Choose the best answer. If necessary, use the paper you were given.
At the factory where he works, Mr. Lopez must make a minimum of 48 circuit boards per day. On Wednesday, he made 60 circuit boards. What percent of the required minimum did he make?
- A. 125%
- B. 112%
- C. 80%
- D. 25%
Correct Answer & Rationale
Correct Answer: A
To find the percentage of the required minimum that Mr. Lopez made, divide the number of circuit boards he produced (60) by the minimum required (48) and then multiply by 100. \[ \text{Percentage} = \left(\frac{60}{48}\right) \times 100 = 125\% \] Option A is correct as it reflects that he made 125% of the minimum requirement. Option B (112%) is incorrect because it underestimates his production relative to the minimum. Option C (80%) is also wrong, as it suggests he produced only a fraction of the required amount. Option D (25%) is far too low, indicating a misunderstanding of the basic calculation.
To find the percentage of the required minimum that Mr. Lopez made, divide the number of circuit boards he produced (60) by the minimum required (48) and then multiply by 100. \[ \text{Percentage} = \left(\frac{60}{48}\right) \times 100 = 125\% \] Option A is correct as it reflects that he made 125% of the minimum requirement. Option B (112%) is incorrect because it underestimates his production relative to the minimum. Option C (80%) is also wrong, as it suggests he produced only a fraction of the required amount. Option D (25%) is far too low, indicating a misunderstanding of the basic calculation.
Other Related Questions
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.
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.
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 \( n \).
Of the following, which is greatest?
- A. -0.75
- B. 5/-2
- C. -3
- D. -2
Correct Answer & Rationale
Correct Answer: A
Option A, -0.75, is the greatest value among the choices since it is the least negative number. Option B, 5/-2, simplifies to -2.5, which is less than -0.75. Option C, -3, is clearly more negative than both -0.75 and -2. Option D, -2, is greater than -3 but still less than -0.75. In summary, -0.75 is the highest value among negative numbers, making it the greatest option in this comparison.
Option A, -0.75, is the greatest value among the choices since it is the least negative number. Option B, 5/-2, simplifies to -2.5, which is less than -0.75. Option C, -3, is clearly more negative than both -0.75 and -2. Option D, -2, is greater than -3 but still less than -0.75. In summary, -0.75 is the highest value among negative numbers, making it the greatest option in this comparison.