Choose the best answer. If necessary, use the paper you were given.
If 40 is 20 percent of a number, then the number is what percent of 40?
- A. 500%
- B. 200%
- C. 80%
- D. 20%
Correct Answer & Rationale
Correct Answer: A
To determine what percent a number (let's call it X) is of 40, we first establish that 40 is 20% of X. This can be represented as the equation: 40 = 0.2X. Solving for X gives us X = 200. Now, to find out what percent 200 is of 40, we use the formula (part/whole) × 100, which results in (200/40) × 100 = 500%. Option B (200%) is incorrect as it mistakenly uses X instead of calculating the percentage of 40. Option C (80%) and Option D (20%) are also incorrect for similar reasons; they do not accurately reflect the relationship between 200 and 40.
To determine what percent a number (let's call it X) is of 40, we first establish that 40 is 20% of X. This can be represented as the equation: 40 = 0.2X. Solving for X gives us X = 200. Now, to find out what percent 200 is of 40, we use the formula (part/whole) × 100, which results in (200/40) × 100 = 500%. Option B (200%) is incorrect as it mistakenly uses X instead of calculating the percentage of 40. Option C (80%) and Option D (20%) are also incorrect for similar reasons; they do not accurately reflect the relationship between 200 and 40.
Other Related Questions
The number p is obtained by moving the decimal point 2 places to the left in the positive number n. The number s is obtained by moving the decimal point 1 place to the right in the number n. The number p + s how many times n?
- A. 1.01
- B. 10.001
- C. 10.01
- D. 10.1
Correct Answer & Rationale
Correct Answer: C
When the decimal point in \( n \) is moved 2 places to the left, \( p \) becomes \( \frac{n}{100} \). Moving the decimal point 1 place to the right gives \( s \) as \( 10n \). Therefore, \( p + s = \frac{n}{100} + 10n \). To combine these, convert \( 10n \) to a fraction: \( 10n = \frac{1000n}{100} \). Thus, \( p + s = \frac{n}{100} + \frac{1000n}{100} = \frac{1001n}{100} \). This simplifies to \( 10.01n \). Option A (1.01) is too low, as it does not account for the large contribution from \( s \). Option B (10.001) and D (10.1) are also incorrect; they either underestimate or overestimate the sum of \( p \) and \( s \). Thus, the correct answer, \( 10.01 \), accurately reflects the relationship between \( p + s \) and \( n \).
When the decimal point in \( n \) is moved 2 places to the left, \( p \) becomes \( \frac{n}{100} \). Moving the decimal point 1 place to the right gives \( s \) as \( 10n \). Therefore, \( p + s = \frac{n}{100} + 10n \). To combine these, convert \( 10n \) to a fraction: \( 10n = \frac{1000n}{100} \). Thus, \( p + s = \frac{n}{100} + \frac{1000n}{100} = \frac{1001n}{100} \). This simplifies to \( 10.01n \). Option A (1.01) is too low, as it does not account for the large contribution from \( s \). Option B (10.001) and D (10.1) are also incorrect; they either underestimate or overestimate the sum of \( p \) and \( s \). Thus, the correct answer, \( 10.01 \), accurately reflects the relationship between \( p + s \) and \( n \).
Charlotte is drilling three holes of different sizes in a bird house that she is making. The diameters of the holes are 1(1/2) inches, 1(3/4) inches, and 1(3/8) inches. Which of the following gives the diameters, in inches, in order from least to greatest?
- A. 1(1/2), 1(3/4), 1(3/8)
- B. 1(1/2), 1(3/8), 1(3/4)
- C. 1(3/8), 1(3/4), 1(1/2)
- D. 1(3/8), 1(1/2), 1(3/4)
Correct Answer & Rationale
Correct Answer: D
To determine the correct order of the hole diameters from least to greatest, we first convert the mixed numbers to improper fractions for easier comparison. - 1(1/2) = 3/2 - 1(3/4) = 7/4 - 1(3/8) = 11/8 By comparing these values, we find that 11/8 (1(3/8)) is the smallest, followed by 3/2 (1(1/2)), and finally 7/4 (1(3/4)). Option A incorrectly lists 1(1/2) as the smallest. Option B misplaces 1(3/8) and 1(3/4). Option C arranges the sizes incorrectly, placing the largest first. Therefore, the correct order is D: 1(3/8), 1(1/2), 1(3/4).
To determine the correct order of the hole diameters from least to greatest, we first convert the mixed numbers to improper fractions for easier comparison. - 1(1/2) = 3/2 - 1(3/4) = 7/4 - 1(3/8) = 11/8 By comparing these values, we find that 11/8 (1(3/8)) is the smallest, followed by 3/2 (1(1/2)), and finally 7/4 (1(3/4)). Option A incorrectly lists 1(1/2) as the smallest. Option B misplaces 1(3/8) and 1(3/4). Option C arranges the sizes incorrectly, placing the largest first. Therefore, the correct order is D: 1(3/8), 1(1/2), 1(3/4).
If 32% of n is 20.8, what is n?
- A. 64
- B. 65
- C. 66
- D. 154
Correct Answer & Rationale
Correct Answer: B
To find n, we start with the equation derived from the problem: \(0.32n = 20.8\). Dividing both sides by 0.32 gives \(n = \frac{20.8}{0.32}\), which simplifies to 65. This confirms that option B is accurate. Option A (64) results from an incorrect calculation of \(0.32n\). Option C (66) overestimates n, suggesting a misunderstanding of the percentage relationship. Option D (154) is far too high, indicating a significant miscalculation. Thus, only option B aligns correctly with the mathematical solution.
To find n, we start with the equation derived from the problem: \(0.32n = 20.8\). Dividing both sides by 0.32 gives \(n = \frac{20.8}{0.32}\), which simplifies to 65. This confirms that option B is accurate. Option A (64) results from an incorrect calculation of \(0.32n\). Option C (66) overestimates n, suggesting a misunderstanding of the percentage relationship. Option D (154) is far too high, indicating a significant miscalculation. Thus, only option B aligns correctly with the mathematical solution.
Of the following, which best expresses 52 as a percent of 170?
- A. 30% of 170
- B. 33% of 170
- C. 35% of 170
- D. 40% of 170
Correct Answer & Rationale
Correct Answer: A
To determine what percent 52 is of 170, divide 52 by 170 and multiply by 100. This calculation yields approximately 30.59%, which rounds to 30%. Option A (30% of 170) is correct, as it closely matches this percentage. Option B (33% of 170) results in 56.1, which is higher than 52. Option C (35% of 170) equals 59.5, also above 52. Option D (40% of 170) gives 68, significantly exceeding 52. Thus, only option A accurately reflects 52 as a percent of 170.
To determine what percent 52 is of 170, divide 52 by 170 and multiply by 100. This calculation yields approximately 30.59%, which rounds to 30%. Option A (30% of 170) is correct, as it closely matches this percentage. Option B (33% of 170) results in 56.1, which is higher than 52. Option C (35% of 170) equals 59.5, also above 52. Option D (40% of 170) gives 68, significantly exceeding 52. Thus, only option A accurately reflects 52 as a percent of 170.