Full Length ISEE Middle Level Practice Test

The correct answer is \(36\) m
One hour equal to \(60\) minutes then, \(5\) hours \(=5 \times 60=300\) minutes
One minute equal to \(60\) seconds then, \(300\) minutes \(=300\times 60=18,000\) seconds
Distance that travel by object is: \(0.2 \times 18,000=3,600\) cm \(=36\) m

The correct answer is \($31.60\)
\(72\%\) of\( \ $42.21=\frac{72}{100}\times 42.21=$30.391\)
\( 4\% \) of \(  $30.391=\frac{4}{100}\times $30.391=$1.2156\)
She pays: \($30.391 \ + \ $1.2156 \cong $31.60\)

The correct answer is \(62.5^°\)
In triangle sum of all angles equal to \(180^°\) then: \(y=180^°\ - \ (90^°\ +\ 27.5^°)=
180^°\ -\ 117.5^°=62.5^°\)

The correct answer is \(37.68\) m
Circumference of circle \(=2\ π\ r=2\ π \times \frac{12}{2}=12 \ π\sim 37.68\) m

The correct answer is \(24\)
\(\frac{4}{7} \) of  \( \ 210\ =\frac{4}{7}\times 210=120\)
\(\frac{2}{5} \) of  \(120=\frac{2}{5}\times 120=48\)
\(\frac{1}{2} \) of \( 48= \frac{1}{2} \times 48 =24\)

The correct answer is \(10,000\)
Number of visiting fans: \(\frac{2\ ×\ 25000}{5}=10,000\)

The correct answer is \(\frac{3}{7},\frac{5}{7},\frac{8}{9},\frac{3}{2}\)
\(\frac{3}{7} \cong 0.42\)     \(\frac{5}{7} \cong 0.71\)     \(\frac{8}{9} \cong 0.88\)      \(\frac{3}{2}=1.5\)

The correct answer is \(5\)
\(3,125=5^5\to \)
\(\frac{5^x}{125}=5^5\to\)
\(\frac{5^x}{5^3} =5^5 \to\)
\(5^{x \ - \ 3}=5^5\to\)
\(x \ - \ 3=5\to x=8\)

The correct answer is \($212.5\)
\(15\% \) of \(\ 250=\frac{15}{100}\times 250=37.5\)
Final sale price is: \(250\ -\ 37.5=$212.5\)

The correct answer is \((230)\  (0.80) \ (0.80)\)
To find the discount, multiply the number by \((100\%\ – \) rate of discount).
Therefore, for the first discount we get: \((230)\  (100\% \ –\  20\%) = (230) \ (0.80) = 184\)
For the next \(20\%\) discount: \((230)\  (0.80) \ (0.80)\)

The correct answer is \(2\)
\(6 \ +\ 3 \ x\leq 12\to\)
\(3\ x\leq 12\ -\ 6\to\)
\(3\ x\leq 6\to\)
\(x\leq \frac{6}{3}\to x\leq 2 \), Then: \( a=2\)

The correct answer is \(20.25 \ π\)
Area of circle with diameter \(18\) is:
\(π\ r^2=π\ (\frac{18}{2})^2=81\ π\)
The area of shaded region is:
\(\frac{81\ π}{4}=20.25 \ π\)

The correct answer is \(40\) cm
One liter \(=1,000\)  cm\(^3\)\(\to 3\) liters \(=3,000\) cm\(^3\)
\(3,000=15\times 5\times h \to\)
\(h=\frac{3000}{75}=40\) cm

The correct answer is \(62\)
\(C=\sqrt{6^2\ +\ 8^2 }=\sqrt{100}=10\)
Perimeter of parallelogram \(=(15\ +\ 6\ +\ 10)\times 2=62\)

The correct answer is \(8\)
The area of trapezoid is: \((\frac{15\ +\ 12}{2}) \ x=108\to 13.5\ x=108 \to x=8\)

The correct answer is \(50\ - \ 4 \ x\)
The amount of petrol consumed after \(x\) hours is: \(4 \ x\)
Petrol remaining: \(50\ -\ 4\ x\)

The correct answer is \(- \ \frac{231}{40}\)
\(\frac{\frac{-\ 10}{2} \ \times \ \frac{3}{5}}{\frac{12}{21}}=\frac{\frac{- \ 10 \ \times \ 3}{2 \ \times \ 5}} {\frac{12}{21}}= -\ \frac{ \frac{33}{10}}{\frac{12}{21}}=-\ \frac{33 \ \times \ 21}{10 \ \times \ 12}=- \ \frac{693}{120}=- \ \frac{231}{40}\)

The correct answer is \(5.55\%\)
\(\frac{0.25}{4.5}\times{100}=5.55\)

The correct answer is \(- \ \frac{ 11}{2}\)
\(4 \ +\ x\ +\ 12 \ (\frac{x}{4})=6 \ x\ +\ 15 \to\)
\(4 \ +\ x\ +\ 3 \ x=6 \ x\ +\ 15 \to \)
\(4 \ + \ 4 \ x = 6 \ x \ + \ 15\)
\(- \ 2 \ x =  15 \ - \ 4 \to \)
\(- \ 2 \ x= 11 \to\)
\( x=- \ \frac{ 11}{2}\)

The correct answer is Mode:\(1, 3\) Median:\(2\)
We write the numbers in the order: \(\ 1\ , \ 1\ , \ 1\ ,\ 2\ ,\ 2\ , \ 3\ ,\ 3\ ,\ 3\ ,\ 4\ ,\ 4\ ,\ 5\)
The mode of numbers is: \(1\) and \(3\) median is: \(3\)

The correct answer is \(0\)
Average\( =\frac{\ sum \ \ of\ \ terms\ }{\ number\ \ of\ \ terms\ } \Rightarrow\)
\(13 =\frac{12\ +\ 16\ +\ 24\ +\ x}{4} \Rightarrow\)
\(52= 52 \ +\  x \Rightarrow x = 0\)

The correct answer is \(30^\circ\)
Plug in \(104\) for \(F\) and then solve for C.
\(C =\frac{3}{5} \ (F \ – \ 54) \Rightarrow C = \frac{3}{5} \ (104 \ – \ 54) \Rightarrow C =\frac{ 3}{5} \ (50) = 30\)

The correct answer is \(7\)
Let \(x\) be the integer. Then: \(5\ x\  –\  6 = 29\)
Add \(6\) both sides: \(5\ x\  = 35\)
Divide both sides by \(5:\  x = 7\)

The correct answer is \(48\%\)
\(\frac{12}{25}\times 100=48\%\)

The correct answer is \(13\ x\ -\ 2 \ y\)
\(2 \ f\ +\ 4\ g\ =\ 6 \ x\ + \ 2 \ y \to\)
\(2 \ f\ +\ 4\ (2\ y\ -\ 5 \ x)=6 \ x\ + \ 2 \ y\to\)
\(2\ f\ +\ 8 \ y\ -\ 20\ x=6 \ x\ +\ 2 \ y\to \)
\(2\ f=26 \ x  \ -\ 6\ y\to f=13\ x\ -\ 2 \ y\)

The quantity in Column B is greater
Column A: \(4^3\ -\ 3^4=64\ -\ 81=- \ 17\)
Column B: \(3^4\ -\ 4^3=81\ -\ 64=17\)

The correct answer is the two quantities are equal
Column A: The slope of the line  \(\ 3\ x\ +\ 5\ y\ =\ 16\)  is \( -\ 2\). 
Write the equation in slope intercept form.
\( 3\ x\ +\ 5\ y\ =\ 16\to 5\ y=-\ 3\ x\ +\ 16\to y=-\ 2\ x\ +\ \frac{16}{3}\)
Column B: The slope of the line that passes through points \((1, 5)\) and \((2, 3)\):
Use slope formula: 
slope of a line=\(\frac{y_2\ -\  y_1}{x_2 \ -\  x_1} =\frac{3\ -\ 5}{2\ -\ 1}=-\ 2\)

The correct answer is  the quantity in Column A is greater
Column A: Simplify.
\(\sqrt{225\ -\ 81}=\sqrt{144}=12\)
Column B: 
\(\sqrt{225}\ -\ \sqrt{81}=15\ -\ 9=6\) 
\(12\) is bigger than \(6\)

The correct answer is the quantity in Column B is greater
\(3\ x^2\ -\ 7=425\to\)
\(3\ x^2=425\ +\ 7=432\to\)
\(x^5=\frac{432}{3}=144\to\)
\(x=\sqrt{144}=12\)
\(\frac{1}{3}\ -\ \frac{y}{5}=-\ \frac{8}{15}\to\)
\(\frac{y}{5}=\frac{1}{3}\ +\ \frac{8}{15}=\frac{5\ +\ 8}{15}=\frac{13}{15}\to\)
\(y=5 \ \times \frac{13}{15}=39\)

The correct answer is the relationship cannot be determined from the information given
Choose different values for \(x\) and find the value of quantity A and quantity B.
\(x=1\), then:
Quantity A: \( x^{15}=1^{15}=1\)
Quantity B: \(x^{30}=1^{30}=1\)
The two quantities are equal.
\(x=2\), then:
Quantity A: \(x^{15}=2^{15}\)
Quantity B: \(x^{30}=2^{30}\)
Quantity B is greater. 
Therefore, the relationship cannot be determined from the information given.

The correct answer is  the quantity in Column A is greater
\(12\% \) of \( x = 15\% \) of \( y\to 0.12 \ x = 0.15 \ y\to x=\frac{0.15}{0.12}\  y\to x=\frac{0.05}{0.04}\  y\to x=\frac{5}{4}\  y\), therefore, \(x\) is bigger than \(y\).

The correct answer is the two quantities are equal
Column A: \(10\%\) of the computer cost is \(30: 10\%\ ×\ 300=0.1\ ×\ 300=30\)
Column B: \(30\)

The correct answer is the quantity in Column B is greater
Simplify both quantities.
Quantity A: \(-\ 6^3=(-\ 6)\times (-\ 6)\times (-\ 6)=- \ 216\)
Quantity B: \(6\times 6\times 6=216\)
The quantity in Column B is greater

The correct answer is if the two quantities are equal
Use exponent “product rule”: \(x^n\times x^m=x^{n \ + \ m}\)
Quantity A: \((1.23)^5\ (1.23)^4=(1.23)^{5 \ +  4}=(1.23)^{9}\)
Quantity B:\( (1.23)^{9}\)
The two quantities are equal.

The correct answer is the quantity in Column A is greater
Column A: Simplify. 
\(\frac{\sqrt{64\ +\ 36}}{\sqrt{25\ -\ 9}}\)=\(\frac{\sqrt{100}}{\sqrt{16}}=\frac{10}{4}=\frac{5}{2}\)
Column B: 
\(\frac{8\ -\ 3}{9\ -\ 2}=\frac{5}{7}\)

The correct answer is the quantity in Column A is greater
prime factoring of \(55\) is: \(5\times 11\)
prime factoring of \(330\) is: \( 2\times 3\times 5\times 11\)
Quantity A \(= 5\) and Quantity B \(= 2\)

The correct answer is  the quantity in Column A is greater
Column A: First, find the integers.
Let \(x\) be the smallest integer. 
Then the integers are \(x, \ (x \ +\ 1), \) and\( (x\ +\ 2)\). The sum of the integers is \(-\ 24\) .
Then: \(x\ +\ x\ +\ 1\ +\ x\ +\ 2=-\ 24\to 3\ x\ +\ 3=-\ 24\to 3\ x=-\ 27\to x=-\ 9\)
Column B: \( -\ 12\)
The smallest integer is \(-\ 12\), therefore, the largest integer is bigger than that.

The correct answer is  the quantity in Column A is greater
Column A: First, find the integers.
Let \(x\) be the smallest integer. 
Then the integers are \(x, \ (x \ +\ 1), \) and\( (x\ +\ 2)\). The sum of the integers is \(-\ 24\) .
Then: \(x\ +\ x\ +\ 1\ +\ x\ +\ 2=-\ 24\to 3\ x\ +\ 3=-\ 24\to 3\ x=-\ 27\to x=-\ 9\)
Column B: \( -\ 12\)
The smallest integer is \(-\ 12\), therefore, the largest integer is bigger than that.

The correct answer is \(10\) cubed
\(10\) cubed is:\(10^3=1,000\)

The correct answer is \(49\)
The area of trapezoid is: \((\frac{10\ +\ 16}{2})\times x=169\to 13\ x=169\to x=13\)
\(y=\sqrt{6^2\ +\ 8^2}=10\) , Perimeter is: \(16\ +\ 13\ +\ 10\ +\ 10=49\)

The correct answer is \(232\)
Prime factorizing of \(42=2\times 3\times 7\), Prime factorizing of \(66=2\times3\times11\)
\( x= LCM=2\times3\times 7\times 11=462\)
\(\frac{462}{2}\ +\ 1=231\ +\ 1=232)

The correct answer is \(130^\circ\)
Angle between \(90^\circ\) and \(180^\circ\) is called obtuse angle.

The correct answer is \(\frac{1}{4}\)
Probability =\(\frac{\ number\ \ of\ \ desired\ \ outcomes\ }{\ number\ \ of\ \ total\ \ outcomes\ } = \frac{18}{\ 12\ +\ 18\ +\ 18\ +\ 24\  } =\frac{ 18}{72} =\frac {1}{4}\)

The correct answer is \(38\%\)
The population is increased by \(15\%\) and \(20\%\). 
\(15\%\) increase changes the population to \(115\%\) of original population.
For the second increase, multiply the result by \(120\%.\)
\((1.15)\times (1.20) = 1.38 = 138\%, 38\) percent of the population is increased after two years.

The correct answer is Cannot be determined
All angles in a parallelogram sum up to \(360\) degrees.
Since, we only have \(2\) angles, therefore the answer cannot be determined.

The correct answer is \(3\)
\(4^{x \ - \ 1} \ - \ 38=218 \to 4^{x \ - \ 1}=218\ +\ 38=256\) and \( 256=4^4\)
\(4^{x \ - \ 1}=4^4\to x \ - \ 1=4 \to x=3\)

The correct answer is \(-\ 11\)
Use PEMDAS (order of operation):
\(12 \ +\  4 \times (–\ 4) \ –\  [2 \ +\  25 \times 3] \div 11 = 12 \ +\  4 \times (–\ 4) \ –\  [2 \ +\  75] \div 11 = \) 
\(12 \ +\  4 \times (–\ 4) \ –\  [77] \div 11 = 12 \ +\  (–\ 16)\   –\  7 = 12 \ – \ 16 \ – \  7 = \ –\ 11\)

The correct answer is \(7,- \ 9\)
\(x^2\ +\ 2\ x\ +\ 1=(x\ +\ 1)^2→(x\ +\ 1)^2=64\to x\ +\ 1=8\to =7 \) or \( x\ +\ 1=- \ 8\to x=- \ 9\)

The correct answer is \(41.1\)
\(\frac{12 \ × \ 24}{7}=\frac{288}{7}=41.142\sim41.1\)

The correct answer is \(560\) seconds
Swing moves once from point A to point B and returns to point A is: \( 28\ +\ 28=56\) seconds
Therefore, for ten times: \(10\times 56=560\) seconds

The correct answer is \(-\ 8 \) and \(8\)
Let \(x\) be the number, then:
\(x^2\ +\ 12=76\to x^2=64\to x^2\ -\ 64=0\to (x\ +\ 8)(x\ -\ 8)=0\to x=8 \) or \( x=-\ 8\)

The correct answer is \(- \ 4.5\) or \(- \ 4 \frac{1}{2}\)
\(\frac{x}{3}\ +\ \frac{11}{3}=\frac{13}{6}\to \frac{x}{3}=\frac{13}{6} \ - \ \frac{11}{3}=\frac{13 \ - \ 22}{6}=- \ \frac{9}{6}= - \ \frac{3}{2}\to\)
\(x=3\times (- \ \frac{3}{2})=- \ 4.5\)

The correct answer is \(I \gt 3000 \ x\  +\  22000\)
Let \(x\) be the number of years.
Therefore, \($3,000\) per year equals \(3000\ x\). 
starting from \($22,000\) annual salary means you should add that amount to \(3000\ x\). 
Income more than that is: \(I \gt 3000 \ x\  +\  22000\)

The correct answer is \(\frac{25}{18}\)
Perimeter \(A=5\times5=25\), Area \(B=3\times6=18\), \(\frac{25}{18}\)

The correct answer is \(30\) minutes
\(1\  \frac{3}{4}=\frac{7}{4}=1.4\)
Speed of the blue car: \(1.4\times60=84\)
Difference of the cars’ speed: \(84\ -\ 60=24\)
The red car is \(12\) km ahead of a blue car.
Therefore, it takes \(30\) minutes to catch the red car.
\(\frac{12}{24}=0.5\) Hour \(=30\) minutes

The correct answer is \(4\)
\(|5\ -\ 9|=|-\ 4|=4\)

The correct answer is \(60^°, 60^°, 60^°\)
The angles of an equilateral triangle are \(60, 60, 60\) degrees.

The correct answer is \((\frac{28}{ 4} \ +\  \frac{8}{2} ) \times 9 \ −\ \frac{9}{ 2} \ +\  \frac{124}{ 4}\)
\((\frac{28}{ 4} \ +\  \frac{8}{2} ) \times 9 \ −\ \frac{9}{ 2} \ +\  \frac{124}{ 4}=\)
\((\frac{28\ +\ 16}{4}\ ×\ 9)\ -\ \frac{9}{2}\ +\ \frac{124}{4}=\)
\(((\frac{44}{4})\times9)\ +\ \frac{- \ 18\ +\ 124}{4}=\)
\((11\times9)\ +\ \frac{106}{4}=99\ +\ 26.5=125.5\)

The correct answer is \(60\)
The area of rectangle is: \(12\times4=48\) cm\(^2\)
The area of circle is: \(π\ r^2=π\times (\frac{12}{2})^2=3\times36=108\)
Difference in area is: \(108\ -\ 48=60\)

The correct answer is \(\frac{9}{80}\)
\(4,500\) out of \(40,000\) equals to \(\frac{4500}{40000} = \frac{45}{400} =\frac{9}{80}\)

The correct answer is \($880\)
\(11\% \) of \( $8000 = \frac{11}{100}\times8000=$880\)

The correct answer is \(121\)
\(121\) is not prime number, it is divided by \(11\)

The correct answer is \(100\) and \(80\)
Weight of blue box \(=\frac{10\ ×\ 90}{9}=100\), Weight of yellow box \(=\frac{100\times100}{25}=80\)

The correct answer is \(7\ x\)
Since, each of the \(x \) students in a team may invite up to \(6\) friends, the maximum number of people in the party is \(7\) times \(x\) or \(7\ x\).
(one student \(\ +\  6\) friends \(= 7\) people)

The correct answer is \(150\)
To find the number of possible outfit combinations, multiply number of options for each factor: \(5 \times 3 \times 10 = 150\)

The correct answer is \(216\)
\(y = 3\ a\ b \ +\  2\ b^3\)
Plug in the values of a and b in the equation: \(a = 2\) and \(b =4\)
\(y = 3 \ (2) \ (4) \ +\ 2\  (4)^3 = 24 \ +\  3\ (64) = 24 \ +\  192 = 216\)

The correct answer is \(125\) degree
\(180^°\ -\ 55^°=125^°\)

The correct answer is \($24\)
Let \(x\) be the price that third person has to pay then; \(94=17.5\ +\ (3\times 17.5)\ +\ x\to 
x=94\ -\ 70=24\)

The correct answer is \(3.5\) Hours
\(60\) minutes \(= 1\) Hours \(\to \frac{210}{60}=3.5\) Hours

The correct answer is \($10\)
Let \(x\) be price of one-kilogram of apple and \(y\) be price of one-kilogram of orange, then: \(x=2\ y\)
\(2\ x\ +\ 3\ y\ =35\to\)
\(2\ (2\ y\ )\ +\ 3\ y\ =35\to\)
\(7\ y\ =35\to y=\frac{35}{7}=5\to x=2\times5=10\)

The correct answer is \(- \ \frac{3}{2 }\)
\(x\ +\ 2\ x\ -\ 15=2\ (\frac{9}{2} \ x\ +\ 2 \ y)\ -\ 12\to\)
\(3 \ x \ - \ 15=9 \ x \ + \ 4 \ y \ - \ 12\to\)
\( 3\ x\ -\ 9\ x\ -\ 4\ y\ =15\ -\ 12\to\)
\(- \ 6 \ x\ -\ 4\ y\ =3\to\) 
\(- \ \frac{1}{2 } \ (- \ 6 \ x\ -\ 4\ y\ =3) \to 3 \ x + \ 2 \ y =- \ \frac{3}{2 }\)

The correct answer is \(24\)
\(c=\sqrt{6^2\ +\ 8^2}=\sqrt{100}=10\)
Perimeter is: \(6\  +\ 8\ +\ 19=24\)

The correct answer is \(61.28\)
average \(=\frac{\ sum\ \ of\ \ terms\ }{\ number\ \ of\ \ terms\ }\)
The sum of the weight of all girls is: \(18 \times 60 = 1080\) kg
The sum of the weight of all boys is: \( 32\times 62 = 1984\) kg
The sum of the weight of all students is: \(1080 \ +\  1984 = 3064\) kg
Average \(=\frac{3064}{50} = 61.28\)

The correct answer is \(24\)
The area of the floor is: \(6\) cm \(\times \  24\) cm\( =216\) cm
The number is tiles needed \(= 216\div 9 = 24\)

The correct answer is \(\sqrt{407}\)
\(x^2\ +\ 13^2=24^2\to x^2=24^2\ -\ 13^2\to x=\sqrt{24^2\ -\ 13^2}\to x=\sqrt{576\ -\ 169}=\sqrt{407}\)

The correct answer is \(94\)
Perimeter \(=2\ π\ r=2\times π\times \frac{30}{2}=30 \ \pi\cong 94.2\cong 94\)

The correct answer is \(-\ 7\)
\((((-\ 16)\ +\ 36)\ ×\ \frac{1}{4})\ +\ (-\ 12)=((20)\times \frac{1}{4})\ -\ 12=5\ -\ 12=-\ 7\)

The correct answer is \(24\)
\((16 \ - \ 12)!=4!=4\times 3\times 2\times 1=24\)

The correct answer is \(5 : 6\)
The average speed of john is: \(120 \div 4 = 30\)
The average speed of Alice is: \(180 \div 5 = 36\)
Write the ratio and simplify. 
\(30 : 36\Rightarrow 5 : 6\)

The correct answer is \(8999\)
Smallest \(4\)–digit number is \(1000\), and biggest \(4–\)digit number is \(9999\).
The difference is: \(8999\)

The correct answer is about \(42.5\) miles per hour
Average speed: \(\frac{510}{12}=42.5\) miles per hour

The correct answer is \(22.5^\circ\)
The sum of supplement angles is \(180\).
Let \(x\) be that angle.
Therefore, \(x \ +\  7\ x = 180\)
\(8\ x\  = 180\), divide both sides by \(8: \ x = 22.5\)

The correct answer is \(19.28\)
Let \(x\) be the number then, \(140\% \) of  \( x=1.4\ x\)
\(1.4\ x=0.30\times 90=27\to x=\frac{27}{1.4}=19.28\)

The correct answer is \(21\)
Number of employees if ratio is \(2 \) to\(\ 5\ :\frac{7\ ×\ 18}{2}=63\)
Number of employees with high school Diploma if ratio is \(2 \) to\( \ 5\ =63\ -\ 18=45\)
Number of employees if ratio is \(3 \) to \( 4:\frac{7\times18}{3}=42\)
Number of employees with high school Diploma if ratio is \(3 \) to \( 4=42\ -\ 18=24\)
Number of employees with High School Diploma should be moved to other departments:
\(45\ -\ 24=21\)

The correct answer is \(4.1841\times10^5\)
\(418,410=4.1841\times10^5\)