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Ratio and proportion: 0.8:10 :: x:100
- A. x = 0.8
- B. x = 80
- C. x = 800
- D. x = 8
Correct Answer: D
Rationale: To solve this proportion problem, start by setting up the given ratio 0.8:10 as a fraction, which is 0.8/10. Then, set this fraction equal to the unknown ratio x:100, represented as x/100. Cross multiplying gives us 0.8 * 100 = 10x. Simplifying the equation, we get 80 = 10x. Solving for x, x = 80/10 = 8. Therefore, the correct answer is D, as x equals 8, not 0.8, 80, or 800.
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Seven girls each have seven cats. How many legs are there in the group?
- A. 210
- B. 63
- C. 186
- D. 49
Correct Answer: A
Rationale: To find the total number of legs, we multiply the number of girls by the number of legs each girl and cat has. 7 girls x (2 legs per girl + 4 legs per cat) x 7 cats = 7 x (2+4) x 7 = 7 x 6 x 7 = 210 legs.
Choice A is correct because it correctly calculates the total number of legs.
Choice B is incorrect as it only considers the girls' legs.
Choice C is incorrect as it does not account for the cats' legs.
Choice D is incorrect as it only considers the number of cats.
A woman received a bottle of perfume as a present. The bottle contains 3/4 oz of perfume. How many milliliters is this?
- A. 20.0 ml
- B. 23.0 ml
- C. 22.5 ml
- D. 22.0 ml
Correct Answer: C
Rationale: To convert ounces to milliliters, we know that 1 fluid ounce (oz) is approximately equal to 29.5735 milliliters (ml). Therefore, 3/4 oz of perfume is equal to (3/4) x 29.5735 ml. Calculating this gives us approximately 22.18 ml, which can be rounded to 22.5 ml. Hence, the correct answer is 22.5 ml. This conversion is essential in various fields, especially in industries where precise measurements are required, such as pharmaceuticals, chemistry, and cooking.
What is the result of dividing 32 by 8/9?
- A. 36
- B. 4&1/9
- C. 28&4/9
- D. 4
Correct Answer: A
Rationale: To divide by a fraction, you multiply by its reciprocal. In this case, dividing 32 by 8/9 is the same as multiplying 32 by 9/8 (reciprocal of 8/9). Calculate 32 * 9/8 to get 36, which is the correct result. Therefore, the correct answer is A: 36. So, the correct answer is 36.
Ratio and proportion 0.1:10::x:400 =
- A. 25
- B. 5
- C. 50
- D. 4
Correct Answer: D
Rationale: To solve this proportion, we can set it up as 0.1/10 = x/400. Cross multiply to get x = (0.1 * 400)/10 = 4. Therefore, x equals 4, making choice D the correct answer. When solving proportions, it's crucial to maintain the same relationship between the numbers on both sides of the proportion. In this case, the ratio of 0.1 to 10 should be equal to the ratio of x to 400. By cross multiplying and simplifying, we find that x is 4, confirming choice D as the correct answer.
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.