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If a recipe requires 3 eggs for every pound of cake, how many pounds of cake can be made with 40 eggs?
- A. 12 pounds
- B. 14 pounds
- C. 13 pounds
- D. 15 pounds
Correct Answer: C
Rationale: To determine the pounds of cake that can be made with 40 eggs, divide the total number of eggs by the eggs needed per pound of cake: 40 eggs · 3 eggs/pound = 13 pounds of cake. Therefore, the correct answer is 13 pounds. Choice A, 12 pounds, is incorrect because it does not consider the ratio of eggs to cake. Choice B, 14 pounds, and Choice D, 15 pounds, are incorrect as they do not reflect the correct calculation based on the given ratio in the question.
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A farmer wants to plant trees around the outside boundaries of his rectangular field with dimensions of 650 meters 780 meters. Each tree requires 5 meters of free space all around it from the stem. How many trees can he plant?
- A. 572
- B. 568
- C. 286
- D. 282
Correct Answer: C
Rationale: To determine the number of trees, reduce the field dimensions by 10 meters (5 meters of space on each side). The effective area is 640 meters 770 meters. Each tree occupies 10 meters 10 meters. Dividing the effective area by the space for each tree gives: (640 770) · (10 10) = 286 trees. Choice A, B, and D are incorrect because they do not consider the reduction in field dimensions and the space required for each tree.
What is 28% of 100?
- A. 28
- B. 20
- C. 25
- D. 30
Correct Answer: A
Rationale: The correct answer is A: 28. To find 28% of 100, you multiply 0.28 (the decimal equivalent of 28%) by 100. This calculation results in 28. Therefore, 28% of 100 is 28. Choice B, 20, is incorrect as it represents 20% of 100. Choice C, 25, is incorrect as it represents 25% of 100. Choice D, 30, is incorrect as it represents 30% of 100.
What percentage of her income is left after Mary spent 15%?
- A. 12%
- B. 85%
- C. 75%
- D. 95%
Correct Answer: B
Rationale: To determine the percentage of income remaining after spending 15%, subtract the percentage spent from 100% (100% - 15% = 85%). Therefore, Mary has 85% of her income left, which aligns with answer choice B. Choice A (12%) is incorrect because it represents the remaining amount after spending 88% of her income. Choice C (75%) is incorrect as it does not account for the 15% already spent. Choice D (95%) is incorrect as it does not consider the amount spent by Mary.
What number is represented by the Roman Numerals XLIV?
- A. 34
- B. 54
- C. 44
- D. 24
Correct Answer: C
Rationale: In Roman numerals, XL represents 40, and IV represents 4. When XL (40) is combined with IV (4), it forms XLIV, which corresponds to the number 44. Therefore, the correct answer is 44. Choice A (34) is incorrect as it does not consider the value of XL and IV. Choice B (54) is incorrect as it miscalculates the value of XL. Choice D (24) is incorrect as it does not account for the value of XL.
If y = 4 and x = 3, solve y x³
- A. -108
- B. 108
- C. 27
- D. 4
Correct Answer: B
Rationale: With y = 4 and x = 3, the expression is y x³. Substituting the values, we get 4 3³ = 4 27 = 108. Therefore, the correct answer is 108. Option A (-108) is incorrect because the negative sign is not part of the result. Option C (27) is incorrect as it only represents x³ without considering the value of y. Option D (4) is incorrect as it represents the initial value of y, not the result of y x³.