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 $4.1841\times10^5$
$418,410=4.1841\times10^5$