HESI Mathematics

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What is the missing value in the ratio and proportion 15:2000::x:200?

  • A. 1.5
  • B. 7.777
  • C. 0.15
  • D. 15
Correct Answer: A

Rationale: To find the missing value x, we set up a proportion: 15/2000 = x/200. Cross multiplying, we get 15 * 200 = 2000x. Solving for x, x = (15 * 200) / 2000 = 1.5. Therefore, the correct answer is A, 1.5, which represents the missing value in the proportion. The ratio 15:2000 can be simplified to 3:400 by dividing both numbers by 5, making the proportion easier to work with. By setting up the proportion correctly and solving for x, we obtain the missing value as 1.5, which completes the proportion 15:2000::1.5:200.

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Ratio and Proportion: 240 : X :: 80 : 0.8 (Enter a numeric value only.)

  • A. 2.4
  • B. 3.2
  • C. 4
  • D. 1.6
Correct Answer: A

Rationale: To solve for X, set up the proportion: 240/X = 80/0.8. Cross-multiply to get 240 * 0.8 = 80 * X, which simplifies to 192 = 80X. Dividing both sides by 80 gives X = 192/80 = 2.4. Therefore, the correct answer is A) 2.4.

1.2:x::14:42 =

  • A. 0.6
  • B. 3.6
  • C. 1.2
  • D. 2.4
Correct Answer: B

Rationale: To solve this proportion, we use the property that the product of the means is equal to the product of the extremes. In this case, we have 1.2 * 42 = 14 * x. Simplifying, we get 50.4 = 14x. To find the value of x, we divide both sides by 14, giving x = 50.4 / 14 = 3.6. Therefore, the correct answer is 3.6, which corresponds to option B. This means that the relationship between 1.2 and x is the same as the relationship between 14 and 42, following a proportional logic where the ratios are equivalent.

2.5:150 :: 20:x = ?

  • A. X = 3000
  • B. X = 1000
  • C. X = 1500
  • D. X = 1200
Correct Answer: D

Rationale: The analogy in the question presents the relationship between 2.5 and 150 as 2.5 multiplied by 60 equals 150. To find the value of x, we should determine what number, when multiplied by 20, equals x. Following the same pattern as the initial analogy, 20 multiplied by 60 equals 1200. Hence, x = 1200, making choice D the correct answer.

Change the decimal to a percent: 0.64 =

  • A. 0.64%
  • B. 64%
  • C. 6.40%
  • D. 0.06%
Correct Answer: B

Rationale: To convert a decimal to a percent, you move the decimal point two places to the right and add a percentage sign. In this case, 0.64 becomes 64%. Therefore, the correct answer is B.

Which is the largest expression?

  • A. 0.195833
  • B. 1:20
  • C. 1:22
  • D. 1:02
Correct Answer: A

Rationale: Correct Answer: A: 0.195833

Rationale: To compare the expressions, convert them to decimal form. A: 0.195833, B: 1.20, C: 1.22, D: 1.02. A is the largest as it is closest to 1. B is 1.20, C is 1.22, and D is 1.02. A is larger than D by 0.175833, which is the greatest difference among the options, making A the largest expression.

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