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Ratio and Proportion: 3: X = 5: 800. What is X? (Enter numeric value only.)
- A. 43.64
- B. 50
- C. 48.5
- D. 60
Correct Answer: A
Rationale: To find the value of X in the given ratio, set up the proportion: (3/X) = (5/800). Cross-multiply to solve for X: 3 — 800 = 5X. This simplifies to 2400 = 5X. Dividing both sides by 5 gives X = 2400/5 = 480. Therefore, the correct answer is A) 43.64.
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A die is rolled. What is the probability of getting a 5?
- A. 50%
- B. 20%
- C. 16.60%
- D. 83.30%
Correct Answer: C
Rationale: The probability of rolling a specific number on a fair six-sided die is calculated by taking the total number of favorable outcomes (which is 1 in this case, as there is only one face with a 5) divided by the total possible outcomes (which is 6 for a standard die). Therefore, the probability of rolling a 5 is 1/6, which is approximately 16.6%. To convert the probability to a percentage, you multiply the fraction by 100, giving you 16.6%. Hence, the correct answer is C, 16.60%.
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.
A library contains 67,982 books. The children's section represents 1/3 of the total books. Of the remaining books, 75% are fiction. How many books are in the non-fiction section?
- A. 11,331
- B. 33,990
- C. 50,986
- D. 45,321
Correct Answer: A
Rationale: To find the number of books in the non-fiction section, start by calculating the number of books in the children's section: 67,982 * 1/3 = 22,661 books. Subtract the children's books from the total to determine the remaining books: 67,982 - 22,661 = 45,321 books. As 75% of the remaining books are fiction, calculate 75% of 45,321 = 33,990 (fiction books). To find the number of non-fiction books, subtract the fiction books from the remaining books: 45,321 - 33,990 = 11,331. Therefore, there are 11,331 non-fiction books in the library.
Compare the relationships of these numbers. ¼ is-------- than 2/24
- A. less than
- B. equal to
- C. greater than
Correct Answer: C
Rationale: To compare ¼ and 2/24, convert both fractions to have a common denominator. LCD is 24. ¼ = 6/24 and 2/24 = 2/24. 6/24 is greater than 2/24 since 6 is larger than 2. Therefore, the correct answer is C (greater than). Choice A (less than) and B (equal to) are incorrect as ¼ is larger than 2/24 when compared using the same denominator. Choice D is incomplete and doesn't provide any comparison.
Ratio and Proportion: 0.5 : 20 :: X : 200
- A. X = 50
- B. X = 5
- C. X = 25
- D. X = 4
Correct Answer: B
Rationale: To find the value of X in the proportion 0.5 : 20 :: X : 200, you can set up the equation as (0.5/20) = (X/200). Cross-multiply to solve for X: 0.5 — 200 = 20 — X. This simplifies to X = (0.5 — 200)/20 = 5. Therefore, the correct answer is B, X = 5.