=\sqrt{23}$$ Column B: $$\sqrt{144}-\sqrt{121}=12-11=1$$ , $$\sqrt{23}$$ is bigger than 1. 31-Choice A is correct Volume of a right cylinder $$= πr^2 h→80π=πr^2 h=π(5)^2 h→h=3.2$$ The height of the cylinder is 3.2 inches which is bigger than 3 inches. 32-Choice D is correct Choose different values for x and find the value of quantity A. $$x=1$$, then: Quantity A: $$\frac{2}{X}+x= \frac{2}{1}+1=3$$, Quantity B is greater $$x=0.1$$, then: Quantity A: $$\frac{2}{X}+x= \frac{2}{0.1}+1=20+1=21$$, Quantity A is greater The relationship cannot be determined from the information given. 33-Choice B is correct Simply change the fractions to decimals. $$\frac{2}{5}=0.40, \frac{5}{9}=0.55…, \frac{5}{8}=0.625,$$ Quantity B is greater 34-Choice A is correct Simplify quantity B. Quantity B: $$(\frac{x}{3})^3=\frac{x^3}{3^3 }$$ Since, the two quantities have the same numerator ($$x^3$$) and the denominator in quantity B is bigger $$(3^3>3)$$, then the quantity A is greater. 35-Choice A is correct Quantity A is: $$\frac{5+6+x}{3}=6→x=7$$, Quantity B is: $$\frac{(7+(7+3)+(7+1)-7)}{4}=4.5$$ 36-Choice C is correct Choose different values for a and b and find the values of quantity A and quantity B. $$a=4$$ and $$b=3$$, then: Quantity A: $$|4 – 3|=|1|=1$$, Quantity B: $$|3 – 4|=|1|=1$$ The two quantities are equal. a=3 and b=-3, then: Quantity A: $$|3+3|=|6|=6$$ Quantity B: $$|- 3 – (3)|=|-6|=6$$, The two quantities are equal. Any other values of a and b provide the same answer. 37-Choice C is correct $$4x^3-80=176→4x^3=176+80=256→x^3=\frac{256}{4}=64→x=\sqrt[3]{64}=\sqrt[3]{4^3}=4$$ $$3-4y=-13→-4y=-13-3=-16→y=\frac{-16}{-4}=4$$ 38-Choice B is correct Number of pencils are blue$$=75-33=42$$, Percent of blue pencils is: $$\frac{42}{75}×100=56\%$$ 39-Choice A is correct $$\frac{4}{6}×120=80$$ 40-Choice C is correct $$2(\frac{3}{5}-\frac{6}{10})+2=2×(\frac{6-6}{10})+2=0+2=2$$ 41-Choice B is correct $$12\%$$ of $$160=\frac{12}{100}×160=19.2$$, Let $$x$$ be the number then, $$x=19.2+15=34.2$$ 42-Choice C is correct Let $$x$$ be the number. Write the equation and solve for $$x$$. $$(21 – 2x) ÷ x = 5$$ Multiply both sides by $$x$$. $$(21 – 2x) = 5x$$, then add x both sides. $$21 = 7x$$, now divide both sides by 7. $$x = 3$$ 43-Choice A is correct $$25\%$$ of $$48$$ is: $$\frac{25}{100}×48=\frac{1200}{100}=12$$, Let $$x$$ be the number then: $$x=12-3=9$$ 44-Choice A is correct The perimeter of rectangle is: $$2×(6+5)=2×11=22$$ The perimeter of circle is: $$2πr=2×3×\frac{12}{2}=36$$, Difference in perimeter is: $$36-22=14$$ 45-Choice A is correct Use this formula: Percent of Change = $$\frac{New \space Value-Old \space Value}{Old \space Valu}× 100 \%$$ $$\frac{21000-25000}{25000} × 100 \% = 16 \% \space and \space \frac{17640-21000}{21000} × 100 \% = 16 \%$$ 46-Choice D is correct $$(2x-3)^3=125→2x-3=\sqrt[3]{125}=\sqrt[3]{5^3} =5→2x=5+3→x=\frac{8}{2}=4$$ 47-Choice B is correct $$(\frac{10}{4}×24)+(\frac{5}{2}×10)=(60)+(25)=85$$ 48-Choice D is correct If $$\frac{x}{2}=24$$, then $$x=48$$, $$\frac{5x}{8}=\frac{5×48}{8}=\frac{240}{8}=30$$ 49-Choice C is correct $$\frac{3}{4}=0.75, \frac{7}{9}=0.77, 85%=0.85$$ 50-Choice B is correct Area$$=πr^2=π×(\frac{22}{2})^2=121π=121×3.14≅379.94=380$$ 51-Choice A is correct First, find the number. Let $$x$$ be the number. Write the equation and solve for $$x$$. $$160 \%$$ of a number is $$128$$, then: $$1.6×x=128 ⇒ x=128÷1.6=80$$, $$60 \% \space$$of$$\space 80 \space is: 0.6 × 80 = 48$$ 52-Choice D is correct $$\frac{3}{5}×45=\frac{135}{5}=27$$ 53-Choice A is correct All angles in a triangle sum up to 180 degrees. Then: $$2α+90^\circ=180^\circ→2α=90→α=45^\circ$$ 54-Choice B is correct The sum of angles in rectangle is 360. 55-Choice B is correct Find the difference of each pairs of numbers: 5,8,13,21,34,_,89 The sum of $$5,8$$ is $$13$$. The sum of $$8,13$$ is $$21$$. The sum of $$13,21$$ is $$34$$. The sum of $$34$$ and x is $$89$$.Thus $$x=89-34=55$$ 56-Choice D is correct $$\frac{4}{6}×96=\frac{384}{6}=64$$ 57-Choice D is correct The capacity of a red box is $$25\%$$ greater than a blue box. Let $$x$$ be the capacity of the blue box. Then: $$x+25\% \space of \space x=40→1.25x=40→x=\frac{40}{1.25}=32$$ 58-Choice C is correct The question is this: 1.65 is what percent of 1.2? Use percent formula: Part = $$\frac{percent}{100}× whole, 1.65= \frac{percent}{100}× 1.2 ⇒ 1.65 = \frac{percent ×1.2}{100} ⇒165 = percent ×1.2 ⇒ percent = \frac{165}{1.2} =137.5$$ 59-Choice A is correct 60 minutes = 1Hours→$$\frac{315}{60}=5.25$$ Hours 60-Choice A is correct Let $$x$$ be the number of shoes the team can purchase. Therefore, the team can purchase $$120 x$$. The team had $$32,000$$ and spent $$20,000$$. Now the team can spend on new shoes $$12000$$ at most. Now, write the inequality: $$140x+20,000≤32,000$$ ## Best ISEE Middle LevelMath Prep Resource for 2021 61-Choice D is correct 78 is not prime number, it is divisible by 3 and13. 62-Choice A is correct The width of a rectangle is $$5x$$ and its length is $$7x$$. Therefore, the perimeter of the rectangle is 24x. Perimeter of a rectangle=2(width+length)$$=2(5x+7x)=2(12x)=24x$$ The perimeter of the rectangle is 108. Then: $$24x=108→x=4.5$$ 63-Choice D is correct$18 is what percent of $63? $$18 ÷ 60 = 0.3 = 30\%$$ 64-Choice B is correct Let x be one-kilogram orange cost, then: $$2x+(5×5.2)=34→2x+26=34→x=34-26→2x=8→x=\frac{8}{2}=4$$ 65-Choice D is correct $$(((-18)+44)×(-4))+80=(26×(-4)+80=(-104)+80=24$$ 66-Choice C is correct The area of the square is 81 inches. Therefore, the side of the square is square root of the area. $$\sqrt{81}=9$$ inches, Four times the side of the square is the perimeter: $$4 × 9 = 36$$ inches 67-Choice C is correct The distance between Jason and Joe is 12 miles. Jason running at 6.4 miles per hour and Joe is running at the speed of 8 miles per hour. Therefore, every hour the distance is 1.6 miles less. $$12 ÷ 1.6 = 7.5$$ 68-Choice A is correct The ratio of lions to tigers is 6 to 4 at the zoo. Therefore, total number of lions and tigers must be divisible by 10. $$6+4=10$$, From the numbers provided, only 64 is not divisible by 10. 69-Choice B is correct The percent of girls playing tennis is: $$30 \% × 50 \% = 0.3 × 0.5 = 0.15 = 15 \%$$ 70-Choice A is correct There are triple as many girls as boys. Let x be the number of girls in the class. Then: $$x+3x=56→4x=56→x=14$$ 71-Choice D is correct Use PEMDAS (order of operation): $$[(-3)×(-12)+4]-(-2)+[3×6]÷6=[36+4]-(-2)+18÷6=40+2+3=45$$ 72-Choice C is correct $$1024=4^x →4^x=4^5→x=5$$ 73-Choice A is correct Number of rotates in 15 second$$=\frac{360×15}{12}=450$$ 74-Choice C is correct $$6x+8=2x-12→4x+8=-12→4x=-20→x=\frac{-20}{4}=-5$$ 75-Choice B is correct Use formula of rectangle prism volume. V = (length) (width) (height) ⇒ 1260 = (18) (14) (height) ⇒ height = $$1260 ÷ 252 = 5$$ 76-Choice B is correct Let x be the original price. If the price of the sofa is decreased by $$20\%$$ to$380, then: $$80 \% \space$$ of$$\space x=380 ⇒ 0.80 x=380 ⇒ x=380÷0.80=475$$

77-Choice A is correct
The area of trapezoid is: $$(\frac{(10+12)}{2})×8=88$$

78-Choice D is correct
Write the equation and solve for B:
$$0.20A=0.40B$$, divide both sides by $$0.40$$, then you will have $$\frac{0.20}{0.40} A=B$$ , therefore: $$B=\frac{1}{2} A$$, and B is $$0.5$$ times of A or it’s $$50\%$$ of A.

79-Choice B is correct
$$2x-(12-x)=x+20→2x-12+x=x+20→2x=32→x=16$$

80-Choice B is correct
15-11.56=\$3.44

81-Choice D is correct
$$12.56÷0.08=\frac{\frac{1256}{100}}{\frac{8}{100}}=\frac{1256}{8}=157$$

82-Choice B is correct
The probability of choosing a Hearts or 10 is(one of 10 is heart) $$\frac{13+(4-1)}{52}=\frac{16}{52}=\frac{4}{13}$$

83Choice C is correct
$$\frac{1}{3}+\frac{\frac{8}{10}}{\frac{6}{12}}=\frac{1}{3}+\frac{812}{106}=\frac{1}{3}+\frac{96}{60}=\frac{20+96}{60}=\frac{116}{60}=1\frac{56}{60}=1\frac{14}{15}$$

84-Choice A is correct
$$\frac{8×14}{90}=\frac{112}{90}=1.24≅1.2$$

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