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
The chart above shows the store's cost and list price for three models of stoves sold by an appliance store.
During a 20 percent off sale, Gene bought a Model Y stove from this store. How much profit did the store
make on Gene's purchase? (Profit = Price paid - Store's cost)
- A. $260
- B. $380
- C. $590
- D. $760
Correct Answer & Rationale
Correct Answer: D
To determine the profit made by the store on Gene's purchase of Model Y, first calculate the sale price. If the list price is $950, a 20% discount reduces it by $190, resulting in a sale price of $760. Next, subtract the store's cost of $0 from the sale price, yielding a profit of $760. Option A ($260) incorrectly assumes a lower sale price or higher cost. Option B ($380) miscalculates by not accurately applying the discount or cost. Option C ($590) likely reflects a misunderstanding of the profit calculation. Only option D correctly reflects the profit based on the sale price and cost.
To determine the profit made by the store on Gene's purchase of Model Y, first calculate the sale price. If the list price is $950, a 20% discount reduces it by $190, resulting in a sale price of $760. Next, subtract the store's cost of $0 from the sale price, yielding a profit of $760. Option A ($260) incorrectly assumes a lower sale price or higher cost. Option B ($380) miscalculates by not accurately applying the discount or cost. Option C ($590) likely reflects a misunderstanding of the profit calculation. Only option D correctly reflects the profit based on the sale price and cost.
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.
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.
If a number rounded to the nearest hundredth is 9.99, which of the following could be the number?
- A. 9.845
- B. 9.983
- C. 9.992
- D. 9.998
Correct Answer & Rationale
Correct Answer: C
Rounding to the nearest hundredth means looking at the third decimal place to determine if the second decimal place should round up or stay the same. For a number rounded to 9.99, the possible range is 9.985 to 9.995. Option A (9.845) rounds to 9.84, which is outside the range. Option B (9.983) rounds to 9.98, also outside the range. Option D (9.998) rounds to 10.00, exceeding the upper limit. Option C (9.992) falls within the range and correctly rounds to 9.99, making it the only viable option.
Rounding to the nearest hundredth means looking at the third decimal place to determine if the second decimal place should round up or stay the same. For a number rounded to 9.99, the possible range is 9.985 to 9.995. Option A (9.845) rounds to 9.84, which is outside the range. Option B (9.983) rounds to 9.98, also outside the range. Option D (9.998) rounds to 10.00, exceeding the upper limit. Option C (9.992) falls within the range and correctly rounds to 9.99, making it the only viable option.