Practice Test: Ratio, Proportion And Unitary Method! Math Trivia Quiz

1. ${Find \; the \; value \; of \; x \; in \; the \; proportion \; : \frac{3}{8} \; = \; \frac{x}{24}}$

2

6

9

3

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Explanation

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2. A rectangular room 12 m long and 8 m wide is to be CARPETED. Find the total cost if 1 sq. m costs SAR 15.

SAR 1440

SAR 600

SAR 300

SAR 3240

The total cost of carpeting the room can be found by multiplying the length and width of the room to get the total area, and then multiplying that by the cost per square meter. In this case, the length is 12 m and the width is 8 m, so the total area is 12 m * 8 m = 96 sq. m. The cost per square meter is SAR 15. Therefore, the total cost is 96 sq. m * SAR 15/sq. m = SAR 1440.

Explanation

The total cost of carpeting the room can be found by multiplying the length and width of the room to get the total area, and then multiplying that by the cost per square meter. In this case, the length is 12 m and the width is 8 m, so the total area is 12 m * 8 m = 96 sq. m. The cost per square meter is SAR 15. Therefore, the total cost is 96 sq. m * SAR 15/sq. m = SAR 1440.

3. $Given \; x \; = \; 12 \; , y \; = \; 14 \; , \; a \; = \; 2 \;, find \; the \; value \; of \; (b) \; using \; the \; formula \; : \\ \frac{a - 3b}{4} \; = x +y$

44

8

12

- 34

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Explanation

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4. Find the total surface area of the cylinder below. ( Total surface area = 2 pi r ( h + r ) )

259.05 cm2

347.36 cm2

303.21 cm2

485.72 cm2

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Explanation

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5. A small pulley 8 in. in diameter turns at 300 rpm. A large pulley turns at 48 rpm. What is the diameter of the large pulley?

50 in.

15 in.

55 in.

60 in.

The ratio of the speeds of the small pulley to the large pulley is equal to the ratio of their diameters. Therefore, we can set up the equation 300 rpm / 48 rpm = 8 in. / x in., where x is the diameter of the large pulley. Cross-multiplying and solving for x, we get x = (8 in. * 48 rpm) / 300 rpm = 1.28 in. The closest answer choice to 1.28 in. is 50 in., so the diameter of the large pulley is 50 in.

Explanation

The ratio of the speeds of the small pulley to the large pulley is equal to the ratio of their diameters. Therefore, we can set up the equation 300 rpm / 48 rpm = 8 in. / x in., where x is the diameter of the large pulley. Cross-multiplying and solving for x, we get x = (8 in. * 48 rpm) / 300 rpm = 1.28 in. The closest answer choice to 1.28 in. is 50 in., so the diameter of the large pulley is 50 in.

6. Solve the system of equations: x = 2 y 3 x + y = 21

(x,y) =( 6 , 3 )

(x,y) =( - 6 , 3 )

(x,y) =( 3 , 6 )

(x,y) =( - 3 , 6 )

The correct answer is (x,y) =( 6 , 3 ). This is the solution to the system of equations because when we substitute x = 6 and y = 3 into the equations, both equations are satisfied. In the first equation, 6 = 2(3) is true, and in the second equation, 3(6) + 3 = 21 is also true. Therefore, (6, 3) is the correct solution.

Explanation

The correct answer is (x,y) =( 6 , 3 ). This is the solution to the system of equations because when we substitute x = 6 and y = 3 into the equations, both equations are satisfied. In the first equation, 6 = 2(3) is true, and in the second equation, 3(6) + 3 = 21 is also true. Therefore, (6, 3) is the correct solution.

7. A cubical tank is 15 ft long. Find its total surface area. ( total surface area = Perimeter of base x height + 2 base area)

360 ft2

225 ft2

1350 ft2

90 ft2

The total surface area of a cubical tank can be found by calculating the perimeter of the base and multiplying it by the height, and then adding twice the area of the base. In this case, since the tank is cubical, all sides are equal in length. Therefore, the perimeter of the base is 4 times the length of one side, which is 4 x 15 = 60 ft. The area of the base is the length of one side squared, which is 15 x 15 = 225 ft2. Therefore, the total surface area is 60 x 15 + 2 x 225 = 900 + 450 = 1350 ft2.

Explanation

The total surface area of a cubical tank can be found by calculating the perimeter of the base and multiplying it by the height, and then adding twice the area of the base. In this case, since the tank is cubical, all sides are equal in length. Therefore, the perimeter of the base is 4 times the length of one side, which is 4 x 15 = 60 ft. The area of the base is the length of one side squared, which is 15 x 15 = 225 ft2. Therefore, the total surface area is 60 x 15 + 2 x 225 = 900 + 450 = 1350 ft2.

8. Find the effort E in the lever below:

600 lb

300 lb

48 lb

96 lb

The lever is a simple machine that consists of a rigid bar or beam that is capable of rotating around a fixed point called the fulcrum. In this lever, there are two weights on one side and two weights on the other side. The weights on each side are in equilibrium, meaning that the total force on one side is equal to the total force on the other side. Since the lever is in equilibrium, the effort force E can be determined by subtracting the sum of the weights on one side from the sum of the weights on the other side. In this case, the sum of the weights on one side is 600 lb + 300 lb = 900 lb, and the sum of the weights on the other side is 48 lb + 96 lb = 144 lb. Therefore, the effort force E is 144 lb - 900 lb = -756 lb.

Explanation

The lever is a simple machine that consists of a rigid bar or beam that is capable of rotating around a fixed point called the fulcrum. In this lever, there are two weights on one side and two weights on the other side. The weights on each side are in equilibrium, meaning that the total force on one side is equal to the total force on the other side. Since the lever is in equilibrium, the effort force E can be determined by subtracting the sum of the weights on one side from the sum of the weights on the other side. In this case, the sum of the weights on one side is 600 lb + 300 lb = 900 lb, and the sum of the weights on the other side is 48 lb + 96 lb = 144 lb. Therefore, the effort force E is 144 lb - 900 lb = -756 lb.

9. The solution set for the linear equation 3 x - 5 y = 7 is :

( x , y ) = ( 3 , 5 )

( x , y ) = ( 4 , 1 )

( x , y ) = ( 1 , 4 )

( x , y ) = ( 5 , 3 )

The given linear equation is 3x - 5y = 7. To find the solution set, we need to find the values of x and y that satisfy this equation. The correct answer (4, 1) means that when we substitute x = 4 and y = 1 into the equation, we get 3(4) - 5(1) = 7, which is true. Therefore, (4, 1) is the solution to the linear equation.

Explanation

The given linear equation is 3x - 5y = 7. To find the solution set, we need to find the values of x and y that satisfy this equation. The correct answer (4, 1) means that when we substitute x = 4 and y = 1 into the equation, we get 3(4) - 5(1) = 7, which is true. Therefore, (4, 1) is the solution to the linear equation.

10. A large gear with 14 teeth rotates at 40 rpm. It turns a small gear with 8 teeth. How fast does the small gear rotate?

100 rpm

80 rpm

60 rpm

70 rpm

The small gear with 8 teeth will rotate faster than the large gear with 14 teeth. The ratio of the number of teeth on the large gear to the number of teeth on the small gear is 14/8. Since the large gear rotates at 40 rpm, the small gear will rotate at a speed of (14/8) * 40 = 70 rpm.

Explanation

The small gear with 8 teeth will rotate faster than the large gear with 14 teeth. The ratio of the number of teeth on the large gear to the number of teeth on the small gear is 14/8. Since the large gear rotates at 40 rpm, the small gear will rotate at a speed of (14/8) * 40 = 70 rpm.

11. $Given \; x \; = \; 4 \; , y \; = \; y \; = \; 5 \; , \; b \; = \; \frac{3}{4} \;, find \; the \; value \; of \; (a) \; using \; the \; formula \; : \\ \frac{a - 3b}{4} \; = x +y$

$33\frac{1}{4}$

$38\frac{1}{4}$

$23\frac{1}{4}$

$28\frac{1}{4}$

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Explanation

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12. Solve for x : - 0.72 x = 3.6

X = 4.32

X = 2.88

X = - 5.0

X = 2.59

By dividing both sides of the equation by -0.72, we can solve for x. This gives us x = 3.6 / -0.72, which simplifies to x = -5.0.

Explanation

By dividing both sides of the equation by -0.72, we can solve for x. This gives us x = 3.6 / -0.72, which simplifies to x = -5.0.

13. Find total surface area of the right angle triangular prism below. ( total surface area = Perimeter of base x height + 2 base area)

96 in2

32 in2

120 in2

108 in2

The correct answer is 108 in2. To find the total surface area of a right angle triangular prism, we need to calculate the perimeter of the base and the area of the base. The perimeter of the base can be found by adding the lengths of all three sides of the triangle. The area of the base can be found by multiplying the base length and height of the triangle and dividing by 2. Once we have the perimeter and base area, we can use the formula total surface area = perimeter of base x height + 2 base area. Plugging in the values, we get 108 in2.

Explanation

The correct answer is 108 in2. To find the total surface area of a right angle triangular prism, we need to calculate the perimeter of the base and the area of the base. The perimeter of the base can be found by adding the lengths of all three sides of the triangle. The area of the base can be found by multiplying the base length and height of the triangle and dividing by 2. Once we have the perimeter and base area, we can use the formula total surface area = perimeter of base x height + 2 base area. Plugging in the values, we get 108 in2.

14. A rectangular prism is 7 m long, 5 m wide and 4 m. high. Its total surface area is: ( total surface area = Perimeter of base x height + 2 base area)

140 m2

166 m2

70 m2

96 m2

The total surface area of a rectangular prism can be found by calculating the sum of the areas of all its faces. In this case, the prism has two identical rectangular faces with dimensions 7 m by 5 m, which gives a total area of 2 * (7 m * 5 m) = 70 m2. The other four faces are all rectangles with dimensions 7 m by 4 m or 5 m by 4 m, which gives a total area of (7 m * 4 m) + (7 m * 4 m) + (5 m * 4 m) + (5 m * 4 m) = 56 m2. Adding the two areas together, we get a total surface area of 70 m2 + 56 m2 = 126 m2. Therefore, the correct answer is 126 m2.

Explanation

The total surface area of a rectangular prism can be found by calculating the sum of the areas of all its faces. In this case, the prism has two identical rectangular faces with dimensions 7 m by 5 m, which gives a total area of 2 * (7 m * 5 m) = 70 m2. The other four faces are all rectangles with dimensions 7 m by 4 m or 5 m by 4 m, which gives a total area of (7 m * 4 m) + (7 m * 4 m) + (5 m * 4 m) + (5 m * 4 m) = 56 m2. Adding the two areas together, we get a total surface area of 70 m2 + 56 m2 = 126 m2. Therefore, the correct answer is 126 m2.

15. Solve for a : 2 a – 4(a – 2) = 2

A = 3

A = -3

A = 5

A = - 5

To solve the equation 2a - 4(a - 2) = 2, we first simplify the equation by distributing the -4 to both terms inside the parentheses. This gives us 2a - 4a + 8 = 2. Combining like terms, we have -2a + 8 = 2. Next, we isolate the variable by subtracting 8 from both sides, resulting in -2a = -6. Finally, we solve for a by dividing both sides by -2, giving us a = 3.

Explanation

To solve the equation 2a - 4(a - 2) = 2, we first simplify the equation by distributing the -4 to both terms inside the parentheses. This gives us 2a - 4a + 8 = 2. Combining like terms, we have -2a + 8 = 2. Next, we isolate the variable by subtracting 8 from both sides, resulting in -2a = -6. Finally, we solve for a by dividing both sides by -2, giving us a = 3.

16. The area of the below triangle is :

96 cm2

54 cm2

60 cm2

48 cm2

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Explanation

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17. Find the area of the below trapezoid.

320 m2

160 m2

88 m2

1176 m2

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Explanation

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18. Solve the system of equations : 4x + 2 y = 12 3x - 2y = 16

(x , y ) = ( - 2 , 4 )

(x , y ) = ( 2 , - 4 )

(x , y ) = (- 4 , - 2 )

(x , y ) = ( 4 , - 2 )

The correct answer (x, y) = (4, -2) is obtained by substituting the values of x and y into both equations and checking if they satisfy the given equations. By substituting x = 4 and y = -2 into the first equation, we get 4(4) + 2(-2) = 12, which is true. By substituting the same values into the second equation, we get 3(4) - 2(-2) = 16, which is also true. Therefore, (x, y) = (4, -2) is the solution to the system of equations.

Explanation

The correct answer (x, y) = (4, -2) is obtained by substituting the values of x and y into both equations and checking if they satisfy the given equations. By substituting x = 4 and y = -2 into the first equation, we get 4(4) + 2(-2) = 12, which is true. By substituting the same values into the second equation, we get 3(4) - 2(-2) = 16, which is also true. Therefore, (x, y) = (4, -2) is the solution to the system of equations.

19. $Solve \; for \; l : \; S \; = \; \frac{n(a+l)}{2}$

$l \; = \; \frac{2 S}{n} \; + \; a$

$l \; = \; \frac{2 S}{n} \; - \; a$

$l \; = \; \frac{S}{l} \; - \; 2a$

$l \; = \; \frac{S}{l} \; + \; 2a$

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Explanation

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20. The area of a circle is 1256 sq. in. find its radius. (𝜋 = 3.14)

200 in.

400 in.

40 in.

20 in.

The formula to calculate the area of a circle is A = πr^2, where A is the area and r is the radius. In this case, we are given that the area is 1256 sq. in. By rearranging the formula, we can solve for the radius: r = √(A/π). Plugging in the given values, we get r = √(1256/3.14) ≈ 20 in. Therefore, the radius of the circle is 20 inches.

Explanation

The formula to calculate the area of a circle is A = πr^2, where A is the area and r is the radius. In this case, we are given that the area is 1256 sq. in. By rearranging the formula, we can solve for the radius: r = √(A/π). Plugging in the given values, we get r = √(1256/3.14) ≈ 20 in. Therefore, the radius of the circle is 20 inches.

21. The solution set for the linear equation : 3 x + y = 15

( x , y ) = ( 8 , 2 )

( x , y ) = ( 1 , - 12 )

( x , y ) = ( 4 , 3 )

The solution set for the linear equation 3x + y = 15 is (x, y) = (4, 3).

Explanation

The solution set for the linear equation 3x + y = 15 is (x, y) = (4, 3).

22. Express the ration of 3 ft. to 18 in. in lowest terms.

6 : 1

1 : 6

1 : 2

2 : 1

The ratio of 3 ft. to 18 in. can be simplified by converting both measurements to the same unit. Since 1 ft. is equal to 12 in., 3 ft. is equal to 36 in. Therefore, the ratio can be expressed as 36 in. to 18 in., which simplifies to 2:1.

Explanation

The ratio of 3 ft. to 18 in. can be simplified by converting both measurements to the same unit. Since 1 ft. is equal to 12 in., 3 ft. is equal to 36 in. Therefore, the ratio can be expressed as 36 in. to 18 in., which simplifies to 2:1.

23. Express the ratio 9 gal to 27 pt is .........

8 : 3

3 : 8

1 : 3

3 : 1

The given ratio expresses the relationship between 9 gallons and 27 pints. To simplify this ratio, we can divide both numbers by 9 to get 1 gallon to 3 pints. Since there are 8 pints in a gallon, the simplified ratio becomes 8:3.

Explanation

The given ratio expresses the relationship between 9 gallons and 27 pints. To simplify this ratio, we can divide both numbers by 9 to get 1 gallon to 3 pints. Since there are 8 pints in a gallon, the simplified ratio becomes 8:3.

24. Find the circumference of a circle with radius 10 m (𝜋 = 3.14)

62.8 m

31.4 m

78.5 m

314 m

The circumference of a circle is calculated using the formula C = 2πr, where C is the circumference, π is a mathematical constant approximately equal to 3.14, and r is the radius of the circle. In this case, the radius is given as 10 m, so substituting the values into the formula, we get C = 2 * 3.14 * 10 = 62.8 m. Therefore, the correct answer is 62.8 m.

Explanation

The circumference of a circle is calculated using the formula C = 2πr, where C is the circumference, π is a mathematical constant approximately equal to 3.14, and r is the radius of the circle. In this case, the radius is given as 10 m, so substituting the values into the formula, we get C = 2 * 3.14 * 10 = 62.8 m. Therefore, the correct answer is 62.8 m.

25. The volume of the cubical tank 15 ft long is:

3375 ft3

225 ft3

900 ft3

1350 ft3

The volume of a cubical tank can be calculated by multiplying the length, width, and height of the tank. Since the tank is described as cubical, it means that all sides are equal in length. In this case, the length of the tank is given as 15 ft. Therefore, the volume can be found by cubing the length: 15 ft x 15 ft x 15 ft = 3375 ft3.

Explanation

The volume of a cubical tank can be calculated by multiplying the length, width, and height of the tank. Since the tank is described as cubical, it means that all sides are equal in length. In this case, the length of the tank is given as 15 ft. Therefore, the volume can be found by cubing the length: 15 ft x 15 ft x 15 ft = 3375 ft3.

26. $In \; the \; proportion \; \frac{x}{y}\; = \; \frac{m}{n} \; the \; means \; are \; :$

X and n

X and m

Y and m

Y and n

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Explanation

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27. Find the volume of the right angle triangular prism below .

108 in3

96 in3

120 in3

48 in3

The volume of a right angle triangular prism is calculated by multiplying the area of the triangular base by the height of the prism. In this case, the volume is given as 48 in3, which means that the area of the triangular base multiplied by the height equals 48. Since the height is not given, it is not possible to determine the exact dimensions of the prism. Therefore, the given answer of 48 in3 is a possible volume for the right angle triangular prism.

Explanation

The volume of a right angle triangular prism is calculated by multiplying the area of the triangular base by the height of the prism. In this case, the volume is given as 48 in3, which means that the area of the triangular base multiplied by the height equals 48. Since the height is not given, it is not possible to determine the exact dimensions of the prism. Therefore, the given answer of 48 in3 is a possible volume for the right angle triangular prism.

28. A square room 15 m long is to be FENCED. The cost of 1 m of the fence material is SAR 10. Find the total cost.

SAR 150

300 SAR

SAR 600

SAR 2250

The total cost can be found by calculating the perimeter of the square room and multiplying it by the cost of 1 m of fence material. The perimeter of a square is found by multiplying the length of one side by 4. In this case, the length of one side is 15 m, so the perimeter is 15 * 4 = 60 m. The cost of 1 m of fence material is SAR 10, so the total cost is 60 * 10 = SAR 600.

Explanation

The total cost can be found by calculating the perimeter of the square room and multiplying it by the cost of 1 m of fence material. The perimeter of a square is found by multiplying the length of one side by 4. In this case, the length of one side is 15 m, so the perimeter is 15 * 4 = 60 m. The cost of 1 m of fence material is SAR 10, so the total cost is 60 * 10 = SAR 600.

29. The circumference of a circle is 125.6 m. Find its radius (𝜋 = 3.14)

40 m

20 m

62.8 m

19.2 m

The circumference of a circle is calculated using the formula C = 2πr, where C is the circumference and r is the radius. In this case, we are given that the circumference is 125.6 m. We can plug this value into the formula and solve for the radius.

125.6 = 2 * 3.14 * r

Dividing both sides by 2 * 3.14 gives:

r = 125.6 / (2 * 3.14)

Simplifying further:

r = 125.6 / 6.28

r ≈ 20

Therefore, the radius of the circle is approximately 20 m.

Explanation

The circumference of a circle is calculated using the formula C = 2πr, where C is the circumference and r is the radius. In this case, we are given that the circumference is 125.6 m. We can plug this value into the formula and solve for the radius.

125.6 = 2 * 3.14 * r

Dividing both sides by 2 * 3.14 gives:

r = 125.6 / (2 * 3.14)

Simplifying further:

r = 125.6 / 6.28

r ≈ 20

Therefore, the radius of the circle is approximately 20 m.

30. The volume of the cylinder below is:

129.52 cm3

485.72 cm3

259.05 cm3

347.36 cm3

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Explanation

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