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What is the sum of 6 3/4 and 8 1/6?
- A. 14 & 11/12
- B. 12 & 3/24
- C. 35/6
- D. 14 & 2/5
Correct Answer: A
Rationale: To add mixed numbers, convert them to improper fractions. 6 3/4 = 27/4, and 8 1/6 = 49/6. Add the fractions: 27/4 + 49/6 = 162/24 + 98/24 = 260/24. Simplify to 10 & 22/24, then to 11 & 10/12 or 11 & 5/6. Therefore, the correct sum is 14 & 11/12.
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Ratio and Proportion: 3:5 :: X:10
- A. X = 10
- B. X = 6
- C. X = 3
- D. X = 8
Correct Answer: B
Rationale: To solve the proportion, set up (3/5) = (X/10). Cross-multiply to get 3 — 10 = 5X, leading to X = 6. This means that the correct choice is B, as X is equal to 6 to maintain the same ratio as 3:5 in the original proportion.
Multiply and reduce to lowest term: (2 x 5/8)
- A. 3\4
- B. 10\8
- C. 5\8
- D. 1 1/4
Correct Answer: D
Rationale: To multiply (2 x 5/8), first multiply the whole number 2 by the numerator 5 to get 10. Then, multiply the result by the denominator 8 to get 10/8. Simplify 10/8 to 1 1/4 by dividing the numerator by the denominator, resulting in 1 whole and 1/4 left over. Therefore, the correct answer is D.
Choice A (3/4) is incorrect because the multiplication result is not 3/4. Choice B (10/8) is incorrect as it represents the result before reducing to lowest terms. Choice C (5/8) is incorrect as it only represents the initial fraction being multiplied, not the final result after multiplication and simplification.
If a person reads two chapters a day, each with 6 pages, and there are a total of 798 pages, how many days will it take to finish reading?
- A. 133 days
- B. 399 days
- C. 66 1/2 days
- D. 75 1/2 days
Correct Answer: C
Rationale: To determine the number of days required to finish reading the book, divide the total number of pages (798) by the number of pages read per day, which is 2 chapters x 6 pages = 12 pages per day. Therefore, 798 pages · 12 pages per day = 66.5 days. It will take approximately 66 1/2 days to complete reading the book at this pace.
How many grams are in 4 kilograms? (Enter numeric value only.)
- A. 400
- B. 4000
- C. 40
- D. 4
Correct Answer: B
Rationale: To convert kilograms to grams, you need to know that there are 1,000 grams in 1 kilogram. Therefore, to find out how many grams are in 4 kilograms, you multiply 4 (kilograms) by 1,000 (grams/kilogram), which equals 4,000 grams. Thus, the correct answer is 4000 grams, as there are 4,000 grams in 4 kilograms.
How many cakes are needed to serve a group of 70 students and 3 staff members if each cake provides 24 servings?
- A. 4
- B. 2
- C. 3
- D. 5
Correct Answer: A
Rationale: To determine the number of cakes needed, add the total number of individuals to be served: 70 students + 3 staff members = 73 individuals. Then, divide the total number of individuals by the number of servings per cake: 73 · 24 = 3 with a remainder. Since you cannot serve a fraction of a cake, you will need an additional cake. Therefore, you would need 4 cakes to serve the group of 70 students and 3 staff members, ensuring each person receives a serving.