HESI Mathematics

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Ratio and Proportion: 100:2 :: 60:X. Find X.

  • A. 1.2
  • B. 2
  • C. 3
  • D. 30
Correct Answer: A

Rationale: To find the value of X when the ratio 100:2 is equivalent to 60:X, set up the proportion: 100/2 = 60/X. Cross-multiply to get 100X = 120. Divide by 100 to isolate X, so X = 120/100 = 1.2. Therefore, X equals 1.2, and the correct answer is A. In this scenario, the correct answer is calculated through cross-multiplication of the given ratio and solving for the unknown value. This method is commonly used to solve ratio and proportion problems. It is essential to understand the concept of ratios and proportions to solve mathematical problems efficiently.

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What is the result of adding 4/3 + 7/3?

  • A. 3 2/3
  • B. 1 5/6
  • C. 2 1/3
  • D. 1 1/6
Correct Answer: A

Rationale: To add the fractions 4/3 and 7/3, combine the numerators: (4 + 7)/3 = 11/3. The sum 11/3 can be expressed as the mixed number 3 2/3. Therefore, the correct answer is A) 3 2/3.

Convert 0.75 to a ratio in simplest form.

  • A. 5:07
  • B. 3:04
  • C. 7:05
  • D. 0.09375
Correct Answer: B

Rationale: To convert 0.75 to a ratio in simplest form, we first need to express 0.75 as a fraction, which is 75/100 or 3/4. The ratio form of 3/4 is 3:4. Therefore, the correct answer is B. Choice A (5:07) is incorrect as it doesn't represent the correct ratio. Choice C (7:05) is also incorrect because it doesn't match the simplified form of 0.75. Choice D (0.09375) is incorrect as it is not in ratio form and does not represent the given decimal value correctly.

What is the numerical value of the Roman numeral XVII?

  • A. 22
  • B. 17
  • C. 48
  • D. 57
Correct Answer: B

Rationale: The Roman numeral XVII represents the number 17. In Roman numerals, 'X' stands for 10, 'V' stands for 5, and 'I' stands for 1. When 'V' is placed before 'X' (V - X), it subtracts 5 from 10, resulting in 10 - 5 = 5. Adding this to the value of 'X,' which is 10, gives a total of 10 + 5 = 15. Finally, adding 'II,' which is equivalent to 2, results in a total of 15 + 2 = 17.

In the ratio 0.6 : X :: 7 : 42, what is X?

  • A. 3
  • B. 3.6
  • C. 4
  • D. 4.2
Correct Answer: B

Rationale: To find the value of X in the given ratio, set up the proportion: (0.6/X) = (7/42). Simplifying this, we get (0.6/X) = (1/6). Cross multiplying gives 0.6 * 6 = X, which results in X = 3.6. Therefore, the correct answer is 3.6, representing the value of X in the given ratio.

Solve for x: 3:2 :: 24:x

  • A. 16
  • B. 12
  • C. 2
  • D. 22
Correct Answer: A

Rationale: To solve this proportion, we use the property that in a proportion, the product of the means is equal to the product of the extremes. So, 3 * x = 2 * 24. By solving for x, we find x = 16. Therefore, the correct answer is A. In this analogy, the relationship between the first pair of numbers (3 and 2) must hold true for the second pair of numbers (24 and x). By setting up the proportion, we can find the missing value x. This type of problem is common in mathematics and helps test your understanding of proportional relationships.

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