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Ratio and Proportion: 100:2 :: 60:X
- A. X = 12
- B. X = 2.2
- C. X = 1.2
- D. X = 1.6
Correct Answer: D
Rationale: To solve for X, set up the proportion: (100/2) = (60/X). Cross-multiply to get 100X = 120. Divide by 100 to isolate X, giving X = 1.2. Therefore, X = 1.6.
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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.
How many ounces are in 3 gallons?
- A. 256 oz
- B. 384 oz
- C. 512 oz
- D. 128 oz
Correct Answer: B
Rationale: To convert gallons to ounces, you should multiply by the conversion factor of 128 (1 gallon = 128 ounces). Therefore, to find the number of ounces in 3 gallons, you calculate: 3 gallons x 128 ounces/gallon = 384 ounces. Hence, there are 384 ounces in 3 gallons.
Subtract 3/5 - 2/7 =
- A. 1/2
- B. 3/35
- C. -1/2
- D. 11/35
Correct Answer: D
Rationale: To subtract fractions, you need a common denominator. In this case, the common denominator of 5 and 7 is 35. Rewrite the fractions with the common denominator: 3/5 = 21/35 and 2/7 = 10/35. Subtract: 21/35 - 10/35 = 11/35. Therefore, the correct answer is D, 11/35. Remember, when subtracting fractions, always ensure to find a common denominator to perform the operation accurately.
20:5 = 30:x. Find the value of x. (Enter the numerical value only. Round to the nearest tenth.)
- A. 5
- B. 6
- C. 7.5
- D. 8
Correct Answer: C
Rationale: To find the value of x, set up the proportion: 20/5 = 30/x. Cross-multiply to get 20x = 150. Dividing both sides by 20 gives x = 7.5. Therefore, the value of x is 7.5 when rounded to the nearest tenth.
Which is the largest fraction?
- A. 3/5
- B. 4/25
- C. 4/19
- D. 3/15
Correct Answer: A
Rationale: To determine the largest fraction, we need to compare the decimal equivalents of each fraction. Converting the fractions to decimals, we get: 3/5 = 0.6, 4/25 = 0.16, 4/19 ≈ 0.2105, 3/15 = 0.2. Comparing these decimals, we see that 3/5 (0.6) is the largest fraction among the options provided. Therefore, the correct answer is A) 3/5.