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How many cakes are needed to provide 24 servings for a class of 70 students and 3 staff members?
- A. 4
- B. 2
- C. 3
- D. 5
Correct Answer: A
Rationale: To calculate the total number of servings needed, we add the number of students and staff members: 70 students + 3 staff members = 73 individuals. Next, we divide the total servings required by the servings per cake: 73 · 24 = 3 with a remainder of 1. Since each cake provides 24 servings, we need 4 cakes to accommodate 73 servings, ensuring there are enough servings for everyone in the class.
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Add 7/8 + 9/10 + 6/5 as mixed numbers.
- A. 3 & 39/40
- B. 22/23
- C. 2 & 39/40
- D. 3 & 22/23
Correct Answer: C
Rationale: To add fractions, it is essential to have a common denominator. The least common multiple of 8, 10, and 5 is 40. Converting each fraction to have a denominator of 40, we get 7/8 as 35/40, 9/10 as 36/40, and 6/5 as 48/40. Adding the numerators gives 35 + 36 + 48 = 119. This is equivalent to 2 wholes (40/40) and a remainder of 39/40. Therefore, the sum is 2 & 39/40.
Add: 5/8 + 1/2 =
- A. 9\8
- B. 7\8
- C. 11\8
- D. 3\4
Correct Answer: C
Rationale: To add fractions, we need a common denominator. In this case, the common denominator for 8 and 2 is 8. So, 5/8 + 1/2 becomes 5/8 + 4/8 = 9/8. Therefore, the correct answer is C: 11/8. Choice A is incorrect because it does not account for the common denominator. Choice B is incorrect as it adds the numerators incorrectly. Choice D is incorrect as it simplifies the fractions incorrectly.
Ratio and Proportion: 0.5:20 :: X:200
- A. X = 50
- B. X = 4
- C. X = 5
- D. X = 25
Correct Answer: A
Rationale: To solve this proportion problem, you need to set up the ratio 0.5/20 equal to X/200. Cross-multiply to solve for X, which gives you 0.5 — 200 = 20X. Simplifying this, you get 100 = 20X, and then by dividing both sides by 20, you find that X = 5. Therefore, the correct answer is A, X = 50.
How many meters are in 3 kilometers? (Enter a numeric value only.)
- A. 300
- B. 3000
- C. 30
- D. 3
Correct Answer: B
Rationale: To convert kilometers to meters, remember that 1 kilometer is equivalent to 1,000 meters. Therefore, to determine how many meters are in 3 kilometers, you multiply 3 (kilometers) by 1,000 (meters), resulting in 3,000 meters. The correct answer is 3,000 meters, which corresponds to option B.
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%.