Choose the best answer. If necessary, use the paper you were given.
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.
Other Related Questions
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.
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).
3(1/2) * 2(1/3) =
- A. 8(1/6)
- B. 7(5/6)
- C. 6(1/6)
- D. 5(5/6)
Correct Answer & Rationale
Correct Answer: A
To solve 3(1/2) * 2(1/3), first convert the mixed numbers to improper fractions: 3(1/2) becomes 7/2 and 2(1/3) becomes 7/3. Multiplying these fractions yields (7/2) * (7/3) = 49/6. Converting 49/6 back to a mixed number gives 8(1/6). Option B, 7(5/6), results from incorrect multiplication. Option C, 6(1/6), miscalculates the product as well. Option D, 5(5/6), reflects a misunderstanding of fraction multiplication. The proper method confirms that 8(1/6) is indeed the accurate result.
To solve 3(1/2) * 2(1/3), first convert the mixed numbers to improper fractions: 3(1/2) becomes 7/2 and 2(1/3) becomes 7/3. Multiplying these fractions yields (7/2) * (7/3) = 49/6. Converting 49/6 back to a mixed number gives 8(1/6). Option B, 7(5/6), results from incorrect multiplication. Option C, 6(1/6), miscalculates the product as well. Option D, 5(5/6), reflects a misunderstanding of fraction multiplication. The proper method confirms that 8(1/6) is indeed the accurate result.
Maria worked 2 weeks, earning $435.50 the first week and $278.38 the second week. If she paid one-half of her two-week earnings for tuition, how much did she pay for tuition?
- A. $713.88
- B. $356.94
- C. $217.75
- D. $139.19
Correct Answer & Rationale
Correct Answer: B
To find the amount Maria paid for tuition, first calculate her total earnings for the two weeks. Adding her earnings from both weeks: $435.50 + $278.38 = $713.88. Since she paid one-half of her total earnings for tuition, divide this amount by 2: $713.88 / 2 = $356.94. Option A ($713.88) represents her total earnings, not the tuition amount. Option C ($217.75) and Option D ($139.19) do not correctly reflect half of her total earnings. Therefore, $356.94 accurately represents the amount she paid for tuition.
To find the amount Maria paid for tuition, first calculate her total earnings for the two weeks. Adding her earnings from both weeks: $435.50 + $278.38 = $713.88. Since she paid one-half of her total earnings for tuition, divide this amount by 2: $713.88 / 2 = $356.94. Option A ($713.88) represents her total earnings, not the tuition amount. Option C ($217.75) and Option D ($139.19) do not correctly reflect half of her total earnings. Therefore, $356.94 accurately represents the amount she paid for tuition.