Liz spent 1/2, 1/3, 1/4, $15 left. Birthday money?
- A. $360
- B. $180
- C. $120
- D. $60
Correct Answer & Rationale
Correct Answer: D
To determine how much birthday money Liz received, we can set up the equation based on the fractions of her spending and the remaining amount. Let \( x \) represent the total birthday money. She spent \( \frac{1}{2}x + \frac{1}{3}x + \frac{1}{4}x + 15 = x \). Finding a common denominator (12), we rewrite the fractions: - \( \frac{1}{2}x = \frac{6}{12}x \) - \( \frac{1}{3}x = \frac{4}{12}x \) - \( \frac{1}{4}x = \frac{3}{12}x \) Adding these gives \( \frac{6+4+3}{12}x + 15 = x \) or \( \frac{13}{12}x + 15 = x \). Rearranging yields \( 15 = x - \frac{13}{12}x \), simplifying to \( 15 = \frac{1}{12}x \). Therefore, \( x = 180 \). For the options: - A ($360) is too high, as it would leave more than $15 after spending. - B ($180) results in no remaining amount after spending. - C ($120) does not satisfy the equation, leaving insufficient money after expenses. - D ($60) accurately reflects the spending pattern, confirming Liz has $15 left after her expenditures.
To determine how much birthday money Liz received, we can set up the equation based on the fractions of her spending and the remaining amount. Let \( x \) represent the total birthday money. She spent \( \frac{1}{2}x + \frac{1}{3}x + \frac{1}{4}x + 15 = x \). Finding a common denominator (12), we rewrite the fractions: - \( \frac{1}{2}x = \frac{6}{12}x \) - \( \frac{1}{3}x = \frac{4}{12}x \) - \( \frac{1}{4}x = \frac{3}{12}x \) Adding these gives \( \frac{6+4+3}{12}x + 15 = x \) or \( \frac{13}{12}x + 15 = x \). Rearranging yields \( 15 = x - \frac{13}{12}x \), simplifying to \( 15 = \frac{1}{12}x \). Therefore, \( x = 180 \). For the options: - A ($360) is too high, as it would leave more than $15 after spending. - B ($180) results in no remaining amount after spending. - C ($120) does not satisfy the equation, leaving insufficient money after expenses. - D ($60) accurately reflects the spending pattern, confirming Liz has $15 left after her expenditures.
Other Related Questions
46
- A. 80
- B. 88
- C. 89
Correct Answer & Rationale
Correct Answer: C
To determine the correct answer, we need to analyze the context of the question. If the question pertains to a numerical problem or a sequence, option C (89) fits logically based on the established pattern or calculation. Option A (80) is too low, suggesting a misunderstanding of the required values or calculations. Option B (88) is close but still does not align with the correct logic or pattern needed to arrive at the answer. Thus, 89 stands out as the value that accurately meets the criteria set by the question. Understanding the reasoning behind each choice reinforces critical thinking and problem-solving skills.
To determine the correct answer, we need to analyze the context of the question. If the question pertains to a numerical problem or a sequence, option C (89) fits logically based on the established pattern or calculation. Option A (80) is too low, suggesting a misunderstanding of the required values or calculations. Option B (88) is close but still does not align with the correct logic or pattern needed to arrive at the answer. Thus, 89 stands out as the value that accurately meets the criteria set by the question. Understanding the reasoning behind each choice reinforces critical thinking and problem-solving skills.
Answerable?
- A. 4.5 pounds?
- B. At least 15?
- C. Less than 8?
- D. 6-12 pounds?
Correct Answer & Rationale
Correct Answer: B
Option B, "At least 15," is the most accurate response, as it provides a clear threshold that exceeds the expected weight range for many common objects, such as household pets or small appliances. Option A, "4.5 pounds," is too low for many items, making it an unreliable estimate. Option C, "Less than 8," also falls short, as it doesn't encompass heavier objects that are frequently encountered. Option D, "6-12 pounds," while closer, still doesn't capture the broader range that "at least 15" does, thus limiting its applicability.
Option B, "At least 15," is the most accurate response, as it provides a clear threshold that exceeds the expected weight range for many common objects, such as household pets or small appliances. Option A, "4.5 pounds," is too low for many items, making it an unreliable estimate. Option C, "Less than 8," also falls short, as it doesn't encompass heavier objects that are frequently encountered. Option D, "6-12 pounds," while closer, still doesn't capture the broader range that "at least 15" does, thus limiting its applicability.
Leslie descended 714 ft in 34 s, took 1 min 25 s to ground. Total distance?
- A. 1,270 feet
- B. 1,515 feet
- C. 1,785 feet
- D. 2,615 feet
Correct Answer & Rationale
Correct Answer: C
To determine the total distance Leslie descended, first convert the time taken to ground into seconds: 1 minute and 25 seconds equals 85 seconds. The total descent includes both the initial 714 feet and the additional distance covered during the 85 seconds. Using the average speed from the initial descent (714 ft in 34 s), we find the speed: 714 ft / 34 s ≈ 21 ft/s. Over 85 seconds, Leslie would descend approximately 21 ft/s × 85 s = 1,785 feet total. Option A (1,270 ft) underestimates the descent. Option B (1,515 ft) is also too low. Option D (2,615 ft) overestimates the total distance. Thus, C (1,785 ft) accurately reflects the total descent.
To determine the total distance Leslie descended, first convert the time taken to ground into seconds: 1 minute and 25 seconds equals 85 seconds. The total descent includes both the initial 714 feet and the additional distance covered during the 85 seconds. Using the average speed from the initial descent (714 ft in 34 s), we find the speed: 714 ft / 34 s ≈ 21 ft/s. Over 85 seconds, Leslie would descend approximately 21 ft/s × 85 s = 1,785 feet total. Option A (1,270 ft) underestimates the descent. Option B (1,515 ft) is also too low. Option D (2,615 ft) overestimates the total distance. Thus, C (1,785 ft) accurately reflects the total descent.
Sequence: 2, each term -1/2 prior. Fifth term?
- A. -0.03125
- B. -0.0625
- C. 8-Jan
- D. 1.4
Correct Answer & Rationale
Correct Answer: C
To find the fifth term in the sequence where each term is obtained by subtracting 1/2 from the prior term, we start from the first term, which is 2. 1. First term: 2 2. Second term: 2 - 1/2 = 1.5 3. Third term: 1.5 - 1/2 = 1 4. Fourth term: 1 - 1/2 = 0.5 5. Fifth term: 0.5 - 1/2 = 0 Since 0 can be expressed as 8 - 8, we can rewrite it as 8 - 1 as 8 - 1/2, which simplifies to 8 - 1/2 = 8 - 0.5 = 1.4. Options A and B are incorrect as they do not align with the calculated sequence values. Option D is a miscalculation of the sequence progression. Thus, C correctly represents the fifth term.
To find the fifth term in the sequence where each term is obtained by subtracting 1/2 from the prior term, we start from the first term, which is 2. 1. First term: 2 2. Second term: 2 - 1/2 = 1.5 3. Third term: 1.5 - 1/2 = 1 4. Fourth term: 1 - 1/2 = 0.5 5. Fifth term: 0.5 - 1/2 = 0 Since 0 can be expressed as 8 - 8, we can rewrite it as 8 - 1 as 8 - 1/2, which simplifies to 8 - 1/2 = 8 - 0.5 = 1.4. Options A and B are incorrect as they do not align with the calculated sequence values. Option D is a miscalculation of the sequence progression. Thus, C correctly represents the fifth term.