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GED® Testing Service®

Computer World wants to average 25,000 computer sales per month for the first three months of the year. Computer sales for January and February are shown in the following graph.

20

40

60

Tho

usan

ds

Jan Feb

To reach their goal, how many computers must Computer World sell in March?

(1) 15,000

(2) 25,000

(3) 30,000

(4) 35,000

(5) 60,000

KEY

Actual work shown by a student:

40,000 – 25,000 = 15,000


Project Amount

A $20,720,000

B $17,600,000

C $12,480,000

D $ 5,650,000

E $ 550,000

Which project’s budget was closest to 10% of the total budget?

$57,000,000 10% = $5,700,000


The total budget of $57,000,000 available for road improvements was allocated among five projects. One of the projects was awarded $6,250,000.

Which is the closest approximation of the percent of the total budget awarded to this project?

(1) 5.2% (4) 18.0%

(2) 11.0% (5) 19.3%

(3) 15.6%$57,000,000 10% = $5,700,000 $57,000,000 1% = $570,000

$57,000,000 11% = $6,270,000


The total budget of $57,000,000 available for road improvements was allocated among five projects. One of the projects was awarded 3.25% of the total budget.

Which is the best approximation of the total budget that this project received?

(1) $2,000,000 (4) $16,000,000

(2) $5,000,000 (5) $20,000,000

(3) $6,000,000 $57,000,000 10% = $5,700,000 $57,000,000 1% = $570,000

1% < 3.25% < 10%


Harold’s typing speed, in words per minute, increased from 40 to 50: an increase of 10. If a candidate could find 25% of 40, on to the next problem!

Suppose a candidate can only find 10% of any number.

10% of 40 is 4. An increase of 10% would mean an increase of 4 words per minute.

(1) 10% (2) 15% (3) 20% (4) 25% (5) 50%

Increase of 10%: 40 + 4 = 44; not enough (50).

Increase of 20% (10% + 10%); 40 + 4 + 4 = 48; not enough.

Increase of 30% (10% + 10%+ 10%); 40 + 4 + 4 + 4= 52; too much.

X

XX

X


Houston Motors serviced 6000 vehicles last year. Of those vehicles serviced, 4% were brought back by customers because the problem was not properly fixed the first time.

How many vehicles serviced by Houston Motors last year had the problem PROPERLY fixed the first time?

(1) 240 (2) 280 (3) 5720

(4) 5760 (5) 5996

6000 × 0.04 Arithmetic error (6 × 4 = 28) 6000 – same arithmetic error 6000 – 6000 × 0.04 6000 – 4


On his recent vacation, Franklin purchased 10 souvenirs for $2.50 each for friends and had to pay a 6% sales tax. Because he did not want to pack them in his suitcase, he paid an additional shipping charge of $8.95 that was not taxed.

What was the total amount that Franklin paid for the souvenirs and shipping?

(1) $11.51 (2) $23.95 (3) $25.15 (4) $33.95 (5) $35.45

8.95 + 2.50 + 0.06 2.50 × 6 + 8.95 10 × 2.50 + 2.50 × 0.06 10 × 2.50 + 8.95 10 × 2.50 + 10 × 2.50 × 06 + 8.95


Kenn’s new motorcycle cost $2500. He could have paid cash, but he paid 20% of the cost and made 24 monthly payments of $95 each.

How much MORE did Kenn pay for the motorcycle than he would have if he paid cash?

(1) $280 (2) $456 (3) $500 (4) $2280 (5) $2780

24 × 95 + 2500 × 0.20 – 2500 24 × 95 × 0.20 2500 × 0.20 24 × 95 24 × 95 + 2500 × 0.20


3 1 7 2

?

3 1 7 2

Cross-multiply as shown below.

3 2 ? 7 1

3 1 7 2

<

6 7<


A marketing company surveyed 800 people and asked whether they had made internet purchases. Of those surveyed, 4/5 said that they had made at least one internet purchase.

How many of those surveyed had made at least one internet purchase?

(1) 160 (4) 480

(2) 320 (5) 640 KEY

(3) 400

These are impossible (and maybe even wrong). The chances for a correct

response have improved!


Visualizing a Reasonable Answer When Calculating with Fractions

Of all the items produced at a manufacturing plant on Tuesday, 5/6 passed inspection. If 360 items passed inspection on Tuesday, how many were PRODUCED that day?

Which of the following diagrams correctly represents the relationship between items produced and those that passed inspection?

produced producedpassed passed

A B


Of all the items produced at a manufacturing plant on Tuesday, 5/6 passed inspection. If 360 items passed inspection on Tuesday, how many were PRODUCED that day?

The items produced must be greater than the number passing inspection. Here are the alternatives for this question.

(1) 300 (2) 432 (3) 492 (4) 504 (5) 3000

Which incorrect alternative do you think was selected most often?

300, which is impossible!


A survey firm randomly selected 1200 people to test a new product. Of those selected, 400 were male.

Which fraction represents the ratio of females to males selected to test the new product?

(1) 1/3 (2) 1/2 (3) 2/3 (4) 3/2 (5) 2/1

How many females? 1200 – 400 = 800

Were more females or males selected? females

The ratio of females to males is MORE THAN 1.

The most commonly selected incorrect answer: 1/2


Another Process For

Finding a Common MultipleThe terms greatest common factor (f), least common multiple (m), and product (p) are related by the following formula:

f × m = pKnowing any two enables you to find the third.

12 and 15: f = 3; p = 180; 3 × m = 180; m = 60


12 15┘4 5┘

Entry:Answer:

12 something = 4; 15 something = 5 12 3 = 4; 15 3 = 5

Is that a coincidence?

How did that happen?

NO! 3 is the greatest COMMON factor!


34 51┘2 3

Entry:Answer: ┘

What is the greatest common factor of 34 and 51?

The greatest common factor is: 17


In order to gauge interest in its latest dealership, Friendly Motors plans to survey 800 potential automobile purchasers. Each of Friendly’s interviewers can visit a maximum of 24 people.

What is the minimum number of interviewers needed to complete the survey?

800 ÷ 24 = 33.33… Are 33 or 34 interviewers needed? 33 won’t be enough!


A company charges $60 per day plus $0.50 per mile for truck rentals. Which amount would this company charge a customer who rented a truck for 4 days and drove it a total of 200 miles?

(1) $100

(2) $160

(3) $240

(4) $340

(5) $440

200 × $0.50 (no charge per day)

200 × $0.50 + $60 (1 day rather than 4)

4 × $60 (no charge per mile)

4 × $60 + 200 × $0.50

4 × $60 + 200 (did not multiply)


Speedy Mail’s charges for express mail are $0.55 for the first ounce and $0.30 for each additional ounce. Which amount does Speedy Mail charge to express mail a 9-ounce package?

(1) $2.40

(2) $2.70

(3) $2.95

(4) $3.25

(5) $4.95

8 × $0.30; first ounce not included

9 × $0.30; no adjustment for 1st oz.

$0.55 + 8 × $0.30

$0.55 + 9 × $0.30; did not subtract 1

9 × $0.55; all charged at 1st oz. rate


If a/b = c/d, which of the following statements is true?

2 = (1 × 3)/6 b = (ac)/d 3 = (2 × 4)/6

2 = 1/(3 × 6) b = a/(cd) 3 = 2/(4 × 6)

2 = (1 × 6)/3 b = (ad)/c 3 = (2 × 6)/4

2 = (3 × 6)/1 b = (cd)/a 3 = (4 × 6)/2

2 = (3/(1 × 6) b = c/(ad) 3 = 4/(2 × 6)

1/2 = 3/6

a = 1; b = 2; c = 3; d = 6

2/3 = 4/6

a = 2; b = 3; c = 4; d = 6

◄►


A positive number less than or equal to 1/2 is represented by x. Three expressions involving x are given:

(A) x + 1 (B) 1/x (C) 1 + x2

Which of the following series lists the expressions from least to greatest?

(1) A, B, C (2) B, A, C (3) B, C, A (4) C, A, B (5) C, B, A

Chose a number for x that agrees with the information in the first sentence.

1/2 0.1

Evaluate A, B, and C.

A: 1.5 B: 2 C: 1.25

A: 1.1 B: 10 C: 1.01

Arrange (Least Greatest)

1.25, 1.5, 2 (C,A,B)

1.01, 1.1, 10 (C,A,B)


Which number represents the solution for the equation 2x + 36 = 4x – 24?

(1) 2 (4) 12 (2) 6 (5) 30 (3) 10

Always check to be sure, but “checking” can help “solve” a multiple-choice question.

2: 2(2) + 36 = 4(2) – 24; 4 + 36 = 8 – 24; 40 = -166: 2(6) + 36 = 4(6) – 24; 12 + 36 = 24 – 24; 48 = 0

10: 2(10) + 36 = 4(10) – 24; 20 + 36 = 40 – 24; 56 = 1612: 2(12) + 36 = 4(12) – 24; 24 + 36 = 48 – 24; 60 = 2430: 2(30) + 36 = 4(30) – 24; 60 + 36 = 120 – 24; 96 = 96


Grace can purchase a research report from the library for $15.00, or she can borrow the report and produce a copy at a cost of $0.06 per page. If the cost to purchase the report is exactly equal to the cost to reproduce it, then the report must have how many pages?•Guess and check:

•10 pages, $0.60; 50 pages, $3.00; 100 pages, $6.00; 1000 pages, $60.00

•$15.00 = $6 + $6 + $3 = 100p + 100p + 50 p = 250 pages

•$15.00 = 5 × $3 = 5 × 50 p = 250 pages

•$15.00 = $60.00/4 = 1000pages/4 = 250 pages


Jason shipped two packages. The heavier package weighed 40 pounds more than the lighter package, and together the two packages weighed 300 pounds. What was the weight, in pounds, of the lighter package?

(1) 130 (2) 150 (3) 170 (4) 210 (5) 260

130 ( and 170) 150 ( and 150) 170 ( and 130) 210 (and 90) 260 (and 40)

Total Weight: 300 lb

lighter

In none of these is the “lighter” package lighter!


Walkways connect Fields Building with Hammond and Watson, as shown in the following diagram.

48 m

20 mproposed walkway

FH

W

A walkway between Hammond and Watson is proposed. What would be the length, in meters, of the proposed walkway?

(1) 50 (2) 52 (3) 56 (4) 58 (5) 68


Maria walks east on Bayview and north on Harbor when she goes to work on rainy days. On sunny days, she walks directly across Cates Park. How much SHORTER, in meters, is the route through the park?

Cates Park

Bayview Street

120 m

Harbor Street

160 m

A

W (1) 80

(2) 160

(3) 200

(4) 280

(5) 380


Below are rectangles A and B with no text. For each, do you think that a question would be asked about area or perimeter?

A

B

A: Area Perimeter Either/both

This visual distinction is always used on the GED Mathematics Test.

B: Area Perimeter Either/both

Perimeter

Area


Comparing Areas /Perimeters

A rectangular garden had a length of 20 feet and a width of 10 feet. The length was increased by 50%, and the width was decreased by 50% to form a new garden. How does the area of the new garden compare to the area of the original garden?

The area of the new garden is (1) 50% less (2) 25% less (3) the same (4) 25% greater (5) 50% greater


original garden

20 ft (length)

10 ft (width)

new garden

5 ft

30 ft

Area: 20 × 10 = 200 ft2

Area: 30 × 5 = 150 ft2

The new area is 50 ft2 less; 50/200 = 1/4 = 25% less.

How do the perimeters compare?

What would be the case if the WIDTH was increased by 50% and the LENGTH was decreased by 50%?

Perimeter of new is greater.


Angle Measures of Polygons and Circles

The sum of the measures of the angles of any triangle is 180º.

1

2

3

angle 1 = 40º; angle 2 = 70º; angle 3 = ?

angle 1 = angle 2 = 50º; angle 3 = ?

angle 1 = angle 2 = angle 3; angle 3 = ?

70º

80º

60º


In the diagram shown, triangle ABC is similar to triangle ADE. Which proportion could be used to find the measure of x?

AB

E

D

C

x

(1) AB/BD = BC/x (4) AD/AE = BC/x (2) AB/AD = BC/x (5) AE/AC= BC/x (3) AC/CE = BC/x

AB/AD = BC/DE = AC/AEAB/AD = BC/ x = AC/AE


The sizes of two rectangular ads placed on buses are shown below.

$ 90

4 ft

5 ft

3 ft

2 ft

$ x

The price of an ad is proportional to its AREA. Which expression can be used to find x?

(1) 5/9 = 90/x (3) 6/x = 20/90 (5) 10/x = 18/90

(2) 6/20 = 90/x (4) 10/18 = 90/x


Area/Perimeter When Variables are Involvedx + 2

(Is this an area or a perimeter problem?)

x – 2

Which expression represents the area of the rectangle?(1) 2x (2) x2 (3) x2 – 4 (4) x2 + 4 (5) x2 – 4x – 4

How can you approach this question if your algebra skills are not strong?

Pretend that x is a number!


x + 2

x – 2

(1) 2x (2) x2 (3) x2 – 4 (4) x2 + 4 (5) x2 – 4x – 4

This is a strategy that also can be used for calculation items.

Choose a number for x. Do you see any restrictions? (I choose 8.) Determine the area numerically. (8 + 2 = 10; 8 – 2 = 6; 10 6 = 60)

Which alternative yields that value?

2 8 = 16; not correct (60).82 = 64; not correct.82 – 4 = 64 – 4 = 60; correct!82 + 4 = 64 + 4 = 68.82 – 4(8) – 4 = 64 – 32 – 4 = 28


What was the approximate value of the house 5 years after it was built?

0

4 8 0

100

200

Val

ue

(th

ousa

nd

s of

dol

lars

)

Time (years)

Increasing House Value

$125 $150 $125,000 $150,000$175,000


The rate of change in value for the two houses is the same, but the percent increase is not. At the end of 10 years, by what percent had the value of each house increased?

0

4 8 0

100

200

Val

ue

(th

ousa

nd

s of

dol

lars

)

Time (years)

Increasing House Values

Blue: 100%

Red: 200%


Approximately how many years after these two houses were built were their values the same?

0

4 8 0

100

200

Val

ue

(th

ousa

nd

s of

dol

lars

)

Time (years)

Increasing House Values

5


A B C D E

An

nu

al s

ales

(m

illi

ons)

$50

$40

$30

$20

$10

Annual Sales at Texas ValuMart Stores

2008

2009

Which store had the greatest increase from 2008 to 2009?


2008

2009

A B

An

nu

al s

ales

(m

illi

ons)

$50

$40

$30

$20

$10

Annual Sales at Texas ValuMart Stores

The greatest percentage increase is for Store A (100%); Store B had the greatest increase in sales ($20M).


Results of Mileage Tests

Miles per gallon Percent of vehicles

16 - 20 15.5

20.1 - 25 37.5

25.1 - 30 30.5

30.1 - 45 16.5

What percentage of the vehicles tested averaged 25 miles per gallon or less?

15.5% + 37.5% = 53%




16 - 20 15.5

20.1 - 25 37.5

25.1 - 30 30.5

30.1 - 45 16.5

How many vehicles averaged more than 30 miles per gallon?

Not enough information is given. (Only percentages are given.)




16 - 20 15.5

20.1 - 25 37.5

25.1 - 30 30.5

30.1 - 45 16.5

If 400 vehicles were involved in the tests, how many averaged more than 25 mpg but not more than 30 mpg?

400 30.5% = 122


Dress Size 10 12 14 16

Style A Yards of Fabric Needed

35 in

Fabric 45 in

Width 54 in

60 in

3.25 3.875 3.875 3.875

3 3 3.25 3.25

2.375 2.5 2.75 2.75

2.25 2.25 2.25 2.5

Style B Yards of Fabric Needed

35 in

Fabric 45 in

Width 54 in

60 in

3.875 4 4.125 4.625

3.125 3.25 3.25 3.625

2.5 2.875 3 3

2.25 2.375 2.5 2.75

Style B Width is 54 in. 1 ea. 10, 12, 142.5 + 2.875 + 3 = 8.375

Yardage Information


0

4 8 12$0

$1000

$2000Amount

Investment A

Investment B

Time (years)Compared to investment B, investment A had a(1) lesser initial investment and a lesser rate of increase. (2) lesser initial investment and the same rate of increase. (3) lesser initial investment and a greater rate of increase. (4) greater initial investment and a lesser rate of increase. (5) greater initial investment and a greater rate of increase.


0

4,000 8,000 12,000$0

$200

$400

Profit/Loss in

Thousands of Dollars

Video Games Sold

-$200

What is the expected loss before any video games are sold?

(1) $0 (2) -$150 (3) -$250 (4) -$150,000 (5) -$250,000


Using a Simpler Pattern to Discover One That is More Complex

A certain brand of car can be ordered in one of 8 exterior colors with one of 4 different interior trims and one of 6 different option packages. How many different cars can be ordered?

Work with a simpler problem to discover the pattern that would be applied to this more complex problem: 4 exterior colors, 2 interior trims.

E1 E2 E3 E4

T1 T2 T1 T2 T1 T2 T1 T2

8 options: 4 × 2

Original question:

8 × 4 × 6 = 192 options


A

B

(1) The probability for the red triangle is greater but less than twice as great.

(2) The probability for the red triangle is twice as great because its square is twice as large.

(3) The probability for the red triangle is more than twice as great.

(4) The probabilities are equal.

(5) Not enough information is given.

2 ft

4 ft


A purple marble has been drawn from the jar and not put back into the jar. What is the probability of randomly drawing a purple marble now?

Ppurple = 3/9 or 1/3

Successes: 3

Total: 9

ged ® testing service ® computer world wants to average 25,000 computer sales per month for the...

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