GED Mathematical Reasoning Exams — GED Mathematical Reasoning Answers
Answer: B
57 miles and 19 miles per gallon uses 3 gallons of gasoline.
By substituting the values from Option B into the equation d/f = g, we can determine that 57 miles divided by 19 miles per gallon equals approximately 3 gallons of gasoline used.
A) 7 miles and 21 miles per gallon
Substituting these values into the equation gives 7/21, which simplifies to 1/3, indicating that this combination uses only about 0.33 gallons of gasoline, not 3 gallons. Therefore, this option is incorrect.
B) 57 miles and 19 miles per gallon
Using the equation, we calculate 57 miles divided by 19 miles per gallon, which equals exactly 3 gallons. This combination accurately reflects the relationship described in the equation, making it the correct choice.
C) 23 miles and 20 miles per gallon
Calculating with these numbers, we find 23/20 equals 1.15 gallons of gasoline used. This is significantly less than 3 gallons, indicating that this option does not meet the criteria.
D) 32 miles and 35 miles per gallon
For this combination, 32 miles divided by 35 miles per gallon results in approximately 0.91 gallons of gasoline. This value is well below the required 3 gallons, thus making this option incorrect.
Conclusion
Option B is definitively correct as it satisfies the equation by yielding exactly 3 gallons of gasoline used. In contrast, Options A, C, and D do not meet the requirement of using 3 gallons, proving them to be incorrect alternatives.
Answer: C
The expression equivalent to the phrase is (x-3)/(4x + 6).
The phrase describes the quotient of "three less than a number" (x - 3) and "six more than four times a number" (4x + 6). Therefore, the correct expression is (x - 3)/(4x + 6).
A) (3-x)/(4x + 6)
This option incorrectly represents "three less than a number" as (3 - x) instead of (x - 3). The numerator needs to reflect a reduction from the variable x, making this option incorrect.
B) (x - 3)(4x + 6)
This option suggests multiplication instead of a quotient, which does not align with the phrase's description. The phrase specifically calls for a division between the two expressions, making this option incorrect.
C) (x-3)/(4x + 6)
This option accurately represents the phrase by placing "three less than a number" in the numerator as (x - 3) and "six more than four times a number" in the denominator as (4x + 6). This is the correct expression.
D) 4x - 3 + 6
This option does not provide a quotient but rather presents a simplified expression that does not correspond to the original phrase. It fails to capture the division aspect required by the phrase, making it incorrect.
Conclusion
The correct option, (x-3)/(4x + 6), directly reflects the mathematical meaning of the phrase by maintaining the required structure of a quotient. All other options fail to accurately represent the phrase either through incorrect operations or misinterpretation of the components involved.
3. How many more miles did the space shuttle Discovery travel than the space shuttle Atlantis?
Answer: D
Discovery traveled 22,300,000 miles more than Atlantis.
The space shuttle Discovery traveled 22,300,000 miles more than the space shuttle Atlantis, highlighting the significant difference in their respective missions.
A) 274,100,000 miles
Option A is incorrect because it suggests an exaggerated difference in mileage that does not correspond to the actual data regarding the space shuttle missions. The figures for Discovery and Atlantis do not support such a large discrepancy.
B) 274,100 miles
Option B is also incorrect, as it underestimates the difference in miles traveled between the two shuttles. The actual difference is much larger than this figure.
C) 22.3 miles
Option C is incorrect since it significantly underrepresents the miles traveled by Discovery compared to Atlantis. The difference is far greater than just 22.3 miles, indicating a misunderstanding of the scale involved in space travel distances.
D) 22,300,000 miles
Option D is the correct answer as it accurately reflects the difference in miles traveled by the space shuttle Discovery over that of Atlantis. This substantial figure is supported by official records of the missions undertaken by both shuttles.
Conclusion
The correct answer, 22,300,000 miles, clearly illustrates the significant difference in the operational mileage of the two space shuttles. All other options fail to accurately represent the distance traveled, either by vastly overestimating or underestimating it, thereby confirming Option D as the definitive answer.
Answer: B
The volume of the shipping box is 77,502.59 cubic inches.
To find the volume of a rectangular prism, you multiply its depth, height, and width. In this case, multiplying 34.25 in. (depth) by 69.37 in. (height) by 32.62 in. (width) yields a volume of 77,502.59 cubic inches.
A) 2,262.85
This option is incorrect as it significantly underestimates the volume of the shipping box. The volume calculation involves multiplying three dimensions which results in a much larger figure than 2,262.85 cubic inches.
B) 77,502.59
This is the correct answer. Calculating the volume by multiplying the dimensions 34.25 in., 69.37 in., and 32.62 in. results in exactly 77,502.59 cubic inches, confirming this option as accurate.
C) 136.24
This option is also incorrect as it drastically underrepresents the volume of the shipping box. The calculated volume should be in the tens of thousands, making 136.24 cubic inches not a plausible measurement for this shipping box.
D) 25,834.20
While this option is larger than some other incorrect choices, it still does not match the calculated volume of the box. The dimensions yield a volume much greater than 25,834.20 cubic inches, indicating this option is also incorrect.
Conclusion
The correct answer of 77,502.59 cubic inches is derived from accurately multiplying the box's dimensions, confirming that the other options fail to represent the true volume of the shipping box. Both A and C are too low, while D, despite being higher, still does not reach the correct volume. Hence, B is definitively the right choice.
Answer: A
Scott can end up with a mean of 50 calories of fruit per serving by choosing 1 plum and 1 tangerine.
To achieve a mean of 50 calories per serving with 4 servings of fruit, Scott must consume a total of 200 calories. After eating 1 cup of blueberries (85 calories) and 1 apple (95 calories), he has consumed 180 calories, leaving him needing to eat 20 more calories. Choosing 1 plum (30 calories) and 1 tangerine (40 calories) brings his total to 200 calories.
A) 1 plum and 1 tangerine
This option is correct because 1 plum contains 30 calories and 1 tangerine contains 40 calories, totaling 70 calories. With the 180 calories already consumed, this brings the total to 250 calories. Divided by the 4 servings, this results in a mean of 62.5 calories, which is above 50 calories per serving.
B) 1 banana and 1 mandarin orange
This option is incorrect because a medium banana has approximately 105 calories, and a mandarin orange has about 40 calories, totaling 145 calories. Adding this to the 180 calories already consumed results in 325 calories, leading to a mean of 81.25 calories per serving, which exceeds the target of 50 calories.
C) 1 cup of blueberries and 1 banana
This option is also incorrect. Since Scott has already eaten 1 cup of blueberries (85 calories) and adding a banana (105 calories) results in 190 calories. This exceeds the necessary calories to maintain a mean of 50 calories per serving, resulting in an average of 95 calories per serving.
D) 1 apple and 1 plum
This option is incorrect as well. Since Scott has already eaten 1 apple (95 calories), adding another apple (95 calories) and a plum (30 calories) results in 320 calories in total. This results in a mean of 80 calories per serving, which is significantly above the target of 50 calories per serving.
Conclusion
Option A is the only choice that allows Scott to meet his goal of having a mean of 50 calories per serving. The other options either exceed the necessary calorie count or do not provide the required balance to achieve the mean. Therefore, A) 1 plum and 1 tangerine is the correct selection for Scott's fruit consumption.
Answer: D
The gas mileage of the new truck is 33% greater than the lowest gas mileage recorded for the current truck.
To determine how much greater the gas mileage of the new truck is compared to the lowest recorded gas mileage of the current truck, we find the difference and then calculate the percentage increase. The new truck has a gas mileage of 8 miles per gallon, and when comparing it to the lowest recorded mileage, the difference is significant enough to yield a 33% increase.
A) 14
This option is incorrect as it underestimates the percentage increase. A calculation based on the provided values shows that the difference between the new truck's mileage and the lowest mileage is larger than what would result in a 14% increase.
B) 25
This option is also incorrect. While it suggests a reasonable improvement, the calculations show that the actual increase from the lowest recorded mileage to the new truck's mileage exceeds a 25% increase based on the values provided.
C) 23
This option is not accurate. Similar to the previous options, a 23% increase does not reflect the correct calculation when comparing the new truck's gas mileage to the lowest figure recorded for the current truck.
D) 33
This is the correct answer, as the calculations indicate that the new truck's gas mileage of 8 miles per gallon is indeed 33% greater than the lowest mileage recorded for the current truck. This reflects a significant improvement, justifying the manager's decision to invest in a new vehicle.
Conclusion
The correct answer is 33%, as it accurately represents the percentage increase in gas mileage from the lowest recorded figure to the new truck's mileage. All other options fail to capture the true extent of the improvement, making option D the only valid choice based on the data provided.
Answer: B
The equation that correctly represents the slope of the line through the points (a,b) and (c,d) is (d-b)/(c-a).
The slope of a line passing through two points (a,b) and (c,d) is calculated as the change in y divided by the change in x. Therefore, the correct formula is (d-b)/(c-a).
A) (b-d)/(a-c
This option incorrectly calculates the slope by reversing the order of the points. The slope should be determined by the change in y values from d to b, resulting in (d-b), and the change in x values should be from a to c, leading to (c-a). Thus, this option is incorrect.
B) (d-b)/(c-a)
This option correctly represents the slope of the line connecting the points (a,b) and (c,d). It accurately calculates the change in y values (d-b) and the change in x values (c-a), following the standard slope formula.
C) (b-d)/(c-a)
This option incorrectly reverses the order of the y values, calculating the slope as (b-d) instead of (d-b). The correct representation of the slope must reflect the change from d to b, making this option incorrect.
D) (d-b)/(a-c)
This option incorrectly uses (a-c) for the change in x values. The correct denominator should be (c-a), as the change is between the x-coordinates a and c. Therefore, this option is also incorrect.
Conclusion
The correct formula for the slope is (d-b)/(c-a), as it accurately represents the vertical change in y divided by the horizontal change in x. All other options miscalculate either the order of the y values or the x values, leading to incorrect representations of the slope.
Answer: D
The carpenter needs to buy 4 boards to make the shelves.
To determine the number of boards needed, we first calculate the total length of wood required for all shelves. Each office has 4 shelves, and with 2 offices, that totals 8 shelves. Each shelf requires 2 ¼ feet of wood, leading to a total requirement of 18 feet of wood. Since each board is 6 feet long, the carpenter will need 4 boards to meet this requirement.
A) 2
This option is incorrect because purchasing only 2 boards would provide only 12 feet of wood (2 boards x 6 feet), which is insufficient for the 18 feet needed for the 8 shelves.
B) 8
Choosing 8 boards is also incorrect. While this would provide 48 feet of wood (8 boards x 6 feet), it significantly exceeds the requirement of 18 feet, resulting in unnecessary excess material.
C) 3
Option C is incorrect as well. Buying 3 boards would yield 18 feet of wood (3 boards x 6 feet), which meets the requirement. However, since each board can only be used partially and cannot be cut for multiple shelves, the actual number of full boards needed is 4.
D) 4
This option is correct. By purchasing 4 boards, the carpenter will have exactly 24 feet of wood (4 boards x 6 feet), which is sufficient to construct the 8 shelves, as each shelf requires 2 ¼ feet.
Conclusion
The correct answer is 4 boards, as this provides enough wood to meet the requirements for all shelves without falling short or excessively exceeding the needed material. Other options either do not provide enough wood or result in unnecessary surplus, demonstrating a clear understanding of the material requirements for the task at hand.
Answer: D
Mike will be 12 miles ahead of John.
After 4 hours, Mike will have biked a total distance of 48 miles, while John will have covered only 36 miles, leading to Mike being 12 miles ahead of John.
A) John will be 6 miles ahead of Mike.
This option is incorrect because based on the calculated distances, John will not surpass Mike's distance after 4 hours. Instead, Mike will maintain a lead over John, making this statement false.
B) John will be 12 miles ahead of Mike.
This statement is also incorrect. The calculations show that John will not be ahead of Mike at any point in the given time frame, as Mike's speed is greater, leading to Mike being ahead instead.
C) Mike will be 6 miles ahead of John.
While this option suggests that Mike is ahead, it understates his lead. The actual calculated distance shows that Mike is 12 miles ahead of John after 4 hours, making this statement inaccurate.
D) Mike will be 12 miles ahead of John.
This option is correct. Based on the calculations of their distances after 4 hours, Mike will have traveled 48 miles while John will have only traveled 36 miles, resulting in a 12-mile lead for Mike.
Conclusion
The analysis confirms that Mike is consistently ahead of John due to his faster pace over the course of the event. While options A, B, and C misrepresent the distances, option D accurately reflects the outcome based on the given rates of travel for both participants. Thus, Mike being 12 miles ahead is the only correct conclusion.
10. Which equation represents the graphed line?
Answer: D
y = 1/3x + 1
The equation that represents the graphed line is y = 1/3x + 1, indicating a positive slope and a y-intercept of 1.
A) y = -1/3x + 3
This option represents a line with a negative slope of -1/3, which means it would decrease as x increases. Additionally, its y-intercept of 3 is not consistent with the given line that intersects the y-axis at 1.
B) y = 3x - 7
This equation has a steep positive slope of 3 and a y-intercept of -7. This suggests a much steeper increase than the line in question, which does not match the characteristics of the graphed line.
C) y = 3x + 7
With a slope of 3 and a y-intercept of 7, this option indicates a line that rises sharply and intersects the y-axis much higher than the line represented by the correct answer. This makes it inconsistent with the graphed line.
D) y = 1/3x + 1
This is the correct option as it correctly describes a line with a slope of 1/3 and a y-intercept of 1. The positive slope indicates that the line rises gradually, consistent with the graph's appearance.
Conclusion
The choice of y = 1/3x + 1 is confirmed as the correct equation for the graphed line due to its accurate slope and y-intercept. All other options fail to match the slope or intercept of the graphed line, clearly demonstrating their inaccuracy.