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ISEE Middle Level
Practice Test 4
Quantitative Reasoning

37 questions
Total time for this section: 35 Minutes
Calculators are not allowed at the test.

If an object travels at $0.2$ cm per second, how many meters does it travel in $5$ hours?

(A)

$35.8$ m

(B)

$36$ m

(C)

$40$ m

(D)

$38$ m

Ava uses a $28\%$ off coupon when buying a sweater that costs $$42.21$. If she also pays $4\%$ sales tax on the purchase, how much does she pay?

(A)

$$30.42$

(B)

$$28.35$

(C)

$$36.20$

(D)

$$31.60$

In the following shape $y$ equals to?
ISEE Middle Level

(A)

$52.3^°$

(B)

$62.5^°$

(C)

$45.2^°$

(D)

$48.6^°$

What’s the circumference of a circle that has a diameter of $12$ m?

(A)

$30.14$ m

(B)

$35$ m

(C)

$37.68$ m

(D)

$42.20$ m

Find $\frac{1}{2}$ of $\frac{ 2}{5}$ of $\frac {4}{7}$ of $210$?

(A)

$48$

(B)

$32$

(C)

$28$

(D)

$24$

If the ratio of home fans to visiting fans in a crowd is $3:2$ and all $25,000$ seats in a stadium are filled, how many visiting fans are in attendance?

(A)

$5,000$

(B)

$8,000$

(C)

$10,000$

(D)

$15,000$

Which of the following shows the numbers in increasing order?

(A)

$\frac{3}{7},\frac{5}{7},\frac{8}{9},\frac{3}{2}$

(B)

$\frac{5}{7},\frac{3}{7},\frac{8}{9},\frac{3}{2}$

(C)

$\frac{3}{2},\frac{5}{7},\frac{8}{9},\frac{3}{7}$

(D)

$\frac{8}{9},\frac{3}{2},\frac{3}{7},\frac{5}{7}$

What is the value of $x$ in the following equation?
$\frac{5^x}{125}=3,125$

(A)

$8$

(B)

$9$

(C)

$5$

(D)

$3$

An item in the store originally priced at $$250$ was marked down $15\%$. What is the final sale price of the item?

(A)

$$212.5$

(B)

$$220$

(C)

$$210.3$

(D)

$$200$

10-

A shirt costing $$230$ is discounted $20\%$. After a month, the shirt is discounted another $20\%$. Which of the following expressions can be used to find the selling price of the shirt

(A)

$(230)\ (0.20) \ (0.20)$

(B)

$(184)\ (0.85) \ (0.85)$

(C)

$(230)\ (0.80) \ (0.80)$

(D)

$(184)\ (0.80) \ (0.80)$

11-

If $x\leq a$ is the solution of $6 \ +\ 3 \ x \leq 12$, what is the value of $a$?

(A)

$2$

(B)

$4$

(C)

$x$

(D)

$2 \ x$

12-

What is the area of the shaded region? (one forth of the circle is shaded)
Diameter = $18$
ISEE Middle Level1

(A)

$24.25 \ π$

(B)

$20.25 \ π$

(C)

$22.50 \ π$

(D)

$25.50 \ π$

13-

$3$ liters of water are poured into an aquarium that's $15$ cm long, $5$ cm wide, and $70$ cm high. How many cm will the water level in the aquarium rise due to this added water? ($1$ liter of water $= 1000$cm$^3$)

(A)

$30$ cm

(B)

$25$ cm

(C)

$54$ cm

(D)

$40$ cm

14-

What is the perimeter of the following parallelogram?
ISEE Middle Level2

(A)

$58$

(B)

$39$

(C)

$74$

(D)

$62$

15-

The area of the trapezoid below is $108$. What is the value of $x$?
ISEE Middle Level3

(A)

$8$

(B)

$11$

(C)

$6$

(D)

$16$

16-

If a car has $50-$liter petrol and after one hour driving the car use $4-$liter petrol, how much petrol remaining after $x-$hours?

(A)

$50\ - \ \frac{4}{2} \ x$

(B)

$50\ - \ 4 \ x$

(C)

$50\ + \ 4 \ x$

(D)

$50\ + \ x$

17-

What is the value of $\frac{\frac{-\ 10}{2} \ \times \ \frac{3}{5}}{\frac{12}{21}}$ = ?

(A)

$- \ \frac{40}{231}$

(B)

$- \ \frac{231}{40}$

(C)

$- \ \frac{231}{30}$

(D)

$- \ \frac{221}{30}$

18-

If Joe was making $$4.50$ per hour and got a raise to $$4.75$ per hour, what percentage increase was the raise?

(A)

$3.33\%$

(B)

$4.44\%$

(C)

$5.55\%$

(D)

$7.77\%$

19-

Solve for $x: \ 4 \ +\ x\ +\ 12 \ (\frac{x}{4})=6 \ x\ +\ 15$

(A)

$- \ \frac{7}{2}$

(B)

$\frac{13}{2}$

(C)

$- \ \frac{ 11}{2}$

(D)

$- \ 5$

20-

What is the value of mode and median in the following set of numbers?
$\ 1\ ,\ 2\ ,\ 2\ ,\ 5\ ,\ 4\ ,\ 4\ ,\ 3\ ,\ 3\ ,\ 3\ ,\ 1\ ,\ 1$

(A)

Mode:$1, 2$ Median:$2$

(B)

Mode:$2, 3$ Median:$2$

(C)

Mode:$1, 3$ Median:$3$

(D)

Mode:$1, 3$ Median:$2, 5$

21-

The average of $\ 12\ , \ 16\ , \ 24$ and $ \ x$ is $ 13$. What is the value of $x$?

(A)

$0$

(B)

$- \ 2$

(C)

$2$

(D)

$1$

22-

Which is the equivalent temperature of $104^°$F in Celsius? (C $=$ Celsius)
$C = \frac{3}{5} \ (F \ – \ 54)$

(A)

$40^\circ$

(B)

$45^\circ$

(C)

$35^\circ$

(D)

$30^\circ$

23-

$6$ less than five times a positive integer is $29$. What is the integer?

(A)

$7$

(B)

$5$

(C)

$3$

(D)

$- \ 3$

24-

In a bundle of $25$ fruits, $12$ are apples and the rest are bananas. What percent of the bundle is composed of apples?

(A)

$48\%$

(B)

$25\%$

(C)

$54\%$

(D)

$39\%$

25-

If $ 2 \ f\ +\ 4\ g\ =6 \ x\ + \ 2 \ y$ and $\ g\ =2\ y\ -\ 5 \ x$, what is $f$?

(A)

$10 \ x\ + \ 2 \ y$

(B)

$13\ x\ -\ 2 \ y$

(C)

$13\ x\ + \ 3 \ y$

(D)

$\frac{8}{13} \ x\ - \ 2 \ y$

26-

Using the information provided below, compare the quantity in column A to the quantity in Column B.

Column A	Column B
$4^3\ -\ 3^4 $	$3^4\ -\ 4^3$

(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

27-

Using the information provided below, compare the quantity in column A to the quantity in Column B. A

Column A	Column B
The slope of the line $\ 3\ x\ +\ 5\ y\ =\ 16$	The slope of the line that passes through points $(1, 5)$ and $(2, 3)$

(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

28-

Using the information provided below, compare the quantity in column A to the quantity in Column B. .

Column A	Column B
$\sqrt{225\ -\ 81}$	$\sqrt{225}\ -\ \sqrt{81}$

(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

29-

Using the information provided below, compare the quantity in column A to the quantity in Column B.
$3 \ x^5\ - \ 7=425$
$\frac{1}{3}\ -\ \frac{y}{5}=-\ \frac{8}{15}$

Column A	Column B
$x $	$y$

(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

30-

Using the information provided below, compare the quantity in column A to the quantity in Column B. $x$ is a positive number..

Quantity A	Quantity B
$x^{15}$	$x^{30}$

(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

31-

Using the information provided below, compare the quantity in column A to the quantity in Column B. $12$ percent of $x$ is equal to $15$ percent of $y$, where $x$ and $y$ are positive numbers.

Quantity A	Quantity B
$x$	$y$

(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

32-

Using the information provided below, compare the quantity in column A to the quantity in Column B. A computer costs $$300$.

Column A	Column B
A sales tax at $10\%$ of the computer cost	$$30$

(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

33-

Using the information provided below, compare the quantity in column A to the quantity in Column B..

Quantity A	Quantity B
$(-\ 6^3)$	$6^3$

(A)

The two quantities are equal

(B)

The relationship cannot be determined from the information given

(C)

The quantity in Column A is greater

(D)

The quantity in Column B is greater

34-

Using the information provided below, compare the quantity in column A to the quantity in Column B..

Quantity A	Quantity B
$(1.23)^5 \ (1.23)^4$	$(1.23)^{9}$

(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

35-

Using the information provided below, compare the quantity in column A to the quantity in Column B.

Column A	Column B
$\frac{\sqrt{64\ +\ 36}}{\sqrt{25\ -\ 9}}$	$\frac{8\ -\ 3}{9\ -\ 2}$

(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

36-

Using the information provided below, compare the quantity in column A to the quantity in Column B..

Quantity A	Quantity B
The least prime factor of $55$	The least prime factor of $330$

(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-

Using the information provided below, compare the quantity in column A to the quantity in Column B.The sum of $2$ consecutive integers is $- \ 24$ .

Column A	Column B
The largest of these integers	$-\ 12$

(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 4

Mathematics Achievement

47 questions
Total time for this section: 40 Minutes
Calculators are not allowed at the test.

38-

Which of the following is not synonym for $10^2$?

(A)

the square of $10$

(B)

$10$ to the second power

(C)

$10$ cubed

(D)

$10$ squared

39-

If the area of trapezoid is $169$, what is the perimeter of the trapezoid?
ISEE Middle Level4

(A)

$49$

(B)

$35$

(C)

$52$

(D)

$40$

40-

If $x=$ lowest common multiple of $42$ and $66$ then $\frac{x}{2}\ +\ 1$equal to?

(A)

$217$

(B)

$307$

(C)

$285$

(D)

$232$

41-

Which of the following angles is obtuse?

(A)

$86^\circ$

(B)

$130^\circ$

(C)

$215^\circ$

(D)

$74^\circ$

42-

Anita’s trick–or–treat bag contains $12$ pieces of chocolate, $18$ suckers, $18$ pieces of gum,$ 24$ pieces of licorice. If she randomly pulls a piece of candy from her bag, what is the probability of her pulling out a piece of sucker

(A)

$\frac{1}{4}$

(B)

$\frac{2}{5}$

(C)

$\frac{3}{8}$

(D)

$\frac{1}{2}$

43-

In two successive years, the population of a town is increased by $15\%$ and $20\%$ . What percent of the population is increased after two years?

(A)

$44\%$

(B)

$32\%$

(C)

$38\%$

(D)

$40\%$

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44-

If angles A and B are angles of a parallelogram, what is the sum of the measures of the two angles?

(A)

Cannot be determined

(B)

$360$ degrees

(C)

$180$ degrees

(D)

$90$ degrees

45-

What is the value of $x$ in the following equation?
$4^{x \ - \ 1} \ -\ 38=218$

(A)

$3$

(B)

$2$

(C)

$5$

(D)

$7$

46-

$12 \ +\ 4 \times (–\ 4) \ –\ [2 \ +\ 25 \times 3] \div 11 = ?$

(A)

$ 11$

(B)

$-\ 13$

(C)

$-\ 11$

(D)

$13$

47-

Solve the following equation?
$(\ x^2\ +\ 2\ x\ +\ 1\ )=64$

(A)

$7,- \ 11$

(B)

$7,- \ 9$

(C)

$9,- \ 11$

(D)

$- \ 9,11$

48-

$\frac{12 \ × \ 24}{7}$ is closest estimate to?

(A)

$39.2$

(B)

$41.1$

(C)

$41.8$

(D)

$39.8$

49-

A swing moves from one extreme point (point A) to the opposite extreme point (point B) in $28$ seconds. How long does it take that the swing moves $10$ times from point A to point B and returns to point A?

(A)

$500$ seconds

(B)

$560$ seconds

(C)

$600$ seconds

(D)

$640$ seconds

50-

When a number is multiplied to itself and added by $12$, the result is $76$. What is the value of the number?

(A)

$-\ 5 $ and $5$

(B)

$-\ 6 $ and $6$

(C)

$-\ 8 $ and $8$

(D)

$8$

51-

Solving the equation: $\frac{x}{3}\ +\ \frac{11}{3}=\frac{13}{6}=$?

(A)

$- \ 4\ \frac{1}{2}$

(B)

$- \ 4 \ \frac{3}{2}$

(C)

$- \ 4 \ \frac{9}{4}$

(D)

$- \ 4\ \sqrt{\frac{1}{2}}$

52-

In $1999$ , the average worker's income increased $$3,000$ per year starting from $$22,000$ annual salary. Which equation represents income greater than average?
($ I =$ income, $x =$ number of years after $1999$)

(A)

$I \gt 3000 \ x\ +\ 22000$

(B)

$I \gt 3000 \ x\ - \ 20000$

(C)

$I \gt 2000 \ x\ + \ 20000$

(D)

$I \leq 3000 \ x\ + \ 22000$

53-

What is ratio of perimeter of figure $A$ to area of figure $B$?
ISEE Middle Level5

(A)

$\frac{5}{9}$

(B)

$\frac{12}{18}$

(C)

$\frac{10}{9}$

(D)

$\frac{25}{18}$

54-

There are $2$ cars moving in the same direction on a road. A red car is $12$ km ahead of a blue car. If the speed of the red car is $60$ km per hour and the speed of the blue car is $1\ \frac{3}{4}$ of the red car, how many minutes will it take the blue car to catch the red car?

(A)

$60$ minutes

(B)

$90$ minutes

(C)

$45$ minutes

(D)

$30$ minutes

55-

What is the absolute value of the quantity five minus nine?

(A)

$- \ 4$

(B)

$- \ 2$

(C)

$2$

(D)

$4$

56-

Which of the following angles can represent the three angles of an equilateral triangle?

(A)

$50^°, 50^°, 80^°$

(B)

$45^°, 45^°, 90^°$

(C)

$60^°, 60^°, 60^°$

(D)

$10^°, 80^°, 90^°$

57-

$125 \ \frac{1}{2}$ is equal to?

(A)

$(\frac{28}{ 4} \ +\ \frac{8}{2} ) \times 9 \ −\ \frac{9}{ 2} \ +\ \frac{124}{ 4}$

(B)

$20 \ −\ (4 \ ×\ 10) \ +\ (6 \times 30)$

(C)

$(\frac{11} {8} \times 72)\ +\ (\frac{125}{ 5} )$

(D)

$(2 \times 10) \ +\ (50 \times 1.5) \ +\ 15$

58-

What is the difference in area between a $12$ cm by $4$ cm rectangle and a circle with diameter of $12$ cm ? $(π=3)$

(A)

$66$

(B)

$42$

(C)

$18$

(D)

$60$

59-

Mr. Jones saves $$4,500$ out of his monthly family income of $$40,000$. What fractional part of his income does he save?

(A)

$\frac{9}{80}$

(B)

$\frac{1}{80}$

(C)

$\frac{1}{20}$

(D)

$\frac{9}{20}$

60-

If you invest $$8,000$ at an annual rate of $11\%$, how much interest will you earn after one year?

(A)

$$880$

(B)

$$88$

(C)

$$80$

(D)

$$800$

61-

Which is not a prime number?

(A)

$151$

(B)

$131$

(C)

$121$

(D)

$181$

62-

There are three boxes, a red box, a blue box, and a yellow box. If the weight of the red box is $80$ kg and the weight of the red box is $90\%$ of the weight of the blue box, and the weight of the blue box is $120\%$ of the weight of the yellow box, what is the weight of blue and yellow boxes respectively?

(A)

$100$ and $80$

(B)

$110$ and $70$

(C)

$80$ and $100$

(D)

$70$ and $70$

63-

Each of the students in a team may invite up to $6$ friends to a party. What is the maximum number of students and guests who might attend the party?

(A)

$5\ x$

(B)

$6\ x$

(C)

$7\ x$

(D)

$8\ x$

64-

How many possible outfit combinations come from five shirts, three slacks, and ten ties?

(A)

$100$

(B)

$150$

(C)

$250$

(D)

$300$

65-

If $y = 3\ a\ b \ + \ 2\ b^3$, what is y when $a = 2$ and $b = 4$?

(A)

$216$

(B)

$327$

(C)

$211$

(D)

$189$

66-

In the figure below, line A is parallel to line B. What is the value of angle $x$?
ISEE Middle Level6

(A)

$135$ degree

(B)

$145$ degree

(C)

$115$ degree

(D)

$125$ degree

67-

Three people go to a restaurant. Their bill comes to $$94.00$. They decided to split the cost. One person pays $$17.5$, the next person pays $3$ times that amount. How much will the third person have to pay?

(A)

$$30$

(B)

$$17.5$

(C)

$$22$

(D)

$$24$

68-

$210$ minutes=…?

(A)

$4.5$ Hours

(B)

$3.5$ Hours

(C)

$5$ Hours

(D)

$3$ Hours

69-

Two-kilogram apple and three-kilograms orange cost $$35$ If price of one-kilogram of apple is twice price of one-kilogram of orange. How much does one kilogram apple cost?

(A)

$$8$

(B)

$$5$

(C)

$$10$

(D)

$$15$

70-

In the following equation, what is the value of $3 \ x\ +\ 2\ y$?
$x\ +\ 2\ x\ -\ 15=2\ (\frac{9}{2} \ x\ +\ 2 \ y)\ -\ 12$

(A)

$- \ \frac{3}{2 }$

(B)

$- \ \frac{1}{2 }$

(C)

$\frac{1}{2 }$

(D)

$2$

71-

What is the perimeter of the below right triangle?
ISEE Middle Level7

(A)

$30$

(B)

$36$

(C)

$24$

(D)

$21$

72-

The average weight of $18$ girls in a class is $60$ kg and the average weight of $32$ boys in the same class is $62$ kg. What is the average weight of all the $50$ students in that class?

(A)

$60.76$

(B)

$80.10$

(C)

$61.28$

(D)

$73.48$

73-

How many tiles of $9$ cm$^2$ is needed to cover a floor of dimension $12$ cm by $18$ cm?

(A)

$18$

(B)

$12$

(C)

$21$

(D)

$24$

74-

What is in the following right triangle?
ISEE Middle Level8

(A)

$\sqrt{403}$

(B)

$\sqrt{401}$

(C)

$20$

(D)

$\sqrt{407}$

75-

Calculate the approximate circumference of the following circle.
ISEE Middle Level9

(A)

$94$

(B)

$76$

(C)

$83$

(D)

$91$

76-

$(((-\ 16)\ +\ 36)\ ×\ \frac{1}{4})\ +\ (-\ 12)$?

(A)

$-\ 5$

(B)

$-\ 7$

(C)

$8$

(D)

$\frac{3}{5}$

77-

What is the value of $(16 \ - \ 12)!$?

(A)

$24$

(B)

$18$

(C)

$30$

(D)

$39$

78-

John traveled $120$ km in $4$ hours and Alice traveled $180$ km in $5$ hours. What is the ratio of the average speed of John to average speed of Alice?

(A)

$5 : 9$

(B)

$9 : 5$

(C)

$6 : 5$

(D)

$5 : 6$

79-

What is the difference of smallest $4$–digit number and biggest $4$–digit number?

(A)

$8974$

(B)

$6774$

(C)

$8999$

(D)

$6989$

80-

You just drove $510$ miles and it took you approximately $12$ hours. How many miles per hour was your average speed?

(A)

$42.5$ miles per hour

(B)

$45.5$ miles per hour

(C)

$44$ miles per hour

(D)

$41.5$ miles per hour

81-

An angle is equal to one seventh of its supplement. What is the measure of that angle?

(A)

$22.5^\circ$

(B)

$24^\circ$

(C)

$34^\circ$

(D)

$34.5^\circ$

82-

If $140\%$ of a number is equal to $30\%$ of $90$ , then what is the number?

(A)

$19.28$

(B)

$16.22$

(C)

$19.12$

(D)

$18.52$

83-

In a department of a company, the ratio of employees with Bachelor’s degree to employees with high school Diploma is $2$ to $5$. If there are $18$ employees with Bachelor’s degree in this department, how many employees with High School Diploma should be moved to other departments to change the ratio of the number of employees with Bachelor’s Degree to the number of employees with High School Diploma to $3$ to $4$ in this department?

(A)

$39$

(B)

$21$

(C)

$28$

(D)

$54$

84-

What is $41,8410$ in scientific notation?

(A)

$4.1841\times10^5$

(B)

$4.1841\times10^3$

(C)

$4184.1\times10^4$

(D)

$41.841\times10^6$

ISEE Middle Level Practice Test Answers and Explanations

1- Choice B is correct

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

2- Choice D is correct

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 $31.60$

3- Choice B is correct

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

4- Choice C is correct

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

5- Choice D is correct

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$

6- Choice C is correct

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

7- Choice A is correct

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

8- Choice A is correct

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

9- Choice A is correct

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

10- Choice C is correct

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: $(230)\ (0.80) \ (0.80)$

11- Choice A is correct

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$

12- Choice B is correct

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:
$\frac{81\ π}{4}=20.25 \ π$

13- Choice D is correct

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

14- Choice D is correct

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

15- Choice A is correct

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

16- Choice B is correct

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

17- Choice B is correct

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

18- Choice C is correct

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

19- Choice C is correct

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}$

20- Choice C is correct

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: $3$

21- Choice A is correct

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

22- Choice D is correct

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

23- Choice A is correct

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 $5:\ x = 7$

24- Choice A is correct

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

25- Choice B is correct

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 $
$2\ f=26 \ x \ -\ 6\ y\to f=13\ x\ -\ 2 \ y$

26- Choice C is correct

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

27- Choice A is correct

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=$\frac{y_2\ -\ y_1}{x_2 \ -\ x_1} =\frac{3\ -\ 5}{2\ -\ 1}=-\ 2$

28- Choice C is correct

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 $6$

29- Choice B is correct

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

30- Choice D is correct

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.

31- Choice A is correct

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 $y$.

32- Choice A is correct

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: $30$

33- Choice D is correct

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

34- Choice C is correct

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.

35- Choice B is correct

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:
$\frac{8\ -\ 3}{9\ -\ 2}=\frac{5}{7}$

36- Choice B is correct

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 $= 2$

37- Choice A is correct

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.

37- Choice A is correct

38- Choice C is correct

The correct answer is $10$ cubed
$10$ cubed is:$10^3=1,000$

39- Choice A is correct

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: $16\ +\ 13\ +\ 10\ +\ 10=49$

40- Choice D is correct

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)

41- Choice B is correct

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

42- Choice A is correct

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

43- Choice C is correct

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.

44- Choice A is correct

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.

45- Choice A is correct

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

46- Choice C is correct

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 = $
$12 \ +\ 4 \times (–\ 4) \ –\ [77] \div 11 = 12 \ +\ (–\ 16)\ –\ 7 = 12 \ – \ 16 \ – \ 7 = \ –\ 11$

47- Choice B is correct

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$

48- Choice B is correct

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

49- Choice B is correct

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

50- Choice C is correct

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$

51- Choice A is correct

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

52- Choice A is correct

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: $I \gt 3000 \ x\ +\ 22000$

53- Choice D is correct

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

54- Choice D is correct

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

55- Choice D is correct

The correct answer is $4$
$|5\ -\ 9|=|-\ 4|=4$

56- Choice C is correct

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

57- Choice A is correct

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

58- Choice D is correct

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: $108\ -\ 48=60$

59- Choice A is correct

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

60- Choice A is correct

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

61- Choice C is correct

The correct answer is $121$
$121$ is not prime number, it is divided by $11$

62- Choice A is correct

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

63- Choice C is correct

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)

64- Choice B is correct

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

65- Choice A is correct

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 $b =4$
$y = 3 \ (2) \ (4) \ +\ 2\ (4)^3 = 24 \ +\ 3\ (64) = 24 \ +\ 192 = 216$

66- Choice D is correct

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

67- Choice D is correct

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

68- Choice B is correct

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

69- Choice C is correct

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

70- Choice A is correct

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$
$- \ 6 \ x\ -\ 4\ y\ =3\to$
$- \ \frac{1}{2 } \ (- \ 6 \ x\ -\ 4\ y\ =3) \to 3 \ x + \ 2 \ y =- \ \frac{3}{2 }$

71- Choice C is correct

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

72- Choice C is correct

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 $=\frac{3064}{50} = 61.28$

73- Choice D is correct

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

74- Choice D is correct

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

75- Choice A is correct

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

76- Choice B is correct

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

77- Choice A is correct

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

78- Choice D is correct

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.
$30 : 36\Rightarrow 5 : 6$

79- Choice C is correct

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

80- Choice A is correct

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

81- Choice A is correct

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 $8: \ x = 22.5$

82- Choice A is correct

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

83- Choice B is correct

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:
$45\ -\ 24=21$

84- Choice A is correct

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