Chapter 8

Section 4: Mathematical Reasoning

The Mathematical Reasoning section consists of a series of questions intended to measure general mathematics skills and problem-solving ability. The questions are based on short readings that may include a graph, chart, or figure.

You have 90 minutes to complete this section. The answers and explanations to this section’s questions are in Chapter 9. Go through the explanations to all the questions, even for the ones you answered correctly. The explanations are a good review of the mathematical techniques we discuss throughout the book.

Formulas you may need are given on the page before the first test question. Only some of the questions require you to use a formula, and you may not need all the formulas given. Note: If you can memorize the formulas and understand how to use them, you’ll save a bit of time on the test, and then you can use that time saved for review or for harder items that you may have more trouble with.

Unless you require accommodations, you’ll be taking the GED test on a computer. Instead of marking your answers on a separate answer sheet, like you do for the practice test sections in this book, you’ll see clickable ovals and fill-in-the-blank text boxes, and you’ll be able to click with your mouse and drag and drop items where indicated. We formatted the question and answer choices in this book to make them appear as similar as possible to what you’ll see on the computer-based test, but we had to retain some A, B, C, D choices for marking your answers, and we provide an answer sheet for you to do so.

Mathematics Formula Sheet

Mathematical Reasoning Test

Time: 90 minutes

Directions: Choose the appropriate answer for each question. Mark your answers on the answer sheet provided by filling in the corresponding oval, writing your answer in the blank box or marking your answer on the graph.

1. Dharma is making sale signs for the Super Summer Sale at the Super Saver Swim Shop. Sales tax in Dharma's state is 5%. She makes a series of signs:

• Sign A: ½ off all merchandise
• Sign B: Buy one item, get the second item of equal value free
• Sign C: 50% off all merchandise
• Sign D: Nine times your sales tax back

What would a shrewd consumer notice about the signs?

(A) Sign A offers a better buy.

(B) Sign C offers the worst deal.

(C) Sign D offers the worst deal.

(D) Sign B offers a better deal.

2. Daryl is framing a picture. He draws the following diagram to help him make it:

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Which of the following is true about the diagram?

(A) ab must be perpendicular to ad.

(B) ab must be parallel to bc.

(C) ad must be parallel to ab.

(D) ab and dc must be perpendicular.

3. The Hammerhill family is building a deck behind their house. The deck is to be 16 feet long and 21 feet wide, and the decking material was priced at $45.00 a square yard. The cost, in dollars, of the decking material would be .

4. Margaret Millsford, the Chief Financial Officer of Aggravated Manufacturing Corporation, has to report to the Board of Directors. She has been instructed to analyze the sales of each of the company's product lines and recommend dropping the least profitable line. She found that although the per-unit profits of grommets and gadgets were the same, producing widgets off-shore doubled the profit. She prepared the following graph to demonstrate the relative volumes and made an oral presentation to illustrate the differing profitability of off-shore production and to back up her recommendation:

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Based on the graph and Margaret's oral presentation, her recommendation would be to drop

(A) widgets

(B) grommets

(C) gadgets

(D) grommets and widgets

5. Quan is obsessive about his marks and how they compare to the rest of his class. On Quan's final report, his results were as follows:

• Computer Studies: 97
• English: 98
• Mathematics: 99
• Physical Education: 87
• Science: 97
• Social Studies: 94
• Spanish: 86

The results for Quan's entire class were

• Average: 93.27
• Median: 96
• Mode: 97
• Range: 14

Calculate Quan's average, median, mode, and range, and then compare them to the results of his class. If Quan is most concerned about being admitted to college, the measure he should be most concerned about is .

6. Alice was trying to explain how the length of time she could run each morning had improved each month since she started, except for the month she twisted her ankle. She drew the following graph to show her friends Mary and Kevin the average length of time (in minutes) she ran each day each month:

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In which month did Alice likely twist her ankle?

(A) June

(B) February

(C) August

(D) September

7. Dominic and Paula were comparing their report cards, as follows:

Dominic's Report Card

Subject	Grade (%)
Mathematics	63
Social Studies	76
Science	65
Language Arts	84
Physical Education	72

Paula's Report Card

Subject	Grade (%)
Mathematics	80
Social Studies	64
Science	76
Language Arts	72
Physical Education	88

The teacher told them that the ratio of their total marks was very close. What is the ratio of Paula's marks to Dominic's marks on these report cards?

(A) 9:10

(B) 18:19

(C) 10:9

(D) 19:18

8 In the series, 4, 6, 10, 18, . . . , the first term that is a multiple of 11 is .

9. Simone follows the stock market very carefully. She has been following Cowardly Corporation the last few months, keeping track of her research in the following table:

Date	Closing Price (In U.S. Dollars)
August 7	15.03
August 17	16.12
September 1	14.83
September 9	15.01
September 16	14.94
September 20	15.06
September 23	15.17
September 24	15.19

Simone bought shares of the stock on September 24 and wants to make money before selling it. She paid 3% commission to her broker for buying and will pay the same again for selling. What is the lowest price (in U.S. dollars) for which Simone can sell each of her shares to break even?

(A) $16.48

(B) $16.13

(C) $15.66

(D) $20.00

10. If , what is the value of a?

(A) 0

(B) –56

(C) 4

(D) –4

Questions 11–12 refer to the following graph.

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11. Calculate the slope of the line AB. The slope of AB is .

12. If the slope of AB remains the same, but it intercepts the y-axis at C (0, 4), where does it intersect the x-axis? Use the graph on the answer sheet to indicate the point where AB intersects the x-axis.

13. If a fire is built in the center of a square barbeque pit, where is the safest place to stand to avoid the intense heat of the fire?

(A) at a corner

(B) along the left side

(C) along the right side

(D) not enough information given

14. Lydia and Wayne are shopping for carpets for their home and are looking for the best carpet at the best price. Carnie's Carpets offers them a wool carpet for $21.50 per square yard. Flora's Flooring says they will match that same carpet for only $2.45 per square foot, while Dora's Deep Discount offers them an 8-x-12-foot rug of the same carpet material for $210.24. What is the lowest price per square foot offered to Lydia and Wayne?

(A) $2.45

(B) $21.90

(C) $2.19

(D) $2.39

15. Miscellaneous Appliances Limited is concerned about its output at Plant A. For its annual report, company officials prepared the following graphs to show the output for each quarter of the last two years:

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Which quarter showed a dramatic increase in production in 2014?

(A) third quarter

(B) first quarter

(C) fourth quarter

(D) second quarter

16. Mr. and Mrs. Ngs are looking to expand their two-story house and have calculated that they need at least another 630 square feet to live comfortably. They want to use the basement level for storage and the rest for living. A contractor quotes them $15.80 per square foot for the renovation without redecoration. A real estate agent tells them that they can increase the value of their home by about $18,000 by building the addition. If they want to add as much additional space as possible for the $18,000 they will recover, they would have to add additional square feet.

17. An experiment involving throws of a 20-sided die produced the following results:

Throw	Left-Handed	Right-Handed
1	2	4
2	4	12
3	5	2
4	9	6
5	11	13
6	10	15
7	4	17
8	6	3
9	7	5

Use the graph on the answer sheet to indicate the point that represents the combined medians of the throws, using the median of the left-handed results as the x-value and the median of the right-handed results as the y-value.

18. LeeAnne is shopping for a new vehicle. She drives about 18,000 miles per year. She is most concerned about the cost of gasoline. She expects gasoline to average $3.50 a gallon during the five years she will own the car and is basing her decision on that price. As she shops, she creates a chart based on her calculations:

Type of Vehicle	Miles per Gallon
SUV	12.8
Sedan	19.6
2-door	19.5
All-wheel drive	17.2
Sports car	18.6

Based on her criteria, which car should LeeAnne buy?

(A) SUV

(B) sedan

(C) 2-door

(D) sports car

19. Tom is worried about getting to the GED testing center on time. He knows that he averages 40 miles per hour on the route to the test. If the test site is 47 miles from Tom's house and he wants to arrive 20 minutes early, how do you figure out how much time he needs to leave for travel and waiting?

(A) add then divide

(B) multiply then add

(C) divide then add

(D) add then multiply

20. Leonora has just received her mid-term report card. Her grades are as follows:

Leonora's Report Card

Subject	Grade (%)
English	84
Geography	78
Mathematics	68
Physical Education	77
Physics	82

Her average grade is 77.8%. To get into the college of her choice, she needs an average of 80%. English is her best subject. By how many percentage points will her English score have to go up, assuming all her other subjects stay the same, to get into college?

(A) 8

(B) 9

(C) 10

(D) 11

21. Sonia has an amazing recipe for rice. For each 1 cup of rice, she adds 2 cups of vegetable soup and a quarter cup of lentils. This weekend, Sonia is having a large dinner party and figures she needs to cook 3½ cups of rice for her guests. How much of the other two ingredients should she use?

(A) 7 cups of soup and ⅞ cup of lentils

(B) 3½ cups of soup and ½ cup of lentils

(C) 7 cups of soup and 1 cup of lentils

(D) 1 cup of soup and 7 cups of lentils

22. In drawing cards from a deck, any single card has an equal chance of being drawn. After six cards have been drawn and removed, what is the probability of drawing an ace of hearts if it has not yet been drawn?

(A) 1:50

(B) 1:48

(C) 1:46

(D) 1:44

23. The Symons are redecorating a room in their house. They have some interesting ideas. They want to put a rug on the floor surrounded by a border of tiles. They are considering teak paneling halfway up each wall. In addition, they may cut away part of the ceiling to put in a skylight. This is a diagram of their room:

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The rug costs $7.50 a square foot, and tile costs $9.00 a square foot. One rug they like is 16 feet by 10 feet, leaving just a little area around the rug for tiles. At the store, however, they see another rug that is only 12 feet by 8 feet, but it's just the right pattern and colors for their room. Which floor treatment is less expensive?

(A) both are the same cost

(B) the larger rug

(C) the smaller rug without the paneling

(D) the smaller rug

24. Brad is a secret shopper for the Friendly Furniture store. His job is to go to competitive stores and price a series of items to make sure his employer can advertise that he has the best prices. His boss wants to start a new advertising campaign: “Friendly Furniture — always lower than the average price of our competitors.” Brad's job is to shop several stores to make sure the claim is accurate. Brad's results are recorded in the following table:

Which item cannot be advertised as “lower than the average price”?

(A) couch

(B) dining room set

(C) loveseat

(D) coffee table

25. In a pistachio-eating contest, Sarah eats 48 pistachios in 18 minutes. If she could maintain her rate of eating pistachios, she could eat pistachios in 2 hours.

26. Kevin wants to paint his room, which is 9 feet 5 inches long, 8 feet 3 inches wide, and 8 feet 2 inches high. The paint can label cautions that air must be exchanged in the room every 12 minutes. When Kevin looks for exhaust fans to keep the air moving, he finds that they are calibrated in cubic feet per minutes. The operation that Kevin has to perform first to figure out which size fan he needs is .

27. Which of these shapes has the same relationship to the horizontal after a 90-degree rotation about a point on the perimeter?

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(A) isosceles triangle

(B) circle

(C) pentagon

(D) not enough information given

28. In a large company, the top four positions are organized as follows:

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Each department has the following budget:

Department	Budget ($ Millions)
Operations	14.7
Human Resources	2.1
Marketing	5.6

What is the ratio of the largest budget to the smallest budget?

29. A company has doubled its sales from the first to the third quarters. Graph indicates this pattern.

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30. A 6-foot tall forester standing some 16 feet from a tree uses his digital rangefinder to calculate the distance between his eye and the top of the tree to be 25 feet. How tall is the tree?

(A)

(B)

(C)

(D) not enough information

31. Lawrie is trying to save money, so she keeps her money in both checking and savings accounts. Each week, she puts $24.00 from her paycheck into her savings account. However, the fourth week, she overdraws her checking account by $7.50, and the bank transfers the money from her savings account. For providing this service, the bank charges Lawrie $10.00. Her savings account balance after the fourth week is $.

32. Sarah is negotiating the price of a chair for her room. The original price was $96.00. Store A offers her 1/3 off. Store B offers her a discount of 30%. She will save $ by taking the lower price.

Questions 33–34 are based on the following information and figure.

While a rock band is setting up for a concert, the audio engineer is calibrating the amplifiers used for the concert. He has an instrument that develops and displays a graph for each setting on the amplifier controls. The graph appears like this:

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33. From the graph, calculate the volume in decibels for a setting of 10 on the amplifier.

(A) 20

(B) 30

(C) 50

(D) 100

34. The equation that produced this graph is V = S², where V is the volume in decibels and S is the volume setting. If the volume is 144, what is the volume setting on the amplifier?

(A) 9

(B) 10

(C) 11

(D) 12

35. In this particular auditorium, the volume of sound decreases by half for every 10 feet away from the stage a person sits. If the volume at the stage is 144 decibels, the volume in decibels for a person sitting 20 feet from the stage will be

(A) 36

(B) 48

(C) 60

(D) 72

36. Gary and Georgina George bought a new car and are trying to estimate the gas mileage. The new car travels 240 miles at a cost of $54.00. The price of gasoline is $2.70 per gallon. They estimate that the car will get 18 miles per gallon. The actual mileage would be miles per gallon.

Question 37 is based on the following figures, which are reprinted from Physical Science: What the Technology Professional Needs to Know, by C. Lon Enloe, Elizabeth Garnett, Jonathan Miles, and Stephen Swanson (Wiley).

©John Wiley & Sons, Inc.

37. If the person pictured wants to remain at a constant temperature, what geometrical shape should he follow as a path?

(A) ellipse

(B) line

(C) square

(D) circle

38. Igor is in charge of the swimming pool at the local recreation center. The pool is 120 feet long and 24 feet wide and holds 12,902 cubic feet of water. The average depth of the pool in feet is .

Questions 39–42 refer to the following table.

*Annual cost includes 15,000 miles driven annually; 55% of the miles in the city and 45% on the highway; standard price of fuel

39. If you were in the market for a car, how much could you save, in dollars, over a three-year period, by buying the most economical car over the least economical car?

(A) 983

(B) 2,520

(C) 5,469

(D) 2,949

40. What is the difference in miles per gallon between the mean city mileage and the median of the city mileages for these vehicles?

(A) 1 2/3

(B) 1/3

(C) 17

(D) 2 1/2

41. Use the graph on the answer sheet to indicate the results for Vehicle A with the difference between city and highway mileage as the appropriate point on the y-axis.

42. To solve a problem in her mathematics class, Jan had to solve the following set of equations:

2x + 3y = 10

5x + 6y = 13

What is the correct value of y?

(A) –8

(B) –6

(C) +6

(D) +8

43. An international survey found the following information about participation in adult education:

Percent of Population over Age 21 Participating in Adult Education in the Year 2003

Country	Tocal Participation Rate (%)
Denmark	62.3
Hungary	17.9
Norway	43.1
Portugal	15.5
United States	66.4

Compare the participation rates of the countries with the highest and lowest participation rates by calculating approximately how many more adults participate in adult education in the country with the highest participation rate than in the country with the lowest participation rate.

(A) 2 times as many

(B) 4 times as many

(C) 6 times as many

(D) 8 times as many

44. Gordon has the following six bills to pay this month:

Bill Payable To	Amount
Bedding by Vidalia	$23.00
Chargealot Credit Corp.	$31.00
Dink's Department Store	$48.00
Furniture Fit for a Princess Shoppe	$13.00
Highest Fidelity Sound Shop	$114.00
Overpriced Gas Corporation	$39.00

Each month, he allocates $250.00 to pay his bills. This month, his bills are over this budget. How much extra money must he find from other parts of his budget to pay all his bills?

(A) $8.00

(B) $268.00

(C) $28.00

(D) $18.00

45. Georgette needs $185 to buy books for her Geography course, but because her hours at work have been cut back this month, she cannot afford to buy them, even though she needs them. Walking to class, she notices a sign offering to loan her $200 for one month for $20 interest. She calculates that if she can repay the money within the month by working extra hours, she will be able to afford the principal and the interest.

When Georgette applies for the loan, she reads the contract carefully and notices that after the initial one-month period, the interest rate climbs to 15% per month and includes the previous month's principal and interest. If she earns $11.00 per hour, how many extra hours (to the nearest hour) would she have to work to pay the additional second month’s interest?

46. Andrew just bought a small circular swimming pool for his children. The diameter of the pool is 12 feet, and Andrew can fill it safely to a depth of 9 inches. If a cubic foot of water weighs 62.42 pounds, how many pounds does the water in Andrew's pool weigh?

(A) approximately 27,000

(B) approximately 2,700

(C) approximately 1,300

(D) approximately 5,300

47. If Giorgio borrows $100 for one year and three months and repays $108 including simple interest, what rate of interest was he charged?

(A) 6.4%

(B) 8.0%

(C) 4.0%

(D) 4.6%

48. Chico went shopping for some groceries for his family. His shopping list was as follows:

• 2 pounds of apples
• 5 bananas
• 1 container of milk
• 1 loaf of bread

If apples were $0.79 a pound, bananas $0.23 each, milk $1.27 a carton, and bread $0.98 a loaf, what is the approximate total cost of the groceries?

(A) $3.90

(B) $4.10

(C) $4.90

(D) $5.50

49. From the numbers listed, what number should go in the box?

SERIES, 4, 7, 12, 19, , 38, . . . .

(A) 28

(B) 26

(C) 24

(D) 22

50. A rectangle 5 units long and 4 units high is represented on a graph. If three of the corners are placed at (3, 2), (3, –2), and (–2, 2), where should the fourth corner be placed?

(A) (–2, 2)

(B) (2, –2)

(C) (–2, –2)

(D) (2, 2)