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.
Other Related Questions
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.
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.
2 + (2 × 2) + 2 =
- A. 8
- B. 10
- C. 12
- D. 16
Correct Answer & Rationale
Correct Answer: A
To solve the expression 2 + (2 × 2) + 2, it’s essential to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). First, calculate the value inside the parentheses: 2 × 2 equals 4. Next, substitute this back into the expression: 2 + 4 + 2. Then, perform the addition from left to right: 2 + 4 equals 6, and then 6 + 2 equals 8. Options B (10), C (12), and D (16) are incorrect because they do not adhere to the proper order of operations or miscalculate the addition steps.
To solve the expression 2 + (2 × 2) + 2, it’s essential to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). First, calculate the value inside the parentheses: 2 × 2 equals 4. Next, substitute this back into the expression: 2 + 4 + 2. Then, perform the addition from left to right: 2 + 4 equals 6, and then 6 + 2 equals 8. Options B (10), C (12), and D (16) are incorrect because they do not adhere to the proper order of operations or miscalculate the addition steps.
Marisol has 5 times as many books as Jerry. Jerry has 15 books. How many books does Marisol have?
- A. 10
- B. 20
- C. 75
- D. 225
Correct Answer & Rationale
Correct Answer: C
To determine how many books Marisol has, start by recognizing that she has 5 times the number of books Jerry has. Since Jerry has 15 books, you multiply 15 by 5: 15 × 5 = 75. Thus, Marisol has 75 books. Option A (10) is incorrect as it suggests Marisol has fewer books than Jerry. Option B (20) also underestimates her total, as it does not account for the multiplication factor of 5. Option D (225) overestimates the total by incorrectly multiplying the number of Jerry's books. Only option C accurately reflects the calculation based on the relationship between Marisol's and Jerry's books.
To determine how many books Marisol has, start by recognizing that she has 5 times the number of books Jerry has. Since Jerry has 15 books, you multiply 15 by 5: 15 × 5 = 75. Thus, Marisol has 75 books. Option A (10) is incorrect as it suggests Marisol has fewer books than Jerry. Option B (20) also underestimates her total, as it does not account for the multiplication factor of 5. Option D (225) overestimates the total by incorrectly multiplying the number of Jerry's books. Only option C accurately reflects the calculation based on the relationship between Marisol's and Jerry's books.