If 22,1/3% of a number n is 938, then n must be?
- A. 281,400
- B. 42,000
- C. 4,960
- D. 4,200
Correct Answer & Rationale
Correct Answer: D
To find the number \( n \), we start by converting \( 22 \frac{1}{3} \% \) to a decimal. This percentage equals \( \frac{67}{3} \% \), or \( \frac{67}{300} \) in decimal form. Setting up the equation \( \frac{67}{300} n = 938 \) allows us to solve for \( n \). Multiplying both sides by \( \frac{300}{67} \) gives \( n = 938 \times \frac{300}{67} = 4,200 \). Option A (281,400) is too high, as it would imply a much larger percentage. Option B (42,000) miscalculates the percentage relation. Option C (4,960) is incorrect, as it does not satisfy the equation derived from the percentage calculation.
To find the number \( n \), we start by converting \( 22 \frac{1}{3} \% \) to a decimal. This percentage equals \( \frac{67}{3} \% \), or \( \frac{67}{300} \) in decimal form. Setting up the equation \( \frac{67}{300} n = 938 \) allows us to solve for \( n \). Multiplying both sides by \( \frac{300}{67} \) gives \( n = 938 \times \frac{300}{67} = 4,200 \). Option A (281,400) is too high, as it would imply a much larger percentage. Option B (42,000) miscalculates the percentage relation. Option C (4,960) is incorrect, as it does not satisfy the equation derived from the percentage calculation.
Other Related Questions
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 \( 0.32n = 20.8 \). By dividing both sides by 0.32, we calculate \( n = \frac{20.8}{0.32} \), which simplifies to 65. Option A (64) is incorrect; it underestimates \( n \) by miscalculating the percentage. Option C (66) slightly overestimates \( n \), failing to accurately reflect the relationship between the percentage and the total. Option D (154) is far too high, indicating a misunderstanding of the percentage calculation. Thus, 65 is the only value that satisfies the equation.
To find \( n \), we start with the equation \( 0.32n = 20.8 \). By dividing both sides by 0.32, we calculate \( n = \frac{20.8}{0.32} \), which simplifies to 65. Option A (64) is incorrect; it underestimates \( n \) by miscalculating the percentage. Option C (66) slightly overestimates \( n \), failing to accurately reflect the relationship between the percentage and the total. Option D (154) is far too high, indicating a misunderstanding of the percentage calculation. Thus, 65 is the only value that satisfies the equation.
Which of the following is equivalent to 1.04?
- A. 52/51
- B. 51/50
- C. 27/25
- D. 26/25
Correct Answer & Rationale
Correct Answer: D
To determine the equivalence to 1.04, we can convert each fraction to a decimal. Option A, 52/51, equals approximately 1.0196, which is less than 1.04. Option B, 51/50, equals 1.02, also less than 1.04. Option C, 27/25, equals 1.08, exceeding 1.04. Option D, 26/25, simplifies to 1.04, matching the target value exactly. Thus, only option D accurately represents 1.04, while the others deviate from this value.
To determine the equivalence to 1.04, we can convert each fraction to a decimal. Option A, 52/51, equals approximately 1.0196, which is less than 1.04. Option B, 51/50, equals 1.02, also less than 1.04. Option C, 27/25, equals 1.08, exceeding 1.04. Option D, 26/25, simplifies to 1.04, matching the target value exactly. Thus, only option D accurately represents 1.04, while the others deviate from this value.
Which of the following is equivalent to 8,1/4?
- A. 0.0825
- B. 0.825
- C. 8.25
- D. 82.5
Correct Answer & Rationale
Correct Answer: c
To convert the mixed number 8 1/4 into an improper fraction, first multiply the whole number (8) by the denominator (4), resulting in 32. Then, add the numerator (1) to get 33, making the improper fraction 33/4. When you divide 33 by 4, you get 8.25. Option A (0.0825) is incorrect as it represents a much smaller value. Option B (0.825) is also incorrect, as it is less than 1. Option D (82.5) is incorrect, being ten times larger than the correct value. Thus, 8.25 accurately reflects the original mixed number.
To convert the mixed number 8 1/4 into an improper fraction, first multiply the whole number (8) by the denominator (4), resulting in 32. Then, add the numerator (1) to get 33, making the improper fraction 33/4. When you divide 33 by 4, you get 8.25. Option A (0.0825) is incorrect as it represents a much smaller value. Option B (0.825) is also incorrect, as it is less than 1. Option D (82.5) is incorrect, being ten times larger than the correct value. Thus, 8.25 accurately reflects the original mixed number.
76 ÷ 0.01 =
- A. 0.76
- B. 7.6
- C. 760
- D. 7,600
Correct Answer & Rationale
Correct Answer: D
To solve 76 ÷ 0.01, it is helpful to recognize that dividing by a decimal is equivalent to multiplying by its reciprocal. The reciprocal of 0.01 is 100, so this operation can be rewritten as 76 × 100, which equals 7,600. Option A (0.76) incorrectly suggests a much smaller result, as it misinterprets the division. Option B (7.6) also underestimates the value, failing to account for the decimal's effect. Option C (760) is closer but still incorrect, as it does not fully account for the multiplication by 100. Therefore, D (7,600) accurately reflects the operation's outcome.
To solve 76 ÷ 0.01, it is helpful to recognize that dividing by a decimal is equivalent to multiplying by its reciprocal. The reciprocal of 0.01 is 100, so this operation can be rewritten as 76 × 100, which equals 7,600. Option A (0.76) incorrectly suggests a much smaller result, as it misinterprets the division. Option B (7.6) also underestimates the value, failing to account for the decimal's effect. Option C (760) is closer but still incorrect, as it does not fully account for the multiplication by 100. Therefore, D (7,600) accurately reflects the operation's outcome.