In 115 minutes, you have to solve a series of questions involving general mathematical skills and problem solving. These questions may be based on short passages, graphs, charts, or figures. You must do the first five questions without a calculator, but after that, you can use a calculator for the rest of the test. You also have at your fingertips a list of formulas to help you with some of the questions. Remember that the calculator and list of formulas aren’t a magic solution. You have to know how to use them.
Memorizing the formulas and knowing how and when to use them will speed things up and can give you valuable time at the end to do any questions you had trouble with. Answer the easy question first to give yourself more time at the end for the more difficult questions.
Unless you require accommodations, you’ll take the actual GED test on a computer, where you use the mouse and the keyboard to indicate your answer. We formatted the questions and answer choices in this book to make them appear as similar as possible to what you’ll see on the computerized test, but we had to retain some A, B, C, D choices and provide an answer sheet for you to mark your answers.
Answer Sheet for Practice Test 2, Mathematical Reasoning
Mathematics Formula Sheet
Mathematical Reasoning Test
TIME: 115 minutes
DIRECTIONS: Mark your answers on the answer sheet provided.
1. Yvonne is studying a map. She is 47 miles due south of where she wants to go, but the road goes 17 miles due west to an intersection that then goes northeast to her destination. Approximately how much farther must she travel because of the way the road goes?
(A) 3 miles
(B) 20 miles
(C) 16 miles
(D) 50 miles
2. After asking for directions to a restaurant, Sarah was told it was 1,000 yards ahead, but her car’s odometer reads distances in miles and tenths of miles. How many miles (to the nearest tenth) does she have to drive to find the restaurant? miles
3. Arthur is making a circular carpet, using small pieces of cloth glued onto a backing. If he wants a carpet that is 7 feet 8 inches across, including a 2-inch fringe all around the carpet backing, how many square feet of backing does he need to cover, rounded to one decimal place?
(A) 42.21
(B) 46.14
(C) 45.7
(D) 42.2
4. The vertices of a triangle are , and C (8, 7). Using the figure on the answer sheet, circle the two ends of the longest side.
5. As an experiment, a class flips three coins 100 times each and charts the results. The coins are not accurately balanced. From the chart, which coin during which series of tosses is closest to being balanced?
(A) coin B, third set
(B) coin C, third set
(C) coin A, second set
(D) coin B, first set
6. Donna is very involved with speed walking. To keep from getting too bored, she has started counting how many breaths she takes for each of her steps. She figured that she takes three breaths for every 27-inch step. How many breaths does she take in a 1,000-yard walk?
(A) 5,332
(B) 2,126
(C) 4,767
(D) 4,000
7. Sam and Arnold were eating ice-cream cones. Arnold wondered what volume of ice cream his cone would hold if filled to the top. Sam measured the cone and found it to be 2½ inches across the top and 5½ inches high. The cone would hold cubic inches of ice cream, rounded to one decimal place, if it were filled to the top.
Question 8 refers to the following table.
Room Level Dimensions
Room
Measurement (In Feet)
Dining Room
Living Room
Kitchen
Solarium
Master Bedroom
Second Bedroom
8. Singh has bought a new apartment and wants to carpet the living room, dining room, and master bedroom. If he budgets $35.00 per square yard for carpeting and installation, how much should he budget for these rooms?
(A) $1,674.08
(B) $1,457.08
(C) $1,724.91
(D) $1,500.08
Questions 9 and 10 refer to the following information.
Carlos wants to buy a used car. He has been told that a car loses 4.3 cents from its book value for every mile over 100,000 that it has traveled. He sees just the car he wants, but it has 137,046 miles on the odometer. The book value of the car is $13,500.
9. Estimate the realistic value of the car to the nearest $10.
(A) $10,907
(B) $13,750
(C) $12,020
(D) $11,000
10. The realistic actual value of the car to the nearest dollar is $ .
11. Elena wants to draw a mural on the wall of her house. The wall is 9 feet high and 17 feet long. To plan the mural, she draws a scale drawing of the area for the mural on a piece of paper 11 inches long. How high, in inches, should the drawing be to maintain scale?
(A) 6.2
(B) 5.8
(C) 8.5
(D) 9.0
12. If the slope of a line is 0.75, and , and , what is the value of ?
(A) 14
(B)
(C) 28
(D)
Questions 13 and 14 refer to the following table.
Literacy Rates in Selected Countries
Country
Population
Literacy Rate (%)
China
1,315,844,000
90.9
Cuba
11,269,000
99.8
Ethiopia
77,431,000
35.9
Haiti
8,895,000
54.8
India
1,103,371,000
61.0
Israel
6,725,000
97.1
Russia
143,202,000
99.4
South Africa
47,432,000
82.4
United States
298,213,000
99.0
13. If the literacy rates of China, the United States, and Russia were compared, the greatest literacy rate would be how many times larger than the least?
(A) 1.0
(B) 1.1
(C) 1.2
(D) 1.3
14. How many more people (in millions) are literate in India than Israel?
(A) 109
(B) 666
(C) 90
(D) 100
15. The probability of an event taking place, P, is equal to the number of ways a particular event can occur, divided by the total number of ways, M, or . To test this theory, a student removes all the picture cards from a deck. What is the probability that a card less than the number 6 will be drawn? (Aces are low in this case.)
(A) 1 in 3
(B) 1 in 5
(C) 1 in 2
(D) 1 in 4
Questions 16 and 17 refer to the following information.
Peter’s grades in his final year of high school classes are 81, 76, 92, 87, 79, and 83.
16. To get a scholarship, Peter’s median grade must be above the median grade for the school, which is 82. By how many points is he above or below that standard?
(A) 2
(B) 1
(C) 0
(D) 3
17. If Peter’s goal is to graduate with a mean grade of 90 percent, by how many total points is he failing to achieve his goal?
(A) 42
(B) 43
(C) 44
(D) 45
18. Olga has a propane-powered car. She was told it was safe to fill her cylindrical propane tank at a rate of cubic feet per minute. If the propane tank measures 4.8 feet long and 2.1 feet in diameter and is empty, it would require minutes to fill it.
19. The formula for compound interest on a loan is , where M is the final amount including the principal, P is the principal amount, i is the rate of interest per year, and n is the number of years invested.
If Amy invested the $1,574 she got as gifts for graduating from elementary school in a Guaranteed Investment Certificate, paying 3.75 percent compound interest calculated annually for the seven years until she graduates from college, how much money would she have?
(A) $1,978.18
(B) $462.67
(C) $2,036.67
(D) $1,878.18
20. Consider the equation . If the value of m triples and the value of c remains constant, the effect on E would be how many times larger?
(A) 9 times larger
(B) 27 times larger
(C) 3 times larger
(D) the same
21. An accident investigator calculates a car’s speed during a skid by multiplying the following: the square root of the radius of the curve that the center of mass, r, follows times a constant, k, times the drag factor of the road, m. If the speed calculated was 47 miles per hour and the drag factor was 0.65, what was the radius of the curve that the car’s center of mass followed?
(A) 8.5
(B) 5.8
(C) 4.9
(D) not enough information given
22. Vladimir is designing gas tanks for trucks. The length of the tanks is fixed, but the diameter can vary from 3 to 4 feet. How many more cubic feet of gas does the largest tank hold?
(A) 3.00
(B) 2.75
(C) 4.75
(D) not enough information given
Questions 23–25 are based on the following situation:
Forty tenth grade social studies students are on a field trip, but many of the students don’t feel well. Ten students are healthy, but each of the remaining thirty has a sore throat, a stomach virus, or both.
23. If 15 students have sore throats and 25 have stomach viruses, how many students have both?
(A) 25
(B) 20
(C) 15
(D) 10
24. If a student is selected randomly from the whole group, what is the probability that he or she has a sore throat?
(A) .275
(B) .375
(C) .475
(D) .575
25. If a student is selected randomly from the whole group, what is the probability that he or she has a stomach virus?
(A) .425
(B) .525
(C) .625
(D) .725
26. Jerry has started a business selling computers. He can buy a good used computer for $299 and sell it for $449. The only question he has is whether he will make money. If his overhead (rent, light, heating, and cooling) amounts to $48 per unit and his taxes amount to $3 per unit, how many computers will he have to sell to make $700 per week profit?
(A) 6
(B) 9
(C) 7
(D) 8
27. To be awarded a scholarship at Constant College, a student must score above the median of all the students in his or her year and have a mean mark of at least 90 percent. Georgio was hoping for a scholarship. Here are his marks:
Mathematics: 94
Applied Science: 92
English: 87
Spanish: 96
Physics: 90
The median mark for the graduating students is 86.5. How many percentage points above the required minimum mean score did Georgio score?
(A) 3.2
(B) 1.8
(C) 86.5
(D) 91.8
Question 28 refers to the following table.
Geothermal-Electric Capacity in Selected Countries in 2004
Country
Installed Capacity (Megawatts)
China
6
Italy
502
New Zealand
248
Russia
26
United States
1,850
28. What is the approximate ratio of Installed Capacity of the largest to the smallest?
(A) 274:2
(B) 308:1
(C) 5:4
(D) 803:1
29. Elayne wants to buy a new fuel-efficient car. She notices that a new car is advertised as getting 100 miles per gallon in city driving and 70 miles per gallon on the highway. After a week of record keeping, she produces the following table for her old car.
Day
City Driving (Miles)
Highway Driving (Miles)
Monday
30
5
Tuesday
35
25
Wednesday
25
10
Thursday
30
20
Friday
20
5
Saturday
5
70
Sunday
5
75
If Elayne’s old car gets 18 miles per gallon in the city and 12 miles per gallon on the highway and gas costs $2.70 a gallon, how much would she save in a week by buying this new fuel-efficient car?
(A) $12.15
(B) $22.50
(C) $57.59
(D) $47.25
Question 30 refers to the following table.
Interest Rates Offered by Different Car Dealerships
Dealer
Interest Rate Offered
A
Prime + 2%
B
7.5%
C
1/2 of prime + 5%
D
Prime + 20% of prime for administrative costs
30. Donald is confused. He is looking for a new car, but each dealership offers him a different interest rate. If the prime lending rate is 6 percent, which dealer is offering Donald the best terms to finance his car?
(A) Dealer D
(B) Dealer C
(C) Dealer B
(D) Dealer A
31. The formula for average deviation in statistics is as follows:
Average deviation =
where x is the deviation, is the absolute value of x, and n is the number of values.
If the values for the deviation are , what is the average deviation?
(A) 6
(B) 7
(C) 8
(D) 9
32. Henry wanted to find out how many people watched Four’s a Mob, the newest sitcom. He did a survey of 12 of his favorite friends and found that 10 of them had seen the last episode. Knowing that the population of the United States is more than 288,000,000, Henry calculated that 240,000,000 people watched his new favorite sitcom. The error in Henry’s conclusion is that .
Questions 33 and 34 refer to the following information.
In September, Ken and Ben wanted to lose some weight by the following July. They figured that by supporting each other, eating a balanced diet with reduced calories and exercising, they could lose 0.5 pound per week.
33. What mathematical operation(s) would you use to calculate the amount of weight Ken and Ben could lose between the beginning of September and the end of June?
(A) counting and adding
(B) division and counting
(C) counting and multiplication
(D) subtraction
34. If Ken and Ben stick to their plans, approximately how much weight could they each lose between the beginning of September and the end of June?
(A) 20 pounds
(B) 30 pounds
(C) 36 pounds
(D) 48 pounds
35. Mary and Samantha are planning a 900-mile trip. Mary says that she can drive at an average speed of 45 miles per hour. Samantha says that she will fly, but it takes her 45 minutes to get to the airport and 1 hour and 15 minutes to get from the airport to her destination after she lands. If she has to be at the airport 3 hours before take-off and the airplane travels an average of 300 miles per hour, how many hours will Samantha have to wait for Mary?
(A) 8
(B) 9
(C) 12
(D) 16
Question 36 refers to the following information and graph.
The Queenly Hat Company of Lansing, Michigan, produces designer hats for women who feel that a hat completes an outfit. Their sales vary from quarter to quarter and factory to factory. The following chart reflects their sales for one year.
36. Of the three factories, which factories and in which quarters are sales figures approximately in the ratio of 2:1?
(A) east and west in 2nd quarter
(B) west and north in 3rd quarter
(C) east and north in 3rd quarter
(D) west and east in 1st quarter
Questions 37 and 38 refer to the following table.
Life Expectancy for Urban Dwellers
Age (In Years)
Males
Females
10
61.4
67.3
20
50.3
55.1
30
40.4
45.1
40
32.8
36.5
50
22.1
26.4
60
15.2
17.8
70
9.9
10.7
37. From the data presented in the table, what interpretation could be reached?
(A) Women age better than men.
(B) Men live longer than women in all age categories.
(C) The number of years yet to live decreases with increasing age.
(D) Urban dwellers live longer than rural dwellers in all age categories.
38. From the data presented, hypothesize why women live longer than men in an urban environment.
(A) Women take better care of their health.
(B) A greater percentage of men work in an urban setting.
(C) Men are involved in more auto accidents in an urban setting.
(D) Not enough information is given.
39. The cost of a finished item is equal to 2 times the production cost, plus 120 percent of the overhead costs at the retail level, plus profit. If three stores, A, B, and C, each sell the product, and Store B has a 50 percent raise in rent, how will this affect the selling price for the item?
(A) The selling price would go down.
(B) The selling price would remain the same.
(C) The selling price would go up.
(D) Every store would raise its prices.
40. Sol wanted to write the population of the United States in scientific notation for a project he was working on. If the population of the United States is 288,257,352 and he wrote it out as , the value for x is .
41. Harry and Karry are preparing for the big race. They have been keeping track of their times in the following table.
Comparative Times
Harry’s Times (In Seconds)
Karry’s Times (In Seconds)
15.6
15.9
14.9
16.1
16.0
15.8
15.8
16.2
16.1
14.8
What conclusion can you reach from comparing their mean times?
(A) Karry is slightly faster.
(B) Harry is slightly slower.
(C) They are about even.
(D) Karry has a higher mean time.
42. Maria bought an apartment. The total floor area is 1,400 square feet. If the ceilings are 9 feet high and her air system withdraws and replaces 63 cubic feet of air each minute, how long, in minutes, does it take to withdraw and replace all the air in her apartment?
(A) 180
(B) 200
(C) 220
(D) 240
43. Peter is emptying his swimming pool. He can pump 9 cubic feet of water per minute. If his pool measures 45 feet by 12 feet with an average depth of 4 feet, when will his pool be empty if he starts pumping at noon on Tuesday?
(A) 4 a.m. on Wednesday
(B) 6 p.m. on Tuesday
(C) 2 p.m. on Tuesday
(D) 4 p.m. on Tuesday
44. Mohammed works in sales. He compares his average paychecks for the last four weeks and finds that he has earned an average of $420.00 per week for the four-week month. If he earned $480.00 the first week, $400.00 the third week, and $550.00 the final week, how much did he earn the second week of the month?
(A) $250.00
(B) $280.00
(C) $340.00
(D) $190.00
45. Georgia started shopping with $500.00 in her purse. When she returned home after shopping, she had $126.00 in her purse and $83.00 in credit card receipts. How much did she spend shopping? $
46. If you open a can flat along the seam and cut almost all the way around each end, what shape would you end up with?
(A) a circle
(B) a rectangle with a circle on each end
(C) a rectangle
(D) a circle with two rectangles on each end
47. Sonya’s car uses gasoline in direct proportion to her speed. If she increases her average speed by 10 miles per hour to save time, the consequence is .
(A) she would save money
(B) she would spend more money on fuel
(C) she would spend the same amount as before
(D) not enough information
48. A circle is drawn with its center at the origin and a diameter of 8 units. Where will the circumference intersect the negative y-axis? Circle this point on the graph.
Unless you require accommodations, you’ll take the actual GED test on a computer, where you use the mouse and the keyboard to indicate your answer. We formatted the questions and answer choices in this book to make them appear as similar as possible to what you’ll see on the computerized test, but we had to retain some A, B, C, D choices and provide an answer sheet for you to mark your answers.
miles
, and C (8, 7). Using the figure on the answer sheet, circle the two ends of the longest side.
, and 
, what is the value of 
?
. To test this theory, a student removes all the picture cards from a deck. What is the probability that a card less than the number 6 will be drawn? (Aces are low in this case.)
cubic feet per minute. If the propane tank measures 4.8 feet long and 2.1 feet in diameter and is empty, it would require 
, where M is the final amount including the principal, P is the principal amount, i is the rate of interest per year, and n is the number of years invested.
. If the value of m triples and the value of c remains constant, the effect on E would be how many times larger?
is the absolute value of x, and n is the number of values.
, what is the average deviation?
, the value for x is 
