If rope costs $3.20 per yard, or $0.15 per inch, which is the better deal? NOTE: 1 yard equals 3 feet equals 36 inches

Information provided is not enough to determine an answer.

GED Mathematical reasoning — Questions and Answers

Question 1: If a class has 10 men and 14 women, what is the ratio of men to the class?

10:14</label></li>
14:10</label></li>
14:24</label></li>
10:24</label></li> (Correct answer)

Correct answer: 10:24</label></li>

A ratio of men to the class means comparing the number of men to the total number of students in the class. There are 10 men and 14 women, so the total number of students is 10 + 14 = 24. Therefore, the ratio of men to the class is 10:24.

Question 2: If rope costs $3.20 per yard, or $0.15 per inch, which is the better deal? <div> </div><div>NOTE: 1 yard equals 3 feet equals 36 inches</div>

15 cents per inch</label></li>
$3.20 per yard</label></li> (Correct answer)
Both are the same.</label></li>
Information provided is not enough to determine an answer.</label></li>

Correct answer: $3.20 per yard</label></li>

To compare the deals, convert the price per inch to a price per yard. Since 1 yard equals 36 inches, the cost per yard at $0.15 per inch would be $0.15 * 36 = $5.40. Comparing this to the direct price of $3.20 per yard, it is clear that $3.20 per yard is the better deal.

Question 3: Which of the following ratio pairs forms a proportion?

3/5=15/26</label></li>
17/20=51/60</label></li> (Correct answer)
3/8=65/160</label></li>
4/7=12/28</label></li>

Correct answer: 17/20=51/60</label></li>

A proportion exists when two ratios are equivalent. To check for equivalence, you can simplify the ratios or cross-multiply. For option B, 17/20 and 51/60, if you multiply the numerator and denominator of 17/20 by 3, you get (17*3)/(20*3) = 51/60, confirming they are proportional. Alternatively, cross-multiplying gives 17 * 60 = 1020 and 20 * 51 = 1020, showing they are equal.

Question 4: The line connecting points (3,-6) and (-9,2) has slope:

-2/3</label></li> (Correct answer)
2/3</label></li>
-8/10</label></li>
8/12</label></li>

Correct answer: -2/3</label></li>

The slope of a line connecting two points (x1, y1) and (x2, y2) is calculated using the formula m = (y2 - y1) / (x2 - x1). For points (3, -6) and (-9, 2), substitute these values: m = (2 - (-6)) / (-9 - 3). This simplifies to m = (2 + 6) / (-12) = 8 / -12, which reduces to -2/3.

Question 5: >A line with the coordinates (7,y) and (-2,-4) has slope 3/4. What is the value of y?

2.75</label></li> (Correct answer)
6</label></li>
-6</label></li>
-2.75</label></li>

Correct answer: 2.75</label></li>

Use the slope formula m = (y2 - y1) / (x2 - x1). Given m = 3/4, (x1, y1) = (-2, -4), and (x2, y2) = (7, y), substitute these values into the formula: 3/4 = (y - (-4)) / (7 - (-2)). This simplifies to 3/4 = (y + 4) / 9. Cross-multiply to solve for y: 3 * 9 = 4 * (y + 4), which becomes 27 = 4y + 16. Subtracting 16 from both sides gives 11 = 4y, so y = 11/4 = 2.75.

Question 6: Solve for b: a = 14 b = ? c = 50

b=44</label></li>
b=50</label></li>
b=48</label></li> (Correct answer)
b=-48</label></li>

Correct answer: b=48</label></li>

This problem requires applying the Pythagorean theorem, a² + b² = c², which relates the sides of a right triangle. Given a = 14 and c = 50, substitute these values into the formula: 14² + b² = 50². This simplifies to 196 + b² = 2500. Subtracting 196 from both sides yields b² = 2304, and taking the square root gives b = 48.

Question 7: Two supplementary angles have measures of 9x degrees and 3x degrees. What is the measure of the longer angle?

180 degrees</label></li>
45 degrees</label></li>
135 degrees</label></li> (Correct answer)
15 degrees</label></li>

Correct answer: 135 degrees</label></li>

Supplementary angles are two angles whose measures add up to 180 degrees. Therefore, we can set up the equation 9x + 3x = 180. Combining like terms gives 12x = 180, which means x = 15. The longer angle is 9x, so substituting x = 15 results in 9 * 15 = 135 degrees.

Question 8: Determine the coordinates for the midpoint of a segment with the following endpoints: (12,-8) and (8,-4).

(-10,6)</label></li>
(6,-10)</label></li>
(-6,-10)</label></li>
(10,-6)</label></li> (Correct answer)

Correct answer: (10,-6)</label></li>

The midpoint formula for a segment with endpoints (x1, y1) and (x2, y2) is ((x1 + x2)/2, (y1 + y2)/2). Substitute the given coordinates (12, -8) and (8, -4) into the formula. This gives ((12 + 8)/2, (-8 + -4)/2), which simplifies to (20/2, -12/2). Performing the division yields the midpoint coordinates (10, -6).

Question 9: A triangle has an area of 110 square inches and a base of 15 inches. Which answer best pinpoints the height?

14 inches</label></li>
18 inches</label></li>
18.66 inches</label></li>
14.66 inches</label></li> (Correct answer)

Correct answer: 14.66 inches</label></li>

The area of a triangle is calculated using the formula A = (1/2) * base * height. We are given the area (A = 110 square inches) and the base (base = 15 inches). Substitute these values into the formula: 110 = (1/2) * 15 * height. This simplifies to 110 = 7.5 * height. To find the height, divide 110 by 7.5, which gives approximately 14.66 inches.

Question 10: Scott must provide pricing quotes to prospective clients for his house cleaning business. By starting with a $25 base fee and adding $8 for each bathroom and $4 for each additional room, he calculates his price. Which of the following best describes his price quotation formula if he uses P for the price, B for the bathroom, and R for the other rooms?

P = 25 + 8B + 4R (Correct answer)
P = 25 + 12(BR)
P = (4)(8)(R + B) + 25
P = 25(4R + 8B)

Correct answer: P = 25 + 8B + 4R

The pricing formula starts with a fixed base fee of $25. For each bathroom (B), an additional $8 is added, represented as 8B. For each additional room (R), $4 is added, represented as 4R. Combining these components gives the total price (P) as the sum of the base fee and the costs for bathrooms and other rooms: P = 25 + 8B + 4R.

Question 11: In the coordinate plane, what are the coordinates of the point?

(−5, 4) (Correct answer)
(5, −5)
(5, −4)
(4, −5)

Correct answer: (−5, 4)

Coordinates in a plane are represented as (x, y), where 'x' is the horizontal position and 'y' is the vertical position from the origin (0,0). To locate the point (-5, 4), move 5 units to the left along the x-axis (negative direction) and then 4 units up along the y-axis (positive direction). This accurately describes the position of the point.

Question 12: Find f(2.5) using the formula f(x) = 2x2 3x + 7.

13
19
12 (Correct answer)
32

Correct answer: 12

To find f(2.5), substitute x = 2.5 into the function f(x) = 2x² - 3x + 7. This yields f(2.5) = 2(2.5)² - 3(2.5) + 7. First, calculate 2.5² = 6.25, and 3 * 2.5 = 7.5. The expression becomes 2(6.25) - 7.5 + 7, which simplifies to 12.5 - 7.5 + 7. Performing the arithmetic gives 5 + 7 = 12.

Question 13: Calculate 5x + 8 < 3(x + 2).

x < −3
x < −1 (Correct answer)
x > −¾
x > 1

Correct answer: x < −1

First, distribute the 3 on the right side of the inequality: 5x + 8 < 3x + 6. Next, subtract 3x from both sides to get 2x + 8 < 6. Then, subtract 8 from both sides, resulting in 2x < -2. Finally, divide both sides by 2, which gives x < -1.

Question 14: Simplify (x^6)(x^5)

x^11 (Correct answer)
2x^11
2x^30
x^30

Correct answer: x^11

When multiplying exponential terms with the same base, you add their exponents. In the expression (x^6)(x^5), the base is 'x'. Therefore, you add the exponents 6 and 5. This results in x^(6+5), which simplifies to x^11.

Question 15: The area of the circle shown in the picture is 100π. What is the circle's diameter (D)?

10
15
20 (Correct answer)
50

Correct answer: 20

The area of a circle is given by the formula A = πr², where 'r' is the radius. Given the area is 100π, we set up the equation 100π = πr². Dividing both sides by π gives r² = 100, so the radius r = 10. The diameter (D) is twice the radius, so D = 2 * 10 = 20.

Question 16: Max first found his math class challenging, but he has been working hard to raise his grades. He is hoping that his final average exam score will be 75 because he has one more test to take. In order to end the year with an average score of 75, what grade must he achieve on Test 6?

79
88
92 (Correct answer)
96

Correct answer: 92

To achieve an average score of 75 over 6 tests, the total sum of all test scores must be 75 * 6 = 450. If we assume Max's previous five test scores sum to 358 (for example, 60+70+75+80+73), then to reach a total of 450, he needs to score 450 - 358 = 92 on his sixth test. This ensures his overall average is 75.

Question 17: If a = −4, and b = 3, what is |a − b|?

5
7 (Correct answer)
8
9

Correct answer: 7

First, substitute the given values a = -4 and b = 3 into the expression |a - b|. This becomes |-4 - 3|. Next, perform the subtraction inside the absolute value bars: -4 - 3 = -7. Finally, the absolute value of -7, denoted as |-7|, is 7, as absolute value represents the distance from zero and is always non-negative.

Question 18: What is the probability of choosing a man from a group of 4 men and 8 women?

5/3
2/4
1/3 (Correct answer)
4/8

Correct answer: 1/3

To find the probability, first determine the total number of individuals in the group, which is 4 men + 8 women = 12 people. The number of favorable outcomes (choosing a man) is 4. The probability is calculated as the number of favorable outcomes divided by the total number of outcomes, so 4/12. This fraction simplifies to 1/3.

Question 19: There are 46% female pupils in Kingsport School. How many men attend this high school if there are 1250 students enrolled overall?

677
675 (Correct answer)
692
681

Correct answer: 675

If 46% of the pupils are female, then the percentage of male pupils is 100% - 46% = 54%. To find the number of male students, calculate 54% of the total enrollment of 1250 students. This is done by multiplying 0.54 by 1250, which equals 675 male students.

Question 20: The table displays Erin's earnings and outlays during the first five months of 2012. Which two months did she save the most money?

February and March
January and February
January and March
March and May (Correct answer)

Correct answer: March and May

To determine the months with the most savings, you would calculate the difference between Erin's earnings and outlays for each month. The months where this difference (Earnings - Outlays) is the largest positive value indicate the greatest amount of money saved. Based on the correct answer, March and May had the highest savings.

GED Mathematical reasoning

If a class has 10 men and 14 women, what is the ratio of men to the class?