The average of 4 numbers is 9. If one of the numbers is 7, what is the sum of the other 3 numbers?
- A. 2
- B. 12
- C. 29
- D. 36
Correct Answer & Rationale
Correct Answer: C
To find the sum of the other three numbers, start by calculating the total sum of all four numbers. Since the average is 9, multiply this by 4, yielding a total of 36. Given that one of the numbers is 7, subtract this from the total: 36 - 7 = 29. Therefore, the sum of the other three numbers is 29. Option A (2) is too low, as it does not account for the total sum needed. Option B (12) underestimates the remaining numbers. Option D (36) mistakenly includes the known number, rather than calculating the sum of the others.
To find the sum of the other three numbers, start by calculating the total sum of all four numbers. Since the average is 9, multiply this by 4, yielding a total of 36. Given that one of the numbers is 7, subtract this from the total: 36 - 7 = 29. Therefore, the sum of the other three numbers is 29. Option A (2) is too low, as it does not account for the total sum needed. Option B (12) underestimates the remaining numbers. Option D (36) mistakenly includes the known number, rather than calculating the sum of the others.
Other Related Questions
What is the range of her scores?
- A. 100
- B. 120
- C. 440
- D. 2,250
Correct Answer & Rationale
Correct Answer: B
To determine the range of her scores, we subtract the lowest score from the highest score. If the highest score is 220 and the lowest is 100, the calculation is 220 - 100 = 120, which represents the range. Option A (100) misrepresents the range as it does not account for the difference between the highest and lowest scores. Option C (440) and Option D (2,250) are excessively high and do not reflect the actual spread of scores based on the provided data. Thus, 120 accurately represents the range of her scores.
To determine the range of her scores, we subtract the lowest score from the highest score. If the highest score is 220 and the lowest is 100, the calculation is 220 - 100 = 120, which represents the range. Option A (100) misrepresents the range as it does not account for the difference between the highest and lowest scores. Option C (440) and Option D (2,250) are excessively high and do not reflect the actual spread of scores based on the provided data. Thus, 120 accurately represents the range of her scores.
The sum of n and the product 3 times n is 12. What is the value of n?
- A. 2
- B. 3
- C. 4
- D. 4 ½
Correct Answer & Rationale
Correct Answer: B
To solve the equation formed by the problem statement, we express it as \( n + 3n = 12 \), which simplifies to \( 4n = 12 \). Dividing both sides by 4 gives \( n = 3 \). Option A (2) does not satisfy the equation, as substituting it results in \( 2 + 6 = 8 \), which is incorrect. Option C (4) leads to \( 4 + 12 = 16 \), also incorrect. Option D (4 ½) results in \( 4.5 + 13.5 = 18 \), which is too high. Thus, only \( n = 3 \) fulfills the original equation, confirming its validity.
To solve the equation formed by the problem statement, we express it as \( n + 3n = 12 \), which simplifies to \( 4n = 12 \). Dividing both sides by 4 gives \( n = 3 \). Option A (2) does not satisfy the equation, as substituting it results in \( 2 + 6 = 8 \), which is incorrect. Option C (4) leads to \( 4 + 12 = 16 \), also incorrect. Option D (4 ½) results in \( 4.5 + 13.5 = 18 \), which is too high. Thus, only \( n = 3 \) fulfills the original equation, confirming its validity.
If an item regularly costs d dollars and is discounted 12 percent, which of the following represents the discounted price in dollars?
- A. 0.12d
- B. 0.88d
- C. 1.12d
- D. d-0.12
Correct Answer & Rationale
Correct Answer: B
To find the discounted price after a 12 percent discount on an item that costs d dollars, we first calculate the amount of the discount, which is 12% of d, or 0.12d. To determine the final price, we subtract this discount from the original price: d - 0.12d = 0.88d. Option A (0.12d) represents only the discount amount, not the final price. Option C (1.12d) incorrectly suggests an increase in price. Option D (d - 0.12) does not account for the percentage; it inaccurately represents the discount as a flat dollar amount rather than a percentage of the original price. Thus, 0.88d correctly reflects the discounted price.
To find the discounted price after a 12 percent discount on an item that costs d dollars, we first calculate the amount of the discount, which is 12% of d, or 0.12d. To determine the final price, we subtract this discount from the original price: d - 0.12d = 0.88d. Option A (0.12d) represents only the discount amount, not the final price. Option C (1.12d) incorrectly suggests an increase in price. Option D (d - 0.12) does not account for the percentage; it inaccurately represents the discount as a flat dollar amount rather than a percentage of the original price. Thus, 0.88d correctly reflects the discounted price.
The price P, in dollars, that a store sets for an item is given by the equation P = C + 1/10 * C where C dollars is the store's cost for the item. If the store sets a price of $55.00 for an item, what is the store's cost for the item?
- A. $50.00
- B. $54.90
- C. $55.10
- D. $60.50
Correct Answer & Rationale
Correct Answer: A
To find the store's cost \( C \), we start with the equation \( P = C + \frac{1}{10}C \). This can be simplified to \( P = 1.1C \). Given that \( P = 55 \), we can set up the equation \( 55 = 1.1C \). Solving for \( C \) gives \( C = \frac{55}{1.1} = 50 \). Option A ($50.00) is correct, as it satisfies the equation. Option B ($54.90) incorrectly suggests a cost that would lead to a higher price than $55 when applying the markup. Option C ($55.10) implies a cost greater than the set price, which is illogical. Option D ($60.50) is also incorrect as it would result in a price far exceeding $55, making it unfeasible.
To find the store's cost \( C \), we start with the equation \( P = C + \frac{1}{10}C \). This can be simplified to \( P = 1.1C \). Given that \( P = 55 \), we can set up the equation \( 55 = 1.1C \). Solving for \( C \) gives \( C = \frac{55}{1.1} = 50 \). Option A ($50.00) is correct, as it satisfies the equation. Option B ($54.90) incorrectly suggests a cost that would lead to a higher price than $55 when applying the markup. Option C ($55.10) implies a cost greater than the set price, which is illogical. Option D ($60.50) is also incorrect as it would result in a price far exceeding $55, making it unfeasible.