GED Mathematical reasoning 3 — Questions and Answers

Question 1: A great circle of a sphere lies on its surface and contains its center. What is the circumference of a great circle of a sphere that has a surface area that measures 1,476 square centimeters? <div><br></div><div>NOTE: <span style="font-family: sans-serif; font-size: 13px; line-height: 19px; background-color: rgb(255, 255, 255);"><span class="texhtml" style="font-family: 'Times New Roman', 'Nimbus Roman No9 L', Times, serif; font-size: 15px; white-space: nowrap;">Π (or Pi) equals 3.14.<b> </b></span></span></div></span> (math4)

Approximately 68.1</span></label></li> (Correct answer)
74.5</span></label></li>
86.1</span></label></li>
54.7</span></label></li>

Correct answer: Approximately 68.1</span></label></li>

First, we use the given surface area of the sphere (1476 cm²) and the formula for the surface area of a sphere (SA = 4πr²) to solve for the radius (r). Once the radius is found (approximately 10.84 cm), we use it in the formula for the circumference of a circle (C = 2πr). Plugging in the values and using π ≈ 3.14, we calculate the circumference to be approximately 68.1 cm.

Question 2: What is the mean of this data set?<div><br></div><div>8, 47, 13, 17, 26, 32</div></span>

23.83</span></label></li> (Correct answer)
23.79</span></label></li>
23.62</span></label></li>
24</span></label></li>

Correct answer: 23.83</span></label></li>

The mean of a data set is calculated by summing all the values in the set and then dividing by the total number of values. For the given data set (8, 47, 13, 17, 26, 32), the sum is 143. Since there are 6 values, dividing 143 by 6 gives a mean of approximately 23.83.

Question 3: What is the median of this data set? <div><br></div><div>17, 42, 53, 97, 102, 82</div></span>

76.5</span></label></li>
53</span></label></li>
67.5</span></label></li> (Correct answer)
42</span></label></li>

Correct answer: 67.5</span></label></li>

To find the median, first arrange the data set in ascending order: 17, 42, 53, 82, 97, 102. Since there is an even number of values (6), the median is the average of the two middle numbers. The two middle numbers are 53 and 82, and their average is (53 + 82) / 2 = 67.5.

Question 4: There are three books sold in different quantities. A $10 book sells six copies. A $5 book sells five copies. A $2 book sells three copies. What is the median price of all the books sold? </span>

$6.50</span></label></li>
$6.50</span></label></li>
$5.00</span></label></li> (Correct answer)
$5.25</span></label></li>

Correct answer: $5.00</span></label></li>

To find the median price, we first list all the individual prices of the books sold in ascending order. There are 3 books at $2, 5 books at $5, and 6 books at $10, totaling 14 books. Since there's an even number of books, the median is the average of the 7th and 8th values in the ordered list. Both the 7th and 8th values are $5, making the median price $5.00.

Question 5: Identify mode for the following data: <div><br></div><div>2, 2, 2, 2, 7, 7, 7, 7, 7, 7, 9, 9, 9, 11, 11, 13, 12, 9, 9, 9, 2, 7, 7, 7</div></span>

2</span></label></li>
7</span></label></li> (Correct answer)
11</span></label></li>
9</span></label></li>

Correct answer: 7</span></label></li>

The mode of a data set is the value that appears most frequently. By counting the occurrences of each number in the given data set, we find that the number 7 appears 9 times, which is more than any other number. Therefore, 7 is the mode.

Question 6: Solve using the substitution method: <div><br></div><div>NOTE: Round long decimals to the nearest one hundredth. <br><div><br></div><div>y = 3x - 87</div><div>3x + 2y = 21</div><div><br></div><div><br></div></div></span>

x=-21.67<BR>y=21.99</span></label></li>
x=21.67<BR>y=-21.99</span></label></li> (Correct answer)
x=21.67<BR>y=21.99</span></label></li>
x=-21.99<BR>y=-21.67</span></label></li>

Correct answer: x=21.67<BR>y=-21.99</span></label></li>

We use the substitution method by plugging the expression for 'y' from the first equation (y = 3x - 87) into the second equation (3x + 2y = 21). This results in 3x + 2(3x - 87) = 21, which simplifies to 9x - 174 = 21. Solving for x gives x ≈ 21.67. Substituting this value of x back into the first equation yields y = 3(21.67) - 87, which calculates to y ≈ -21.99.

Question 7: If the product of 6 and an integer, n, is increased by 13, the result is -14. What is the value of n? </span>

-4.5</span></label></li> (Correct answer)
4.5</span></label></li>
162</span></label></li>
148</span></label></li>

Correct answer: -4.5</span></label></li>

The problem translates to the algebraic equation 6n + 13 = -14. To solve for n, first subtract 13 from both sides, resulting in 6n = -27. Then, divide both sides by 6, which gives n = -4.5.

Question 8: Solve for the positive value of c. <div><br></div><div>9c<sup>2</sup> - 11 = 718</div></span>

6</span></label></li>
9</span></label></li> (Correct answer)
11</span></label></li>
4</span></label></li>

Correct answer: 9</span></label></li>

To solve for c, first isolate the c² term by adding 11 to both sides of the equation, yielding 9c² = 729. Next, divide both sides by 9 to get c² = 81. Finally, take the square root of both sides, which gives c = ±9. Since the question asks for the positive value of c, the answer is 9.

Question 9: Solve for x: <BR><div> </div><BR><div>-5x - 5 > 15</div></span>

x > -4</span></label></li>
x < -4</span></label></li> (Correct answer)
x > 4</span></label></li>
x = -4</span></label></li>

Correct answer: x < -4</span></label></li>

To solve the inequality -5x - 5 > 15, first add 5 to both sides, resulting in -5x > 20. When dividing both sides of an inequality by a negative number, it is crucial to reverse the direction of the inequality sign. Dividing by -5 yields x < -4.

Question 10: What value does this numerical expression indicate?

8
10 (Correct answer)
56
89

Correct answer: 10

Without the specific numerical expression provided in the image, we assume it evaluates to 10. For example, if the expression was '2 * 5', multiplying these numbers directly gives 10. If it was '12 - 2', subtracting 2 from 12 also results in 10.

Question 11: Which expression describes the distance between the two spots indicated on this number line most accurately?

|−1 + 5|
−1 − 5
−1 + 5
|−1 − 5| (Correct answer)

Correct answer: |−1 − 5|

The distance between two points on a number line is found by taking the absolute value of their difference. If the two points indicated are -1 and 5, the distance can be expressed as |(-1) - 5| or |5 - (-1)|. Both expressions simplify to |-6| or |6| respectively, which both equal 6, representing the distance between the points.

Question 12: 8.32 × 3.2 =

17.416
26.624 (Correct answer)
201.64
143.24

Correct answer: 26.624

To multiply 8.32 by 3.2, first multiply the numbers as if they were whole numbers: 832 × 32 = 26624. Then, count the total number of decimal places in the original numbers (two in 8.32 and one in 3.2, for a total of three). Place the decimal point three places from the right in the product, resulting in 26.624.

Question 13: A building can be painted in 5 days by 10 persons. How much of the building could 7 individuals paint in 5 days if they all painted as quickly as the others?

7/10 (Correct answer)
9/7
7/5
6/5

Correct answer: 7/10

This is a direct proportion problem involving work rate. If 10 people can paint an entire building in 5 days, then each person contributes 1/10 of the work in those 5 days. Therefore, if 7 individuals work for the same 5 days, they will complete 7 times the amount of work one person does, which is 7 * (1/10) = 7/10 of the building.

Question 14: In 21 feet, how many meters are there?

5.258
64.25
6.4615 (Correct answer)
516.15

Correct answer: 6.4615

To convert feet to meters, we use the conversion factor that 1 foot is approximately equal to 0.3048 meters. Multiplying 21 feet by this conversion factor (21 * 0.3048) gives approximately 6.4008 meters. Among the given options, 6.4615 meters is the closest value.

Question 15: What value of x results in y = 15 - 3x and y = 0?

5 (Correct answer)
8
15
17

Correct answer: 5

To find the value of x when y = 0, substitute 0 for y in the equation y = 15 - 3x. This results in 0 = 15 - 3x. Then, add 3x to both sides to get 3x = 15. Finally, divide by 3, which yields x = 5.

Question 16: Arrange the following four fractions: 1/4, 2/3, 4/7, and 1/2 from smallest to largest.

1/2, 2/3, 1/4, 4/7
1/4, 1/2, 4/7, 2/3 (Correct answer)
1/4, 1/2, 2/3, 4/7
1/4, 4/7, 1/2, 2/3

Correct answer: 1/4, 1/2, 4/7, 2/3

To arrange the fractions from smallest to largest, convert each fraction to its decimal equivalent: 1/4 = 0.25, 1/2 = 0.5, 4/7 ≈ 0.571, and 2/3 ≈ 0.667. Ordering these decimals from least to greatest gives 0.25, 0.5, 0.571, 0.667. Therefore, the fractions in ascending order are 1/4, 1/2, 4/7, 2/3.

Question 17: What is the distance between -3/7 and -2/3 on a number line?

5/21 (Correct answer)
2/4
3/14
9/22

Correct answer: 5/21

The distance between two numbers on a number line is found by taking the absolute value of their difference. First, find a common denominator for -3/7 and -2/3, which is 21, converting them to -9/21 and -14/21 respectively. Then, calculate the absolute difference: |-9/21 - (-14/21)| = |-9/21 + 14/21| = |5/21|. The distance is therefore 5/21.

Question 18: Two of the sides of an isosceles triangle are equal. What is the triangle's perimeter if two of its sides are 5 inches and 2 inches?

6 inches
12 inches (Correct answer)
18 inches
24 inches

Correct answer: 12 inches

An isosceles triangle has two sides of equal length. Given sides of 5 inches and 2 inches, there are two possibilities for the side lengths: (5, 5, 2) or (2, 2, 5). However, for a triangle to be valid, the sum of the lengths of any two sides must be greater than the length of the third side. The combination (2, 2, 5) is invalid because 2 + 2 is not greater than 5. Therefore, the sides must be 5, 5, and 2 inches, making the perimeter 5 + 5 + 2 = 12 inches.

Question 19: The volume of the cylinder below, measured to the nearest cubic inch, is 6283 cubic inches with r = 10 inches. To the nearest inch, determine the cylinder's height.

20 inches (Correct answer)
14 inches
26 inches
13 inches

Correct answer: 20 inches

The volume of a cylinder is calculated using the formula V = πr²h, where V is volume, r is radius, and h is height. Given the volume is 6283 cubic inches and the radius is 10 inches, we can plug these values into the formula: 6283 = π(10)²h. Using π ≈ 3.14, this becomes 6283 = 3.14 * 100 * h, or 6283 = 314h. Dividing 6283 by 314 yields h ≈ 20.009, which rounds to 20 inches for the cylinder's height.

Question 20: The equation h=-t2+3t+10, where t is time in seconds and h is height above a platform and is in computer units, can be used to simulate the trajectory of a rocket on a computer screen. Find out how long it takes the rocket to arrive at the platform.

4 seconds
5 seconds (Correct answer)
11 seconds
16 seconds

Correct answer: 5 seconds

The rocket arrives at the platform when its height (h) is 0. So, we set the equation h = -t² + 3t + 10 to 0: 0 = -t² + 3t + 10. Multiplying by -1 to make the leading coefficient positive gives t² - 3t - 10 = 0. Factoring this quadratic equation yields (t - 5)(t + 2) = 0, which gives possible solutions of t = 5 or t = -2. Since time cannot be negative in this context, the rocket takes 5 seconds to arrive at the platform.

GED Mathematical reasoning 3

A great circle of a sphere lies on its surface and contains its center.
What is the circumference of a great circle of a sphere that has a surface area that measures 1,476 square centimeters?
NOTE: Π (or Pi) equals 3.14. (math4)