1 Choice D is correct
The correct answer is \(35\) \(\frac{30}{A} \ + \ 3=9 → \frac{30}{A}=9 \  \ 3=6\) →\(30=6 \ A → A=\frac{30}{6}=5\) \(30 \ + \ A=30 \ + \ 5=35\)

2 Choice A is correct
The correct answer is \(600\) Number of rotates in \(16\) second equals to: \(\frac{450 \ × \ 16}{12}=600\)

3 Choice B is correct
The correct answer is \(16\) The area of the floor is:\(4\) cm \(× \ 20\) cm \(= 80\) cm\(^2\) The number of tiles needed \(= 80 \ ÷ \ 5 = 16\)

4 Choice C is correct
The correct answer is \(9\) The digit in tens place is \(2\). The digit in the thousandths place is \(7\). Therefore; \(2 \ + \ 7=9\)

5 Choice A is correct
The correct answer is number of books sold in April is was \(\frac{1}{2}\)the number of books in sold in July. A:Number of books sold in April is: \(380\) Number of books sold in July is: \(760→ \frac{ 380}{760}=\frac{38}{76}=\frac{1}{2}\) B:number of books sold in July is: \(760\) Half the number of books sold in May is:\(\frac{1140}{2}=570 → 760 \ >570\) C:number of books sold in June is: \(190\) Half the number of books sold in April is:\(380 \ × \ 2=760 → 760 \ > \ 190\) D:\(380 \ + \ 190=570 \ < \ 760\) E:\(380 \ < \ 760\)

6 Choice E is correct
The correct answer is \(6\) Number of packs equal to: \(\frac{24}{4}=6\) Therefore, the school must purchase \(6\) packs.

7 Choice A is correct
The correct answer is \(2,541\) \(15.246 \ ÷ \ 0.006=\frac{\frac{15,246}{1,000}}{{\frac{6}{1,000}}}=\frac{15,246}{6}=2,541\)

8 Choice C is correct
The correct answer is \(23\) The amount of money that Alex earns for one hour: \(\frac{$\ 460}{20}=$\ 23\) Number of additional hours that he needs to work in order to make enough money is: \(\frac{$\ 630 \  \ $\ 460}{2.5 \ × \ $\ 23}≅3\) Number of total hours is: \(20 \ + \ 3=23\)

9 Choice A is correct
The correct answer is \(35\) First, find the number. Let \(x\) be the number. Write the equation and solve for \(x\). \(120\%\) of a number is \(60\), then: \(1.2 \ × \ x=→x=60 \ ÷ \ 1.2=50\) \(70\%\) of \(50\) is:\(0.7 \ × \ 50=35\)

10 Choice A is correct
The correct answer is \(4.68\) \(\frac{1 \ \frac{5}{2} \ + \ \frac{3}{5}}{4 \ \frac{3}{2} \  \ \frac{15}{4}} = \frac{\frac{7}{2} \ + \ \frac{3}{5}}{\frac{11}{2} \  \ \frac{15}{4}} = \frac{\frac{35 \ + \ 6}{10}}{\frac{22 \  \ 15}{4}}\) \(\frac{\frac{41}{10}}{\frac{7}{4}} = \frac{41 \times 2}{7 \times 5} = \frac{164}{35} \cong 4.68\)

11 Choice C is correct
The correct answer is \(70\) Average \(=\frac{sum \ of \ terms }{number \ of \ terms}\) The sum of the weight of all girls is: \(12 \ × \ 62 = 744\) kg The sum of the weight of all boys is: \(24 \ × \ 74 = 1776\) kg The sum of the weight of all students is: \(744 \ + \ 1776 =2520\) kg The average weight of the \(36\) students: \(\frac{2520}{36}=70\)

12 Choice D is correct
The correct answer is \(7\) \(2 \ ≤ \ x \ < \ 6 \)→ Multiply all sides of the inequality by \(2\). Then: \(2 \ × \ 2 \ ≤ \ 2 \ × \ x \ < \ 2 \ × \ 6 → 4 \ ≤ \ 2 \ x \ < \ 12\) All \(3\) to all sides. Then: →\(4 \ + \ 3 \ ≤ \ 2\ x \ + \ 3 \ < \ 12 \ + \ 3→ 7 \ ≤ \ 2 \ x \ + \ 3 \ < \ 15\) Minimum value of \(2 \ x \ + \ 3\) is \(7\)

13 Choice B is correct
The correct answer is \(42.5\) \(8.5 \ ÷ \ 0.20=\frac{8.5}{0.20}=\frac{\frac{{85}}{10}}{\frac{20}{100}}=\frac{85 \ × \ 100}{20 \ × \ 10}=\frac{85}{20} \ × \frac{100}{10}=4.25 \ × \ 10=42.5\)

14 Choice D is correct
The correct answer is \(5\) \(4∎9=\sqrt{4^2 \ + \ 9}=\sqrt{16 \ + \ 9}=\sqrt{25}=5\)

15 Choice A is correct
The correct answer is \(2000\) Let \(x\) be the capacity of one tank. Then, \(\frac{1}{2} x=250→ x=250 \ × \ 2=500\) Liters The amount of water in four tanks is equal to: \(4 \ × \ 500=2000\) Liters

16 Choice A is correct
The correct answer is \($\ 10\) Let \(x\) be the cost of onekilogram orange, then: \(3 \ x \ + \ (2 \ × \ 3.2)=36.4→\) \(3 \ x \ + \ 6.4=36.4→\) \(3 \ x=36.4 \  \ 6.4→\) \(3 \ x=30→\) \(x=\frac{30}{3}=$\ 10\)

17 Choice A is correct
The correct answer is \(138\) minutes Let \(b\) be the amount of time Mary can do the job, then, \(\frac{1}{a} \ + \ \frac{1}{b}=\frac{1}{100}→\) \(\frac{1}{360} \ + \ \frac{1}{b}=\frac{1}{100}→\) \(\frac{1}{b}=\frac{1}{100} \  \ \frac{1}{360}=\frac{3.6 \  \ 1}{360}=\frac{2.6}{360}=\frac{1}{138}\) Then: \(b=138\) minutes

18 Choice C is correct
The correct answer is \(145\) degrees All angles in a triangle sum up to \(180\) degrees. Then: \(x=35 \ + \ 110=145\)

19 Choice D is correct
The correct answer is \( \ 15\) The smallest number is \( \ 12\). To find the largest possible value of one of the other five integers, we need to choose the smallest possible integers for four of them. Let \(x\) be the largest number. Then: \( \ 65=( \ 12) \ + \ ( \ 11) \ + \ ( \ 10) \ + \ ( \ 9) \ + \ ( \ 8) \ + \ x→\) \( \ 65= \ 50 \ + \ x→\) \(x= \ 65 \ + \ 50= \ 15\)

20 Choice B is correct
The correct answer is \(6\) Let’s review the choices provided. A. \(4\). In \(4\) years, David will be \(46\) and Ava will be \(10\). \(46\) is not \(4\) times \(10\). B. \(6\). In \(6\) years, David will be \(48\) and Ava will be \(12\). \(48\) is \(4\) times \(12\)! C. \(8\). In \(8\) years, David will be \(80\) and Ava will be \(14\). \(50\) is not \(4\) times \(14\). D. \(10\). In \(10\) years, David will be \(52\) and Ava will be \(16\). \(52\) is not \(4\) times \(16\). E. \(14\). In \(14\) years, David will be \(56\) and Ava will be \(20\). \(56\) is not \(4\) times \(20\).

21 Choice C is correct
The correct answer is \(40\) Choices A, B, D and E are incorrect because \(60\%\) of each of the numbers is nonwhole number. A. \(26\), \(60\%\) of \(26 = 0.60 \ × \ 26=15.6 \) B. \(32\), \(60\%\) of \(32=0.60 \ × \ 32=19.2\) C. \(40\), \(60\%\) of \(40=0.60 \ × \ 40=24\) D. \(41\), \(60\%\) of \(41=0.60 \ × \ 41=24.6\) E. \(16\), \(60\%\) of \(16=0.60 \ × \ 16=9.6\)

22 Choice C is correct
The correct answer is \(  \ \frac{1}{3}\) The equation of a line in slope intercept form is: \(y=m \ x \ + \ b\) Solve for \(y\). \(6 \ x \  \ 2 \ y=16 ⇒\) \( \ 2 \ y=16 \  \ 6 \ x ⇒\) \(y=(16 \  \ 6 \ x) \ ÷ \ ( \ 2) ⇒\) \(y=3 \ x \  \ 8\) The slope is \(3\). The slope of the line perpendicular to this line is: \(m_{1} \ × \ m_{2} =  \ 1 ⇒ 3 \ × \ m_{2} =  \ 1 ⇒\) \(m_{2} =  \ \frac{1}{3}\)

23 Choice C is correct
The correct answer is \(\frac{90 \ x \ + \ 750}{x}\) The amount of money for \(x\) bookshelf is: \(90 \ x\) Then, the total cost of all bookshelves is equal to: \(90 \ x \ + \ 750\) The total cost, in dollar, per bookshelf is: \(\frac{Total \ cost}{number \ of \ items}=\frac{90 \ x \ + \ 750}{x}\)

24 Choice A is correct
The correct answer is \(288\) cm\(^3\) If the length of the box is \(24\), then the width of the box is one fourth of it, \(6\), and the height of the box is \(2\) (one third of the width). The volume of the box is: V \(=\) (length) (width) (height) \(= (24) \ (6) \ (2) =288\) cm\(^3\)

25 Choice C is correct
The correct answer is \(42\) miles Use the information provided in the question to draw the shape. Use Pythagorean Theorem: \(a^2 \ + \ b^2 = c^2\) \(60^2 \ + \ 120^2 = c^2 ⇒\) \(3600 \ + \ 14400 = c^2 ⇒\) \(18000 = c^2 ⇒\) \(c =42\)

25 Choice C is correct
The correct answer is \(42\) miles Use the information provided in the question to draw the shape. Use Pythagorean Theorem: \(a^2 \ + \ b^2 = c^2\) \(60^2 \ + \ 120^2 = c^2 ⇒\) \(3600 \ + \ 14400 = c^2 ⇒\) \(18000 = c^2 ⇒\) \(c =42\)

26 Choice A is correct
The correct answer is \(1\) \(\frac{13 \ + \ 11}{2}=\frac{24}{2}=12\) Then: \(12 \  \ 11=1\)

27 Choice C is correct
The correct answer is \(385\) \(\frac{84752}{202} \cong 385.2363 \cong 385\)

28 Choice C is correct
The correct answer is \(80\) liters The Area that one liter of paint is required: \(45\) cm \(× \ 100\) cm = \(4,500\) cm\(^2\) Remember: \(1\) m\(^2 = 10,000\) cm\(^2 \ (100 \ × \ 100 = 10,000)\), then, \(4,500\) cm\(^2 = 0.45\) m\(^2\) Number of liters of paint we need: \(\frac{36}{0.45}=80\) liters

29 Choice C is correct
The correct answer is \(6\) Let’s review the choices provided: A. \(x=2→\) The perimeter of the figure is: \(2 \ + \ 4 \ + \ 2 \ + \ 2 \ + \ 2=12≠ 20\) B. \(x=3→\) The perimeter of the figure is: \(2 \ + \ 4 \ +\ 2 \ + \ 3 \ + \ 3=14≠20\) C. \(x=6→\) The perimeter of the figure is: \(2 \ + \ 4 \ + \ 2 \ + \ 6 \ + \ 6=20=20\) D. \(x=9→\) The perimeter of the figure is: \(2 \ + \ 4 \ + \ 2 \ + \ 9 \ + \ 9=26≠20\) E. \(x=12→\) The perimeter of the figure is: \(2 \ +\ 4 \ + \ 2 \ + \ 12 \ + \ 12=32≠20\)

30 Choice A is correct
The correct answer is \(14 \  \ k\) Will’s mark is \(k\) less than John’s mark. Then, from the choices provided Will’s mark can only be \(14 \  \ k\)

31 Choice A is correct
The correct answer is \(4\) hours and \(32\) minutes Number of times that the driver rests \(=\frac{24}{6}=4\) Driver’s rest time \(= 1\) hour and \(8\) minutes \(= 68\) minutes Then, \(4 \ × \ 68\) minutes \(=272\) minutes \(1\) hour \(= 60\) minutes \(→ 272\) minutes \(= 4\) hours and \(32\) minutes

32 Choice A is correct
The correct answer is \($\ 600\) Let \(x\) be the original price. If the price of the sofa is decreased by \(25\%\) to \($450\), then: \(75\%\) of \(x=450 ⇒\) \(0.75 \ x=450 ⇒\) \(x=450 \ ÷ \ 0.75=$\ 600\)

33 Choice E is correct
The correct answer is \(6 \ × \ \frac{1}{6}\) Let’s review the options provided: A. \(12 \ × \ \frac{1}{2}=\frac{12}{2}=6=6\) B. \(24 \ × \ \frac{1}{4}=\frac{24}{4}=6=6\) C. \(4 \ × \ \frac{3}{2}=\frac{12}{2}=6=6\) D. \(6 \ × \ \frac{5}{5}=\frac{30}{5}=6=6\) E. \(6 \ × \ \frac{1}{6}=\frac{6}{6}=1≠6\)

34 Choice B is correct
The correct answer is \(40,500\) Number of Mathematics book: \(0.25 \ × \ 900=225\) Number of English books: \(0.20 \ × \ 900=180\) Product of number of Mathematics and number of English books: \(225 \ × \ 180=40,500\)

35 Choice A is correct
The correct answer is \(108^°, 54^°\) The angle \(\alpha\) is: \(0.3 \ × \ 360=108^°\) The angle \(β\) is: \(0.15 \ × \ 360=54^°\)

36 Choice B is correct
The correct answer is \(1.5\) \(6 \ y \ + \ 6 \ < \ 24→\) \(6 \ y \ < \ 24 \  \ 6→\) \(6 \ y \ < \ 18→y \ < \ 3\) The only choice that is less than \(3\) is B.

37 Choice C is correct
The correct answer is \(24\) \(x \ + \ 1=1 \ + \ 1 \ + \ 1→x=2\) \(y \ + \ 6 \ + \ 2=5 \ + \ 4→y \ + \ 8=9→y=1\) Then, the perimeter is: \(1 \ + \ 5 \ + \ 1 \ + \ 4 \ + \ 1 \ + \ 2 \ + \ 1 \ + \ 6 \ + \ 2 \ + \ 1=24\)

38 Choice A is correct
The correct answer is \(45\) Since, E is the midpoint of AB, then the area of all triangles DAE, DEF, CFE and CBE are equal. Let \(x\) be the area of one of the triangle, then: \(4\ x=90→x=22.5\) The area of DEC \(=2 \ x=2 \ (22.5)=45 \)

39 Choice A is correct
The correct answer is: it cannot be determined from the information given We have two equations and three unknown variables, therefore \(x\) cannot be obtained.

40 Choice C is correct
The correct answer is \(25\) The capacity of a red box is \(20\%\) bigger than the capacity of a blue box and it can hold \(30\) books. Therefore, we want to find a number that \(20\%\) bigger than that number is \(30\). Let \(x\) be that number. Then: \(1.20 \ × \ x=30\), Divide both sides of the equation by \(1.2\). Then: \(x=\frac{30}{1.20}=25\)

41 Choice A is correct
The correct answer is \(40.46\) liters Amount of available petrol in tank: \(70.5 \  \ 4.65 \  \ 35.7 \ + \ 10.31=40.46\) liters

42 Choice C is correct
The correct answer is \(34\) Perimeter of figure A is: \(2 \ π \ r=2 \ π \ \frac{12}{2}=12 \ π=12 \ × \ 3=36\) Area of figure B is: \(4 \ × \ 8=32\) Average \(=\frac{36 \ + \ 32}{2}=\frac{68}{2}=34\)

43 Choice B is correct
The correct answer is \(3\) Let’s review the choices provided: A. \(x=\frac{1}{2}→ \frac{4}{7} \ + \ \frac{1}{2}=\frac{8 \ + \ 7}{14}=\frac{15}{14} \cong 1.071 \ < \ 3\) B. \(x=3→ \frac{5}{9} \ + \ 3=\frac{4 \ + \ 21}{7}=\frac{25}{7} \cong 3.6 \ >\ 3\) C. \(x=\frac{4}{3}→ \frac{4}{7} \ + \frac{4}{3}=\frac{12 \ +\ 28}{21}=\frac{40}{21} \cong 1.91 \ < \ 3\) D. \(x=\frac{4}{6}→ \frac{4}{7} \ + \ \frac{4}{6}=\frac{24 \ + \ 28}{42}=\frac{52}{42} \cong 1.238 \ < \ 3\) E. \(x=\frac{2}{5}→ \frac{4}{7} \ + \ \frac{2}{5}=\frac{20 \ + \ 14}{35}=\frac{34}{35} \cong 0.9 \ <\ 3\)

44 Choice E is correct
The correct answer is \(4 \times a \times b\) Let put some values for \(a\) and \(b\). If \(a=9\) and \(b=2 →a \ × \ b=18 →\) \(\frac{18}{3}=6→18\) is divisible by \(3\) then; A. \(a \ + \ b=9 \ + \ 2=11\) is not divisible by \(3\) B. \(3 \ a \  \ b=(3 \ × \ 9) \  \ 2=27 \  \ 2=25\) is not divisible by \(3\) If \(a=11\) and \(b=3 →a \ × \ b=33 →\) \(\frac{33}{3}=11\) is divisible by \(3\) then; C. \(a \  \ 3 \ b=11 \  \ (3 \ × \ 3)=11 \  \ 9 =2\) is not divisible by \(3\) D. \(\frac{a}{b}=\frac{11}{3}\) is not divisible by \(3\) E. \(4 \ × \ 11 \ × \ 3=132\) \(132\) is divisible by \(3\). If you try any other numbers for \(a\) and \(b\), you will get the same result.

45 Choice C is correct
The correct answer is \(30\) The angles on a straight line add up to \(180\) degrees. Let’s review the choices provided: A. \(y=10→ x \ + \ 45 \ + \ y\ + \ 2 \ x \ + \ y=25 \ + \ 45 \ + \ 10 \ + \ 2 \ (25) \ + \ 10=140≠180\) B. \(y=25→ x \ + \ 45 \ + \ y\ + \ 2 \ x \ + \ y=25 \ + \ 45 \ + \ 25 \ + \ 2 \ (25) \ + \ 25=170≠180\) C. \(y=30→ x \ + \ 45\ + \ y \ +\ 2 \ x \ + \ y=25 \ + \ 45 \ + \ 30 \ + \ 2 \ (25) \ + \ 30=180\) D. \(y=35→ x \ +\ 45 \ + \ y \ +\ 2 \ x \ + \ y=25 \ + \ 45 \ + \ 35 \ + \ 2 \ (25) \ + \ 35=190≠180\) E. \(y=40→ x \ + \ 45 \ + \ y \ + \ 2 \ x \ + \ y=25 \ + \ 45 \ +\ 40 \ + \ 2 \ (25) \ + \ 40=200≠180\)

46 Choice C is correct
The correct answer is \(\frac{8}{20}\) Set of numbers that are not composite between \(1\) and \(20\): A \(= \left\{2, 3, 5, 7, 11, 13, 17, 19, \right\}\) Probability \(=\frac{number \ of \ desired \ outcomes}{number \ of \ total \ outcomes} = \frac{8}{20}\)

47 Choice E is correct
The correct answer is \(15\) \(\frac{3}{4} \ × \ 20=\frac{60}{4}=15\)

48 Choice A is correct
The correct answer is \(\frac{800}{6} \ + \ \frac{50}{6} \ + \ \frac{5}{6}\) \(855 \ ÷ \ 6=\frac{855}{6}=\frac{800 \ + \ 50 \ + \ 5}{6}=\frac{800}{6} \ + \ \frac{50}{6} \ + \ \frac{5}{6}\)

49 Choice C is correct
The correct answer is \(29\) Find the difference of each pairs of numbers: \(1 \ , 2, 4, 7, 11, 16, 22\), ___, \(37\) The difference of \(1\) and \(2\) is \(1, \ 2\) and \(4\) is \(2, \ 4\) and \(7\) is \(3, \ 7\) and \(11\) is \(4, \ 11\) and \(16\) is \(5, \ 16\) and \(22\) is \(6, \ 22\) and next number should be \(7\). The number is \(22 \ + \ 7 = 29\)

50 Choice A is correct
The correct answer is \(444 \frac{5}{7}\) \(450 \  \ 5 \ \frac{4}{14}=(449 \  \ 5) \ + \ (\frac{14}{14} \  \ \frac{4}{14})= 444 \frac{10}{14} =444 \frac {5}{7}\)
