The apartments in Greg's building are named using the letters A, B, C, and D and the digits 1 through 9. How many apartments are there in Greg's building if each apartment is named by a single letter followed by a single digit?
- A. 36
- B. 16
- C. 40
- D. 13
Correct Answer & Rationale
Correct Answer: A
To determine the total number of apartments, consider the naming convention: each apartment consists of one letter and one digit. There are 4 letters (A, B, C, D) and 9 digits (1-9). Calculating the combinations, multiply the number of letters by the number of digits: 4 letters × 9 digits = 36 unique apartment names. Options B (16) and D (13) do not account for all possible combinations, while option C (40) incorrectly assumes more letters or digits than provided. Thus, option A accurately reflects the total possible apartments in Greg's building.
To determine the total number of apartments, consider the naming convention: each apartment consists of one letter and one digit. There are 4 letters (A, B, C, D) and 9 digits (1-9). Calculating the combinations, multiply the number of letters by the number of digits: 4 letters × 9 digits = 36 unique apartment names. Options B (16) and D (13) do not account for all possible combinations, while option C (40) incorrectly assumes more letters or digits than provided. Thus, option A accurately reflects the total possible apartments in Greg's building.
Other Related Questions
The graph shows data for a 5-hour glucose tolerance test for four patients.
Symptoms of a patient with diabetes during a 5-hour glucose tolerance test include a high blood-glucose level that increases quickly and then decreases only minimally over the 5-hour period. Which patient displays symptoms of diabetes?
- A. patient 2
- B. patient 1
- C. patient 4
- D. patient 3
Correct Answer & Rationale
Correct Answer: C
Patient 4 exhibits a rapid increase in blood glucose levels followed by a minimal decrease over the 5-hour test, indicating poor glucose regulation typical of diabetes. This pattern reflects the body's inability to effectively utilize insulin. In contrast, Patient 1 shows a quick rise followed by a significant decline, suggesting normal glucose metabolism. Patient 2 may demonstrate a slight increase but returns to baseline, indicating no diabetes. Patient 3's levels remain stable, which is also indicative of normal glucose tolerance. Thus, only Patient 4 aligns with the expected symptoms of diabetes during the test.
Patient 4 exhibits a rapid increase in blood glucose levels followed by a minimal decrease over the 5-hour test, indicating poor glucose regulation typical of diabetes. This pattern reflects the body's inability to effectively utilize insulin. In contrast, Patient 1 shows a quick rise followed by a significant decline, suggesting normal glucose metabolism. Patient 2 may demonstrate a slight increase but returns to baseline, indicating no diabetes. Patient 3's levels remain stable, which is also indicative of normal glucose tolerance. Thus, only Patient 4 aligns with the expected symptoms of diabetes during the test.
At what point does the function stop decreasing and start increasing?
- A. (1, -4)
- B. (3, 0)
- C. (-4, 1)
- D. (0, -3)
Correct Answer & Rationale
Correct Answer: A
To determine where the function stops decreasing and starts increasing, we look for a local minimum, which occurs where the derivative changes from negative to positive. Option A: (1, -4) indicates a point where the function transitions from decreasing to increasing, making it a local minimum. Option B: (3, 0) does not represent a minimum; the function is still increasing here. Option C: (-4, 1) is not relevant to the transition, as it does not indicate a change in direction. Option D: (0, -3) also does not represent a point of change, as the function continues to decrease. Thus, A is the point where the function stops decreasing and begins to increase.
To determine where the function stops decreasing and starts increasing, we look for a local minimum, which occurs where the derivative changes from negative to positive. Option A: (1, -4) indicates a point where the function transitions from decreasing to increasing, making it a local minimum. Option B: (3, 0) does not represent a minimum; the function is still increasing here. Option C: (-4, 1) is not relevant to the transition, as it does not indicate a change in direction. Option D: (0, -3) also does not represent a point of change, as the function continues to decrease. Thus, A is the point where the function stops decreasing and begins to increase.
Simplify 6^2 - 3^2
- A. 6
- B. 9
- C. 27
- D. 3
Correct Answer & Rationale
Correct Answer: C
To simplify \(6^2 - 3^2\), we apply the difference of squares formula, which states \(a^2 - b^2 = (a - b)(a + b)\). Here, \(a = 6\) and \(b = 3\). Thus, we have: \[ 6^2 - 3^2 = (6 - 3)(6 + 3) = 3 \times 9 = 27 \] Option A (6) is incorrect as it miscalculates the expression. Option B (9) mistakenly considers only one of the squared terms. Option D (3) misinterprets the operations involved, leading to an incorrect result. The correct evaluation yields 27, confirming option C as the accurate answer.
To simplify \(6^2 - 3^2\), we apply the difference of squares formula, which states \(a^2 - b^2 = (a - b)(a + b)\). Here, \(a = 6\) and \(b = 3\). Thus, we have: \[ 6^2 - 3^2 = (6 - 3)(6 + 3) = 3 \times 9 = 27 \] Option A (6) is incorrect as it miscalculates the expression. Option B (9) mistakenly considers only one of the squared terms. Option D (3) misinterprets the operations involved, leading to an incorrect result. The correct evaluation yields 27, confirming option C as the accurate answer.
Two points (a,b) and (c,d) are shown on a graph. Which of the following equations correctly represents the slope of the line that passes through these points.
- A. (b-d)/(a-c)
- B. (d-b)/(c-a)
- C. (b-d)/(c-a)
- D. (d-b)/(a-c)
Correct Answer & Rationale
Correct Answer: B
To determine the slope of a line passing through two points, the formula used is \((y_2 - y_1) / (x_2 - x_1)\). In this case, for points \((a, b)\) and \((c, d)\), we can label \((x_1, y_1) = (a, b)\) and \((x_2, y_2) = (c, d)\). Option B, \((d - b) / (c - a)\), correctly applies this formula, with \(d\) as \(y_2\) and \(b\) as \(y_1\). Option A, \((b - d) / (a - c)\), incorrectly reverses the subtraction for both \(y\) and \(x\). Option C, \((b - d) / (c - a)\), misplaces the order of \(y\) values, leading to an incorrect slope sign. Option D, \((d - b) / (a - c)\), also incorrectly reverses the \(x\) values, yielding an incorrect result.
To determine the slope of a line passing through two points, the formula used is \((y_2 - y_1) / (x_2 - x_1)\). In this case, for points \((a, b)\) and \((c, d)\), we can label \((x_1, y_1) = (a, b)\) and \((x_2, y_2) = (c, d)\). Option B, \((d - b) / (c - a)\), correctly applies this formula, with \(d\) as \(y_2\) and \(b\) as \(y_1\). Option A, \((b - d) / (a - c)\), incorrectly reverses the subtraction for both \(y\) and \(x\). Option C, \((b - d) / (c - a)\), misplaces the order of \(y\) values, leading to an incorrect slope sign. Option D, \((d - b) / (a - c)\), also incorrectly reverses the \(x\) values, yielding an incorrect result.