50 acres, 23 apple. Percent left?
- A. 27%
- B. 46%
- C. 54%
- D. 77%
Correct Answer & Rationale
Correct Answer: C
To determine the percentage of land left after allocating 23 acres for apple trees from a total of 50 acres, first calculate the remaining land: 50 - 23 = 27 acres. Then, to find the percentage of land left, divide the remaining acres by the total acres and multiply by 100: (27/50) * 100 = 54%. Option A (27%) miscalculates the percentage of land used instead of what remains. Option B (46%) incorrectly assumes a different allocation of land. Option D (77%) mistakenly represents a higher percentage than what is left. Thus, option C accurately reflects the remaining percentage of land.
To determine the percentage of land left after allocating 23 acres for apple trees from a total of 50 acres, first calculate the remaining land: 50 - 23 = 27 acres. Then, to find the percentage of land left, divide the remaining acres by the total acres and multiply by 100: (27/50) * 100 = 54%. Option A (27%) miscalculates the percentage of land used instead of what remains. Option B (46%) incorrectly assumes a different allocation of land. Option D (77%) mistakenly represents a higher percentage than what is left. Thus, option C accurately reflects the remaining percentage of land.
Other Related Questions
Digit 1 in ten thousands 9 in ones? Select ALL.
- A. 12,679
- B. 12,769
- C. 12,796
- D. 21,679
- E. 21,769
Correct Answer & Rationale
Correct Answer: A,B: 1 ten thousands, 9 ones. C: 6 ones. D,E,F: 2 ten thousands. Place values must match both conditions.
To identify numbers with 1 in the ten thousands place and 9 in the ones place, we analyze each option. - **A (12,679)**: The digit 1 is in the ten thousands place, and 9 is in the ones place, meeting both criteria. - **B (12,769)**: Here, 1 is again in the ten thousands place, and 9 is in the ones place, satisfying the conditions. - **C (12,796)**: The digit in the ones place is 6, not 9, which disqualifies it. - **D (21,679)**: The digit in the ten thousands place is 2, failing to meet the first condition. - **E (21,769)**: Similarly, 2 is in the ten thousands place, not 1. - **F (21,796)**: Again, 2 is in the ten thousands place, disqualifying this option. Only options A and B fulfill both requirements, confirming their validity.
To identify numbers with 1 in the ten thousands place and 9 in the ones place, we analyze each option. - **A (12,679)**: The digit 1 is in the ten thousands place, and 9 is in the ones place, meeting both criteria. - **B (12,769)**: Here, 1 is again in the ten thousands place, and 9 is in the ones place, satisfying the conditions. - **C (12,796)**: The digit in the ones place is 6, not 9, which disqualifies it. - **D (21,679)**: The digit in the ten thousands place is 2, failing to meet the first condition. - **E (21,769)**: Similarly, 2 is in the ten thousands place, not 1. - **F (21,796)**: Again, 2 is in the ten thousands place, disqualifying this option. Only options A and B fulfill both requirements, confirming their validity.
(2x+3y-7)-(2x-3y-8)?
- A. 1
- B. -15
- C. 6y+1
- D. 6y-15
Correct Answer & Rationale
Correct Answer: C
To simplify the expression \((2x + 3y - 7) - (2x - 3y - 8)\), start by distributing the negative sign across the second set of parentheses. This results in \(2x + 3y - 7 - 2x + 3y + 8\). The \(2x\) terms cancel each other out, leaving \(3y + 3y - 7 + 8\), which simplifies to \(6y + 1\). Option A (1) is incorrect as it ignores the \(6y\) term. Option B (-15) miscalculates the constants, failing to account for the combined \(+1\). Option D (6y - 15) incorrectly subtracts instead of adding the constants. Thus, the simplification leads to \(6y + 1\), confirming option C.
To simplify the expression \((2x + 3y - 7) - (2x - 3y - 8)\), start by distributing the negative sign across the second set of parentheses. This results in \(2x + 3y - 7 - 2x + 3y + 8\). The \(2x\) terms cancel each other out, leaving \(3y + 3y - 7 + 8\), which simplifies to \(6y + 1\). Option A (1) is incorrect as it ignores the \(6y\) term. Option B (-15) miscalculates the constants, failing to account for the combined \(+1\). Option D (6y - 15) incorrectly subtracts instead of adding the constants. Thus, the simplification leads to \(6y + 1\), confirming option C.
p=5n, questions n, points p. True?
- A. Points dependent
- B. Questions dependent
- C. 5 points dependent
- D. 1/5 question dependent
Correct Answer & Rationale
Correct Answer: A
In the equation \( p = 5n \), points \( p \) are directly calculated based on the number of questions \( n \). This indicates that points are dependent on the number of questions asked, making option A accurate. Option B incorrectly suggests that questions are dependent on points, which is the reverse of the relationship defined. Option C is misleading as it implies a fixed point value per question without considering the variable nature of \( n \). Option D suggests an inverse relationship, indicating fewer questions yield more points, which contradicts the original equation. Thus, option A accurately reflects the dependency of points on the number of questions.
In the equation \( p = 5n \), points \( p \) are directly calculated based on the number of questions \( n \). This indicates that points are dependent on the number of questions asked, making option A accurate. Option B incorrectly suggests that questions are dependent on points, which is the reverse of the relationship defined. Option C is misleading as it implies a fixed point value per question without considering the variable nature of \( n \). Option D suggests an inverse relationship, indicating fewer questions yield more points, which contradicts the original equation. Thus, option A accurately reflects the dependency of points on the number of questions.
Favorite food via survey numbers. Best measure?
- A. Mean
- B. Median
- C. Mode
- D. Mean+median
Correct Answer & Rationale
Correct Answer: C
When analyzing survey data on favorite foods, the mode is the best measure since it identifies the most frequently chosen option, reflecting the popular preference among respondents. The mean can be skewed by outliers, making it less reliable in this context. The median, while useful for understanding the middle value, does not capture the most popular choice effectively. Combining mean and median (option D) does not address the core goal of identifying the favorite food, which is best represented by the mode. Thus, the mode provides a clear insight into the most favored food item.
When analyzing survey data on favorite foods, the mode is the best measure since it identifies the most frequently chosen option, reflecting the popular preference among respondents. The mean can be skewed by outliers, making it less reliable in this context. The median, while useful for understanding the middle value, does not capture the most popular choice effectively. Combining mean and median (option D) does not address the core goal of identifying the favorite food, which is best represented by the mode. Thus, the mode provides a clear insight into the most favored food item.