Ratio and Proportion Quiz

If y : 196 :: 196 : 784, then what is the value of y?

• 16

• 49

• 7

• 4

Answer explanation

The relationship is that 196 is the square of 14 (14^2 = 196), and 784 is the square of 28 (28^2 = 784). Therefore, y must be the square of 7 (7^2 = 49) to maintain the same relationship. Thus, y = 49.

If 144 : y :: y : 225, and y > 0, find the value of y.

• 130

• 210

• 120

• 180

Answer explanation

To solve 144 : y :: y : 225, we set up the proportion 144/y = y/225. Cross-multiplying gives 144 * 225 = y^2. Calculating this, y^2 = 32400, so y = 180 (since y > 0). Thus, the correct answer is 180.

If 144 : b :: b : 36, and b > 0, find the value of b.

• 12

• 36

• 27

• 72

Answer explanation

To solve 144 : b :: b : 36, we set up the proportion 144/b = b/36. Cross-multiplying gives 144 * 36 = b^2. Thus, b^2 = 5184, leading to b = 72 (since b > 0). Therefore, the correct answer is 72.

If 1.6 : 0.6 :: 0.6 : x, find the value of x.

• 0.98

• 0.25

• 0.275

• 0.225

Answer explanation

To solve the proportion 1.6 : 0.6 :: 0.6 : x, we can set up the equation 1.6/0.6 = 0.6/x. Cross-multiplying gives 1.6x = 0.36. Solving for x, we find x = 0.225. Thus, the correct answer is 0.225.

Find the fourth proportion of the 15, 10 and 12.

• 6

• 12

• 10

• 8

Answer explanation

To find the fourth proportion of 15, 10, and 12, use the formula: (b * c) / a = x. Here, x = (10 * 12) / 15 = 8. Thus, the fourth proportion is 8.

If 48 : x :: x : 75, and x > 0, then what is the value of x?

• 60

• 63

• 57

• 51

Answer explanation

To solve 48 : x :: x : 75, we set up the proportion 48/x = x/75. Cross-multiplying gives 48 * 75 = x^2. Thus, x^2 = 3600, leading to x = 60 (since x > 0). Therefore, the correct answer is 60.

What is the compound ratio of 45 : 75, 3 : 5, 51 : 68 and 256 : 81?

• 64/75

• 32/45

• 128/75

• 75/32

Answer explanation

To find the compound ratio, multiply the ratios: (45/75) * (3/5) * (51/68) * (256/81). Simplifying gives 64/75, which is the correct answer.

What will be the third proportional of 16 and 40?

• 10

• 100

• 640

• 40

Answer explanation

To find the third proportional of 16 and 40, use the formula: (b^2)/a. Here, a = 16 and b = 40. So, (40^2)/16 = 1600/16 = 100. Thus, the third proportional is 100.

The fourth proportional to 4, 9, 12 is: ______

• 48

• 36

• 27

• 72

Answer explanation

To find the fourth proportional to 4, 9, and 12, use the formula: (b * c) / a = (9 * 12) / 4 = 27. Thus, the fourth proportional is 27.

If 12, x, 48 are in ratio, then find the value of x.

• 24

• 21

• 36

• 16

Answer explanation

To find x in the ratio 12:x:48, set up the proportion 12/x = x/48. Cross-multiplying gives 12*48 = x^2. Thus, x^2 = 576, leading to x = 24. Therefore, the correct answer is 24.