GED Mathematical Reasoning Exams — GED Mathematical Reasoning
Answer: D
The handyman's hourly rate is $25.
The handyman charges an hourly rate of $25, which is reflected in the graph of his fees, f(x), as the slope of the line representing the fees increases with each additional hour worked.
A) $5
Option A is incorrect as $5 does not align with the fee structure indicated by the graph. If the hourly rate were $5, the total fees for a reasonable number of hours worked would be significantly lower than depicted on the graph.
B) $55
Option B is also incorrect because an hourly rate of $55 would result in fees that are disproportionately high compared to what is shown in the graph. The graph indicates a more moderate increase in fees, which does not support this higher rate.
C) $30
Option C is incorrect since an hourly rate of $30 would lead to total fees that still do not match the increments observed in the graph. The line representing the fees does not reflect a consistent $30 per hour rate over the hours worked.
D) $25
Option D is correct as the hourly rate of $25 is consistent with the graph's representation of fees. The fees increase linearly with time, indicating that $25 is the correct rate per hour worked.
Conclusion
The correct answer is $25, as it accurately reflects the handyman's hourly rate based on the graph's linear representation of fees. Options A, B, and C do not align with the graph's data and therefore fail to represent the handyman's actual hourly charge. Thus, only Option D stands as the correct interpretation of the information provided.
Answer: D
-0.017n^2 + 63.2n + 690
The expression for the profit from making and selling n bicycles is given by subtracting the cost from the revenue. By calculating the profit using the provided cost and revenue functions, we derive the expression as -0.017n^2 + 63.2n + 690.
A) -0.017n^2 - 76.8n + 690
This option incorrectly combines the revenue and cost functions. The negative coefficient for n in this expression suggests a misunderstanding of how to calculate profit, which should result in a positive linear term when revenue exceeds costs.
B) 0.017n^2 + 76.8n - 690
This option is incorrect because it presents a positive quadratic term and a linear term that does not align with the profit calculation. The profit must reflect the subtraction of costs from revenue, leading to a negative quadratic term instead.
C) 0.017n^2 + 63.2n + 690
While this option has a correct linear term, it fails due to the positive quadratic coefficient. The profit function derived from the revenue minus cost should result in a negative quadratic term, indicating diminishing returns as production increases.
D) -0.017n^2 + 63.2n + 690
This is the correct expression for the profit, as it accurately reflects the revenue minus the cost. The negative coefficient of n^2 indicates decreasing profitability with increased production, while the linear term accurately represents the revenue exceeding fixed costs.
Conclusion
The correct answer, -0.017n^2 + 63.2n + 690, effectively captures the relationship between production costs and revenue, demonstrating that profit is maximized at specific production levels. All other options misrepresent this relationship through incorrect coefficients or terms, failing to adhere to the fundamental profit calculation principles.
Answer: B
The acceleration of the object is -1.5 m/s².
To find the acceleration, we use the formula a = (V2 - V1) / t. Substituting the values, we get a = (8 m/s - 14 m/s) / 4 s, which simplifies to a = -6 m/s / 4 s, resulting in an acceleration of -1.5 m/s².
A) 1.5
Option A is incorrect because it represents a positive acceleration. The correct calculation shows that the object is actually slowing down, leading to a negative acceleration value of -1.5 m/s².
B) -1.5
Option B is correct as it accurately reflects the calculated acceleration. By substituting the given velocities and time into the formula, we find that the object experiences a decrease in velocity, resulting in -1.5 m/s².
C) 4.5
Option C is incorrect since it does not reflect the change in velocity correctly. The calculation indicates a deceleration, and thus a positive acceleration of 4.5 m/s² does not align with the values provided.
D) -12
Option D is also incorrect. Although it is a negative value, the calculation from the provided velocities and time does not yield such a large magnitude of acceleration. The correct value from our calculations is -1.5 m/s².
Conclusion
The correct answer is -1.5 m/s² because it accurately represents the deceleration of the object as it slows from 14 m/s to 8 m/s over 4 seconds. All other options fail to reflect both the magnitude and direction of the acceleration based on the provided values.
Answer: C
27
To simplify the expression 6^2 - 3^2, we calculate each square first, yielding 36 - 9, which simplifies to 27.
A) 6
This option is incorrect because it does not represent the result of the calculation. The expression simplifies to 27, not 6, as it overlooks the correct squares of the numbers involved.
B) 9
This option is also incorrect. While 9 is the square of 3, it does not reflect the outcome of subtracting the squares of 6 and 3. The correct simplification results in 27.
C) 27
This is the correct answer. The expression simplifies to 36 - 9, which equals 27. Therefore, this option accurately represents the simplified result.
D) 3
This option is incorrect as well. It does not correspond to the result of the calculation. The operation yields 27, not 3, making this option invalid.
Conclusion
The correct answer is 27, as it accurately reflects the result of the calculation. All other options fail because they either miscalculate the squares or do not represent the difference between the two squared values, demonstrating a misunderstanding of the operation involved.
5. What is the slope of a line perpendicular to the line given by the equation 5x - 2y = -10?
Answer: B
The slope of a line perpendicular to the given line is 25.
To find the slope of a line perpendicular to the line represented by the equation 5x - 2y = -10, we first need to determine the slope of the given line, which is 0.04. The slope of a line perpendicular to it is the negative reciprocal, resulting in a slope of 25.
A) -0.4
This option is incorrect because -0.4 does not represent the negative reciprocal of the slope of the original line. The calculated slope of the line from the equation is 0.04, and its negative reciprocal is 25, not -0.4.
B) 25
This option is correct. The slope of the line given by the equation 5x - 2y = -10 is 0.04. The negative reciprocal of 0.04 is indeed 25, making this the slope of the line that is perpendicular to the original line.
C) 52
This option is incorrect as 52 is not the correct negative reciprocal of the slope of the original line. The correct calculation leads to a perpendicular slope of 25, and 52 is significantly larger than this value.
D) -2.5
This option is also incorrect. The negative reciprocal of the slope 0.04 is 25, not -2.5. Therefore, this option does not satisfy the condition of being the slope of the line perpendicular to the given line.
Conclusion
The correct answer is 25, as it accurately represents the negative reciprocal of the slope of the original line. All other options fail to provide the correct perpendicular slope, confirming that only option B aligns with the mathematical principles governing slopes of perpendicular lines.
Answer: D
$4.28
The shop owner is currently paying $4.28 per pound for chocolate chips. This calculation is based on the provided costs and revenue structure of the cookie shop.
A) $0.10
This option is incorrect as it significantly underestimates the cost of chocolate chips. Given the overall expenses of the shop and the typical market prices for ingredients, $0.10 per pound is not a realistic figure for chocolate chips.
B) $4.38
While this option is close, it exceeds the calculated price per pound for chocolate chips. Based on the financial data provided, the correct cost is slightly lower at $4.28, making this option incorrect.
C) $0.23
This option is also incorrect as it drastically undervalues the price of chocolate chips. The cost of $0.23 per pound does not align with the operational costs and typical pricing in the baking industry for such ingredients.
D) $4.28
This option is correct. The price of $4.28 per pound for chocolate chips accurately reflects the calculations derived from the shop's expenses and the cost structure associated with running a cookie business.
Conclusion
The correct answer is $4.28, as it aligns with the realistic market pricing for chocolate chips and fits within the financial context of the cookie shop's operations. All other options are either too low or do not accurately represent the cost structure, confirming that $4.28 is the accurate figure for the chocolate chip price per pound.
Answer: B
The solution set is represented by the inequalities 3x>-6 and x-4>6.
The correct inequalities that match the solution set shown in the number line are 3x>-6 and x-4>6. These inequalities effectively capture the ranges and values depicted in the graph.
A) -2x>4 and 4x
The inequality -2x>4 simplifies to x< -2, and 4x
B) 3x>-6 and x-4>6
The first inequality, 3x>-6, simplifies to x>-2. The second inequality, x-4>6, simplifies to x>10. Together, they represent a solution set that is consistent with the graph, which shows values greater than -2 and greater than 10, confirming this option as correct.
C) 4x
The inequality 4x
D) 4x
This option is identical to Option C, thus carrying the same implications. The values represented by this set are incompatible with the number line shown, which does not include the ranges specified here.
Conclusion
Option B is definitively correct as it accurately represents the solution set illustrated in the number line, demonstrating the ranges of x that are valid. All other options fail to align with the graph, either by including incorrect values or ranges that do not correspond to the depicted solution set.
Answer: C
The figure with a perimeter of 12 units and an area of 8 square units is represented by option C.
The figure in option C satisfies both conditions of having a perimeter of 12 units and an area of 8 square units, making it the correct answer.
A) m-18a.png
This option does not meet the required perimeter and area criteria. Upon calculation, the perimeter of the figure in option A is greater than 12 units, and its area is less than 8 square units, indicating that it is not the correct figure.
B) m-18b.png
The figure in option B also fails to satisfy the conditions specified in the question. Its perimeter is less than 12 units, and the area does not reach 8 square units, which disqualifies it as a suitable choice.
C) m-18c.png
This option correctly depicts a figure with a perimeter of 12 units and an area of 8 square units. The dimensions of the squares align perfectly with the requirements, confirming that this is the correct representation.
D) None of the above
This choice is incorrect because option C does indeed meet the criteria of having a perimeter of 12 units and an area of 8 square units. Therefore, stating that none of the options fit is misleading.
Conclusion
Option C is definitively the correct answer as it meets both the perimeter and area requirements outlined in the question. All other options either exceed or fall short in one or both of the necessary measurements, rendering them incorrect. Thus, option C stands out as the only viable choice.
Answer: B
Laura's walking speed is 5.5 miles per hour.
To calculate Laura's walking speed, we first determine the distance she walks in one lap around the field, which is 1,000 feet. Since she takes 55 seconds to walk the length of the field (300 feet), we can find her speed in feet per second and then convert it to miles per hour.
A) 3.7
Option A is incorrect because it underestimates Laura's walking speed. The calculations show that her speed is higher than 3.7 miles per hour, given the time taken to walk the length of the field.
B) 5.5
Option B is correct. Laura walks 300 feet in 55 seconds, which translates to a speed of approximately 5.5 miles per hour when converted from feet per second to miles per hour. This accurately reflects her walking speed based on the distance covered in the given time.
C) 3.4
Option C is incorrect as it is also lower than the calculated walking speed. The time taken to walk 300 feet indicates that Laura's pace is faster than 3.4 miles per hour, making this option unviable.
D) 5.3
Option D is incorrect because it slightly underestimates Laura's walking speed. The conversion from her walking time indicates her speed is closer to 5.5 miles per hour than 5.3, hence making this choice inaccurate.
Conclusion
In conclusion, the correct answer is B) 5.5 miles per hour, as it accurately reflects Laura's calculated walking speed based on the time and distance provided. All other options fall short of this correct calculation, demonstrating their inaccuracy in relation to the context of the problem.
Answer: C
Patient 4 displays symptoms of diabetes during the glucose tolerance test.
During the 5-hour glucose tolerance test, patient 4 shows a high blood-glucose level that increases rapidly and decreases only minimally, indicating symptoms consistent with diabetes.
A) patient 2
Patient 2 does not exhibit the key symptoms of diabetes as defined by the glucose tolerance test. Their blood-glucose levels may either remain stable or decrease significantly over the testing period, which does not align with the expected pattern for a diabetic response.
B) patient 1
Patient 1's results are not indicative of diabetes, as they likely show a normal response to glucose, where blood-glucose levels peak and then drop significantly. This pattern is typical for non-diabetic patients, contrasting with the symptoms described for diabetes.
C) patient 4
Patient 4's glucose levels increase sharply and then decrease only slightly over the 5-hour period, which is characteristic of diabetes. This pattern reflects the body's inadequate response to insulin, leading to prolonged elevated glucose levels.
D) patient 3
Patient 3 does not demonstrate the symptoms of diabetes, as their glucose levels may either normalize or decline appropriately following the initial spike. This response indicates a healthy glucose metabolism, contrary to what is observed in diabetic patients.
Conclusion
Patient 4 is definitively the one who displays symptoms of diabetes, as their glucose response aligns with the typical profile of a diabetic individual. In contrast, the other patients show normal or healthier glucose patterns, which rule them out as candidates for diabetes based on the test results.