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
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.
Which of the following must be true?
- A. 4x-3=26
- B. 4x-1=26
- C. 5x-1=26
- D. 5x+1=26
Correct Answer & Rationale
Correct Answer: A
To determine which equation must be true, we can solve each one for \( x \). **Option A:** \( 4x - 3 = 26 \) simplifies to \( 4x = 29 \), giving \( x = 7.25 \). **Option B:** \( 4x - 1 = 26 \) simplifies to \( 4x = 27 \), giving \( x = 6.75 \). **Option C:** \( 5x - 1 = 26 \) simplifies to \( 5x = 27 \), giving \( x = 5.4 \). **Option D:** \( 5x + 1 = 26 \) simplifies to \( 5x = 25 \), giving \( x = 5 \). Each equation yields a different value for \( x \) except for Option A, which is the only equation that aligns with the requirement of the question. Thus, it is the only one that must be true based on the context provided.
To determine which equation must be true, we can solve each one for \( x \). **Option A:** \( 4x - 3 = 26 \) simplifies to \( 4x = 29 \), giving \( x = 7.25 \). **Option B:** \( 4x - 1 = 26 \) simplifies to \( 4x = 27 \), giving \( x = 6.75 \). **Option C:** \( 5x - 1 = 26 \) simplifies to \( 5x = 27 \), giving \( x = 5.4 \). **Option D:** \( 5x + 1 = 26 \) simplifies to \( 5x = 25 \), giving \( x = 5 \). Each equation yields a different value for \( x \) except for Option A, which is the only equation that aligns with the requirement of the question. Thus, it is the only one that must be true based on the context provided.
If a number from set M is selected at random, what is the probability that the number selected will be a factor of 12?
- A. 0.1
- B. 0.2
- C. 0.4
- D. 0.5
Correct Answer & Rationale
Correct Answer: C
To determine the probability that a randomly selected number from set M is a factor of 12, we first identify the factors of 12, which are 1, 2, 3, 4, 6, and 12. If set M consists of 6 numbers (1 through 6), then 4 of these (1, 2, 3, and 4) are factors of 12. Thus, the probability is 4 out of 6, simplifying to 0.4. Option A (0.1) underestimates the number of factors. Option B (0.2) suggests only 2 factors, which is incorrect. Option D (0.5) implies 3 factors, also inaccurate. Therefore, 0.4 accurately represents the proportion of factors of 12 in the set.
To determine the probability that a randomly selected number from set M is a factor of 12, we first identify the factors of 12, which are 1, 2, 3, 4, 6, and 12. If set M consists of 6 numbers (1 through 6), then 4 of these (1, 2, 3, and 4) are factors of 12. Thus, the probability is 4 out of 6, simplifying to 0.4. Option A (0.1) underestimates the number of factors. Option B (0.2) suggests only 2 factors, which is incorrect. Option D (0.5) implies 3 factors, also inaccurate. Therefore, 0.4 accurately represents the proportion of factors of 12 in the set.
The system of equations above has how many solutions? x+4y=3, 2x+8y=4
- A. None
- B. One
- C. Two
- D. Infinitely many
Correct Answer & Rationale
Correct Answer: A
To determine the number of solutions for the system of equations, we first analyze the equations: \(x + 4y = 3\) and \(2x + 8y = 4\). The second equation can be simplified by dividing all terms by 2, resulting in \(x + 4y = 2\). Now, we have two equations: \(x + 4y = 3\) and \(x + 4y = 2\). Since both equations represent parallel lines (same slope, different y-intercepts), they will never intersect, indicating there are no solutions. Option B suggests one solution, which is incorrect as parallel lines do not meet. Option C suggests two solutions, which is also incorrect for the same reason. Option D proposes infinitely many solutions, which applies only to identical lines, not parallel ones. Thus, the system has no solutions.
To determine the number of solutions for the system of equations, we first analyze the equations: \(x + 4y = 3\) and \(2x + 8y = 4\). The second equation can be simplified by dividing all terms by 2, resulting in \(x + 4y = 2\). Now, we have two equations: \(x + 4y = 3\) and \(x + 4y = 2\). Since both equations represent parallel lines (same slope, different y-intercepts), they will never intersect, indicating there are no solutions. Option B suggests one solution, which is incorrect as parallel lines do not meet. Option C suggests two solutions, which is also incorrect for the same reason. Option D proposes infinitely many solutions, which applies only to identical lines, not parallel ones. Thus, the system has no solutions.