GED Mathematical Reasoning Answers

Question 1

Last weekend, 625 runners entered a 10,000-meter race. A 10,000- meter race is 6.2 miles long. Ruben won the race with a finishing time of 29 minutes 51 seconds.
The graphs show information about the top 10 runners.
Based on the scatter plot, what is the range of ages of the top 10 runners?

Your Answer: Option(s)

Correct Answer: Option(s) C

Rationale

The range of ages of the top 10 runners is 16.

The range of ages can be determined by finding the difference between the highest and lowest ages among the top 10 runners. In the given scatter plot, the highest age is 36 and the lowest age is 20. Calculating the difference between these ages gives a range of 16.

A) 9
This is incorrect as the range of ages of the top 10 runners is not 9. The difference between the highest and lowest ages is 16, not 9.

B) 1
This is incorrect as the range of ages of the top 10 runners is not 1. The actual range, as calculated from the scatter plot, is 16.

C) 16
This is the correct answer. The range of ages of the top 10 runners is indeed 16, as determined by subtracting the lowest age (20) from the highest age (36).

D) 40
This is incorrect as the range of ages of the top 10 runners is not 40. The difference between the highest and lowest ages is 16, not 40.

Conclusion
By analyzing the scatter plot provided for the top 10 runners in the race, it is evident that the range of ages among these individuals is 16. This range is calculated by subtracting the lowest age from the highest age, resulting in a span of 16 years across the top 10 participants.

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Question 2

Last weekend, 625 runners entered a 10,000-meter race. A 10,000- meter race is 6.2 miles long. Ruben won the race with a finishing time of 29 minutes 51 seconds.
The graphs show information about the top 10 runners.
Based on the histogram, which statement describes the finishing time of the runner in position 3?

Your Answer: Option(s)

Correct Answer: Option(s) C

Rationale

The finishing time was between 31 and 32 minutes.

Position 3 on the histogram falls within the time range of 31 to 32 minutes, indicating the finishing time of the runner in that position.

A) The finishing time was between 30 and 31 minutes
This statement does not align with the data shown in the histogram, as the time range for position 3 is slightly higher.

B) The finishing time was between 33 and 34 minutes
This time range is higher than the actual finishing time of the runner in position 3 as per the histogram data.

D) The finishing time was between 32 and 33 minutes
While close, this time range does not accurately represent the finishing time of the runner in position 3 based on the given histogram.

Conclusion
By analyzing the histogram data provided for the top 10 runners in the race, it is evident that the runner in position 3 completed the race within the time frame of 31 to 32 minutes. This conclusion is drawn directly from the graphical representation of the finishing ×, highlighting the performance of the third-place finisher in the context of the overall race results.

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Question 3

The equation and the graph represent two linear functions.
Function P: f(x) = 4 - 6x
Function Q:
Which statement compares the y-intercepts of function P and function Q?

Your Answer: Option(s)

Correct Answer: Option(s) D

Rationale

The y-intercept of function P is 4 which is greater than the y-intercept of function Q.

The y-intercept of a linear function represents the value of the function when x = 0. In function P, when x = 0, f(x) = 4, indicating the y-intercept is at 4. Therefore, the y-intercept of function P is 4, which is greater than the y-intercept of function Q.

A) The y-intercept of function P is -6 which is less than the y-intercept of function Q.
This statement is incorrect because the y-intercept of function P is 4, not -6. The y-intercept of function P is positive, not negative.

B) The y-intercept of function P is 4 which is equal to the y-intercept of function Q.
This statement is incorrect. The y-intercept of function P is indeed 4, but it does not equal the y-intercept of function Q, which is not provided in the question.

C) The y-intercept of function P is -6 which is greater than the y-intercept of function Q.
This statement is incorrect. The y-intercept of function P is not -6; it is 4. Therefore, it is not greater than the y-intercept of function Q as stated.

Conclusion
The correct answer is D. The y-intercept of function P is 4, as represented by the constant term in the function f(x) = 4 - 6x. This value of 4 is greater than the y-intercept of function Q, which is not explicitly provided in the question. The comparison clearly shows that the y-intercept of function P is greater than that of function Q.

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Question 4

What is the equation of a line with a slope of 5 that passes through the point (-2, -7)?

Your Answer: Option(s)

Correct Answer: Option(s) C

Rationale

y=5x-17

Given a slope of 5 and a specific point (-2, -7) on the line, the equation can be determined using the point-slope form: y - yâ‚ = m(x - xâ‚), where m represents the slope and (xâ‚, yâ‚) is the point. Substituting -2 for xâ‚, -7 for yâ‚, and 5 for the slope m, the equation becomes y - (-7) = 5(x - (-2)), which simplifies to y + 7 = 5(x + 2) and further reduces to y + 7 = 5x + 10, finally yielding y = 5x - 17 after isolating y.

A) y=5x+3
This equation incorrectly adds 3 instead of subtracting 17, thus not reflecting the line's passage through the given point (-2, -7) with a slope of 5.

B) y=5x-3
Similar to choice A, this option erroneously adjusts the y-intercept to -3 instead of -17, deviating from the correct equation.

C) y=5x-17
The correct answer, accurately reflecting the line's slope of 5 and its passage through the point (-2, -7) by subtracting 17 from the product of 5 and x.

D) y=5x+17
In contrast to the correct equation, this choice incorrectly adds 17 instead of subtracting it, leading to an inaccurate representation of the line's characteristics and point of intersection.

Conclusion
By applying the point-slope formula with the given slope and point, the correct equation y=5x-17 defines a line that satisfies both conditions simultaneously: a slope of 5 and passage through the point (-2, -7). The correlation between the slope and the specific point allows for a unique equation that precisely describes the line in question, showcasing the importance of understanding the point-slope form in determining linear relationships.

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Question 5

The Great Pyramid at Giza in Egypt is a square pyramid that measures approximately 756 feet on each side. The height of the pyramid is approximately 450 feet. What is the approximate volume, in cubic feet, of the pyramid?

Your Answer: Option(s)

Correct Answer: Option(s) B

Rationale

Choice B) 85,730,400

The volume of a square pyramid is calculated using the formula V = (1/3) * base area * height. Given the base of the pyramid is a square with sides of 756 feet and a height of 450 feet, the volume can be determined by substituting these values into the formula.

A) 51,030,000
This value does not align with the correct calculation for the volume of a square pyramid with the provided dimensions. The error likely stems from an incorrect application of the volume formula or a miscalculation of the base area.

C) 226,800
This value is significantly lower than the correct answer and does not represent the volume of the Great Pyramid at Giza based on the given dimensions. It seems to be a miscalculation or misinterpretation of the volume formula for a square pyramid.

D) 453,600
This value is also incorrect when determining the volume of the pyramid. The calculation appears to have deviated from the correct formula or involved incorrect substitutions of the base area and height into the volume equation.

Conclusion
The volume of the Great Pyramid at Giza, a square pyramid with 756-foot sides and a height of 450 feet, is approximately 85,730,400 cubic feet. This calculation follows the formula for the volume of a square pyramid and accurately represents the three-dimensional space enclosed by the pyramid's structure.

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The range of ages of the top 10 runners is 16.

The finishing time was between 31 and 32 minutes.

The y-intercept of function P is 4 which is greater than the y-intercept of function Q.

y=5x-17

Choice B) 85,730,400

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