gre math 강좌 set 4

GRE Math 강좌 Set 4

윤태화 영어연구실, http://www.vstudy.co.kr , [email protected] , 02-538-5999,

Chapter 4 Ratio, Proportion, and Fraction

1. A certain club has 35 male members and 45 female members. Which of the following equals

the ratio of the number of male members to the number of female members?

(A) 16:7

(B) 9:5

(C) 7:5

(D) 4:3

(E) 9:7

2. What is the ratio of 4

3 to the product

43

4 ?

(A) 4

1

(B) 3

1

(C) 9

4

(D) 4

9

(E) 4

3. If 7

2 of the 210 students in a class attended graduate school, what was the total number of

students in the class who did not attend graduate school?

(A) 42

(B) 60

(C) 105

(D) 142

(E) 150



4. A certain test consists of 8 sections with 25 questions numbered from 1 to 25, in each section.

If a student answered all of the even-numbered questions correctly and 4

3 of the odd-

numbered questions correctly, what was the total number of questions he answered

correctly?

(A) 150

(B) 172

(C) 174

(D) 175

(E) 176

5. Two cities that are geographically 380 miles apart are 2 inches apart on a certain map. If

the map is drawn to scale, how many miles apart are two cities that are 2

17 inches apart on

the map?

(A) 665

(B) 1,330

(C) 1,425

(D) 2,090 (E) 2,850

6. Lou and Selma were hired to paint a room for a total of $72. They completed the job with

Lou working 3 hours and 20 minutes and Selma working 2 hours and 40 minutes. If they

decided to split the $72 in proportion to the amount of time each spent on the job, how much

did Lou receive?

(A) $32.00

(B) $36.00

(C) $40.00

(D) $41.14

(E) $43.20



7. Kathy bought 4 times as many shares in Company X as Carl, and Carl bought 3 times as many shares in the same company as Tom. Which of the following is the ratio of the

numbers of shares bought by Kathy to the number of shares bought by Tom?

(A) 4

3

(B) 3

4

(C) 1

3

(D) 1

4

(E) 1

12

8. Of the 40 schools invited to participate in a research study, 8

7 agreed to participate. If 60

questionnaires were sent to each of the participating schools and 5

4 of these questionnaires

were completed and returned, what was the total number of questionnaires completed and

returned?

(A) 28

(B) 1,344

(C) 1,680

(D) 1,920

(E) 2,100

9. If a printer can 2 pages of text per second, then, at this rate, approximately how many minutes

will it take to print 5,000 pages of text?

(A) 4

(B) 25

(C) 42

(D) 250

(E) 417



10. If $160 is divided among 3 people in the ratio 8:5:3 , what is the least amount received by

any one person?

(A) $80

(B) $50

(C) $30

(D) $20

(E) $10

11. Which three of the following fractions are equivalent?

80

5=v , 08.0

05.0=w , 0.8

5.0=x , 8.0

05.0=y , 008.0

05.0=z

(A) v , w , and x

(B) v , x , and y

(C) w , x , and y

(D) w , y , and z

(E) x , y , and z

12. A study based on a random sample revealed that, on average, 2 out of 5 adults have high blood

pressure. If these results hold true for the 580,000 adults in City A , approximately how

many adults in City A have high blood pressure? (A) 116,000

(B) 145,000

(C) 232,000

(D) 250,000

(E) 290,000



13. Two boxes of pudding mix cost a total of $0.73 and 1 box of cake mix costs twice as much as

two boxes of pudding mix. At these rates, what is the cost of 3 boxes of pudding mix and 3

boxes of cake mix?

(A) $1.10

(B) $3.29

(C) $4.38 (D) $5.48

(E) $6.57

14. Out of their annual net income, a couple spent 25 percent for food, 13.5 percent for

entertainment, 20 percent for housing, 8 percent for car expenses, 15 percent for clothing, and

saved the rest. What was the ratio of the amount saved to the amount spent for

entertainment?

(A) 27

19

(B) 5

6

(C) 27

37

(D) 9

19

(E) 3

7

15. Approximately how many minutes will it take a secretary who types at an average rate of 60

words per minute to type a 5-page report with 250 words per page? (A) 4

(B) 12

(C) 21

(D) 30

(E) 75



16. If the speed of an airplane is 360 kilometers per hour, how many meters will it travel in one

second? (1 kilometer = 1,000 meters)

(A) 100

(B) 360

(C) 1,000

(D) 3,600 (E) 6,000

<High Level Questions>

17. The total time required to transport rail freight from City X to City Y is 4 days, 15 hours.

If, by eliminating certain intermediate stops, the total time were reduced by 3

1, the total

transport time required would be

(A) 1 day, 3

15 hours

(B) 1 day, 13 hours

(C) 2 days, 3

210 hours

(D) 2 days, 3

215 hours

(E) 3 days, 2 hours

18. A small firm spent 4

1 of its annual budget during the first 2 months of its fiscal year and

spent 2

1 of its remaining budget during the next 5 months. What fraction of the annual

budget remained unspent at the end of the first 7 months?

(A) 16

3

(B) 4

1

(C) 16

5

(D) 8

3

(E) 12

5



19. Members of a social club met to address 280 newsletters. If they addressed 4

1 of the

newsletters during the first hour and 5

2 of the remaining newsletters during the second hour,

how many newsletters did they address during the second hour?

(A) 28 (B) 42 (C) 63 (D) 84 (E) 112

20. In a certain used-car lot, there are 4 times as many blue cars as green cars and 3

1 as many

green cars as red cars. If there are q4 red cars in the lot, how many blue cars are in the lot?

(A) q12

(B) 3

16q

(C) q3

(D) 3

4q

(E) 4

3q

21. When Inez and Fernando purchased a property for $20,000. Fernando contributed 3

1 the

amount contributed by Inez for the purchase. If they sold the property for $40,000 and

shared this amount in proportion to their respective contributions, how much was Fernando’s

share? (A) $5,000

(B) $10,000

(C) $13,333

(D) $20,000

(E) $26,666



22. Of Amy’s monthly salary, 4

1 goes to rent and

5

1 to food. If the remainder of her monthly

salary amounts to $990, what is Amy’s monthly salary? (A) $1,042

(B) $1,273

(C) $1,800

(D) $1,980

(E) $2,200

23. When 9

2 of the votes on a certain resolution have been counted,

4

3 of those counted are in

favor of the resolution. What fraction of the remaining votes must be against the resolution

so that the total count will result in a vote of 2 to 1 against the resolution?

(A) 14

11

(B) 18

13

(C) 7

4

(D) 7

3

(E) 14

3

24. In a certain population, there are 3 times as many people aged twenty-one or under as there

are people over twenty-one. The ratio of those twenty-one or under to the total population is

(A) 1 to 2

(B) 1 to 3

(C) 1 to 4

(D) 2 to 3

(E) 3 to 4



25. Last year Department Store X had a sales total for December that was 4 times the average (arithmetic mean) of the monthly sales totals for January through November. The sales total

for December was what fraction of the sales total for the year?

(A) 4

1

(B) 15

4

(C) 3

1

(D) 11

4

(E) 5

4

26. Millie and Rick addressed 150 invitations. If Millie addressed 2

11 times as many as Rick

addressed, how many of the invitations did Rick address?

(A) 30

(B) 60

(C) 75

(D) 90

(E) 100

27. In 1990 a total of x earthquakes occurred worldwide, some but not all of which occurred in

Asia. If m of these earthquakes occurred in Asia, which of the following represents the

ratio of the number of earthquakes that occurred in Asia to the number that did not occur in

Asia?

(A) m

x

(B) x

m

(C) mx

m

−

(D) mx

x

−

(E) x

m−1



28. The ratio of two quantities is 3 to 4. If each of the quantities is increased by 5, what is the

ratio of these two new quantities?

(A) 4

3

(B) 9

8

(C) 19

18

(D) 24

23

(E) It cannot be determined from the information given.

29. Of the people who responded to a market survey, 120 preferred Brand X and the rest

preferred Brand Y . If the respondents indicated a preference for Brand X over Brand

Y by a ratio of 3 to 1, how many people responded to the survey?

(A) 80

(B) 160

(C) 240

(D) 360

(E) 480

30. Orange juice of normal strength is prepared by adding three 6-ounce cans of water to the

contents of a 6-ounce can of orange juice concentrate. If 1 ounce of the can of concentrate

was already used for some other purpose, how many 6-ounce cans of water should be added to

the remainder of the concentrate to prepare juice of normal strength?

(A) 3

21

(B) 2

(C) 3

12

(D) 2

12

(E) 6

52



31. A coffee merchant makes a house blend of coffee using 4 pounds of Arabian beans costing $3

per pound, 2 pounds of Java beans costing $4 per pound, and 4 pounds of Brazilian beans

costing $1 per pound. If the merchant sold all of the blend for 50 percent more than the total

cost of the beans used, at what price per pound was the blend sold?

(A) $1.20

(B) $2.40 (C) $3.00

(D) $3.60

(E) $4.50

32. The current ratio of men to women on a certain board of trustees is 2 to 5. If 4 men were

added to the board, the ratio of men to women would be 2 to 3. How many men are currently

on the board?

(A) 2

(B) 4

(C) 5

(D) 6

(E) 8

33. A custom blend of paint is made by mixing red, yellow, and black paints in the ratio of 12 to 11

to 1. If all of the paints are sold only in pint-sized containers, how many containers of yellow

are used in preparing 6 gallons of the blend? (8 pints = 1 gallon)

(A) 2

(B) 3

(C) 11

(D) 22

(E) 24



34. A rectangular office floor is 28 meters by 20 meters. A custodian, working at a constant rate,

waxes a section of the floor that is 5 meters by 20 meters in 4

3 hour. How many hours does

it take the custodian, working at this same constant rate, to wax the entire floor?

(A) 2.52

(B) 3

(C) 3.45

(D) 4.2

(E) 7

35. A glucose solution contains 15 grams of glucose per 100 cubic centimeters of solution. If 45

cubic centimeters of the solution were poured into an empty container, how many grams of

glucose would be in the container?

(A) 3.00

(B) 5.00

(C) 5.50

(D) 6.50

(E) 6.75

36. Dan bought x pencils, some at 10 cents each and the rest at 6 cents each. For the same

amount of money that he spent on these pencils, he could have bought x pencils at 9 cents

each. What is the ratio of the number of 10-cent pencils purchased to the number of 6-cent

pencils purchased?

(A) 1 : 1

(B) 2 : 1

(C) 3 : 1

(D) 4 : 1

(E) 5 : 1

37. A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black

paint. If 2 gallons of the mixture is needed and the individual colors can be purchased only in

one-gallon or half-gallon cans, what is the least amount of paint, in gallons, that must be

purchased in order to measure out the portions needed for the mixture?

(A) 2

(B) 2

12

(C) 3

(D) 2

13

(E) 4



38. Working alone, printers X , Y , and Z can do a certain printing job, consisting of a large number of pages, in 12, 15, and 18 hours, respectively. What is the ratio of the time it takes

printer X to do the job, working alone at its rate, to the time it takes printers Y and Z to do the job, working together at their individual rates?

(A) 11

4

(B) 2

1

(C) 22

15

(D) 15

22

(E) 4

11

39. The ratio, by volume, of soap to alcohol to water in a certain solution is 2:50:100. The

solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to

water is halved. If the altered solution will contain 100 cubic centimeters of alcohol, how

many cubic centimeters of water will it contain?

(A) 50 (B) 200 (C) 400 (D) 625 (E) 800

40. Tom and Carlos begin to play a series of four games with 400 chips each. At the end of each

game, there is a loser who must surrender half of his chips to the winner. If Tom wins only

the first and third games, how many chips does he have after the pay-off at the end of the

fourth game?

(A) 200

(B) 275

(C) 400

(D) 525

(E) 550

STOP



수학해설 Category 4 Ratio and Proportion

1. A certain club has 35 male members and 45 female members. Which of the following equals the ratio of the number of male members to the number of female members?

(A) 16:7

(B) 9:5

(C) 7:5

(D) 4:3

(E) 9:7

35 : 45 = 5×7: 5×9 = 9:79

7

95

75==

××

: 정답은 (E) :

2. What is the ratio of 4

3 to the product

4

34 ?

(A) 4

1

(B) 3

1

(C) 9

4

(D) 4

9

(E) 4

4

3 :

43

4 = 1: 4 = 4

1

: 정답은 (A) :



3. If 7

2 of the 210 students in a class attended graduate school, what was the total number of

students in the class who did not attend graduate school? (A) 42 (B) 60 (C) 105 (D) 142 (E) 150

210 명 중에 2/7 가 대학원에 다녔다면, 5/7 은 대학원에 다니지 않은 사람이네요.

따라서 210 ×7

5= 150,

: 정답은 (E) :

4. A certain test consists of 8 sections with 25 questions numbered from 1 to 25, in each section.

If a student answered all of the even-numbered questions correctly and 4

3 of the odd-

numbered questions correctly, what was the total number of questions he answered correctly?

(A) 150

(B) 172

(C) 174

(D) 175

(E) 176

25 문제로 8 개의 sections 으로 구성된 시험에서 한 학생이 짝수 문제는 모두 맞추었고, 홀수

문제는 3/4 맞추었다면 총 맞은 문제수가 몇 개 인가를 묻는 문제네요. 일단 25 문제에서

짝수 문제 수는 12 문제이고 이것이 8sections 이니까 8 을 곱하면 96 을 구할 수 있네요. 마

찬가지 방법으로 홀수 문제는 13 × 8 = 104 문제네요. 짝수 문제는 다 맞혔으니까 96, 홀수문

제는 104 × 4

3= 78 문제, 이 둘을 합치면 96 + 78 = 174 입니다.

: 정답은 (C) :

5. Two cities that are geographically 380 miles apart are 2 inches apart on a certain map. If the

map is drawn to scale, how many miles apart are two cities that are 2

17 inches apart on the

map?

(A) 665 (B) 1,330

(C) 1,425

(D) 2,090

(E) 2,850

Proportion 을 묻는 문제네요. A : B = C : D ⇒ AD = BC, 또는 D

C

B

A=

380 miles : 2 inches = X : 2

17 inches , 왼쪽의 식을 정리하면 X = 1,425 입니다.

: 정답은 (C) :



6. Lou and Selma were hired to paint a room for a total of $72. They completed the job with Lou

working 3 hours and 20 minutes and Selma working 2 hours and 40 minutes. If they decided

to split the $72 in proportion to the amount of time each spent on the job, how much did Lou

receive?

(A) $32.00

(B) $36.00 (C) $40.00

(D) $41.14

(E) $43.20

Lou은 3시간 20분 = 200분 , Selma은 2시간 40분 = 160분

둘의 시간에서 Lou 가 차지하는 비율은 95

360200 = , 여기에 둘이 나누기로 한 돈 $72을 곱하

면 Lou의 몫이 나오네요 40$72$9

5=× ,

: 정답은 (C) :

7. Kathy bought 4 times as many shares in Company X as Carl, and Carl bought 3 times as many shares in the same company as Tom. Which of the following is the ratio of the numbers

of shares bought by Kathy to the number of shares bought by Tom?

(A) 4

3 (B)

3

4 (C)

1

3 (D)

1

4 (E)

1

12

1Kathy 의 주식수 = 4 Carl, 2Carl = 3 Tom

2 식을 1 에 대입하면 Kathy = 12 Tom 식을 만들 수 있네요. 따라서 이 식을 정리하면

Kathy : Tom = 12 : 1 입니다.

: 정답은 (E) :

8. Of the 40 schools invited to participate in a research study, 8

7 agreed to participate. If 60

questionnaires were sent to each of the participating schools and 5

4 of these questionnaires

were completed and returned, what was the total number of questionnaires completed and

returned?

(A) 28 (B) 1,344 (C) 1,680 (D) 1,920 (E) 2,100

40개 학교 중에서 8

7이 research study 에 참가하기로 했다 :40×

8

7= 35 학교

참가 학교에 60 문제가 보내졌는데 5

4의 문제만 작성되어서 돌아옴 : 60 ×

5

4=48

문제는 40개 학교에서 completed 돌아온 총 문제의 수를 묻는 문제입니다.

즉 (35 학교 × 48) = 1,680,

: 정답은 (C) :



9. If a printer can 2 pages of text per second, then, at this rate, approximately how many minutes

will it take to print 5,000 pages of text?

(A) 4

(B) 25

(C) 42

(D) 250 (E) 417

2 pages : 1 second = 5,000 pages : X

위의 식을 정리하면 X= 2,500 seconds 이네요. 다시 second을 minute 단위로 바꾸면 2,500÷60

≅ 42 minutes 입니다.

: 정답은 (C) :

10. If $160 is divided among 3 people in the ratio 8:5:3 , what is the least amount received by

any one person?

(A) $80

(B) $50 (C) $30

(D) $20

(E) $10

$160이 세 사람에게 16

8,

16

5,

)853(16

3

++= 각각 나누어질 때, 누가 얼마의 가장 적은 돈을 받

는지를 계

산하는 문제네요. 세 분수 중에서 3/16이 제일 작으니까 (3/16)×$160 = $30

: 정답은 ( C ) :

11. Which three of the following fractions are equivalent?

80

5=v ,

08.0

05.0=w ,

0.8

5.0=x ,

8.0

05.0=y ,

008.0

05.0=z

(A) v , w , and x

(B) v , x , and y

(C) w , x , and y

(D) w , y , and z

(E) x , y , and z

해설이 필요 없는 문제이네요. 가끔은 이런 문제도 실제 시험에서 나옵니다. 하지만 37문제

중에

2 ~ 3 개 정도 나오니까 이런 문제를 보고 수학이 쉽다고 말하면 안되죠!

v , x , and y 의 fractions을 정리하면 모두 0.0625 의 값이 나오네요.

: 정답은 (B) :



12. A study based on a random sample revealed that, on average, 2 out of 5 adults have high blood

pressure. If these results hold true for the 580,000 adults in City A , approximately how

many adults in City A have high blood pressure?

(A) 116,000

(B) 145,000

(C) 232,000

(D) 250,000

(E) 290,000

5 명 중에 2명이 고혈압을 겪고 있는데, 이것을 580,000명에게 적용시키면

000,232000,5805

2=× ,

: 정답은 (C) :

13. Two boxes of pudding mix cost a total of $0.73 and 1 box of cake mix costs twice as much as

two boxes of pudding mix. At these rates, what is the cost of 3 boxes of pudding mix and 3

boxes of cake mix?

(A) $1.10

(B) $3.29

(C) $4.38

(D) $5.48

(E) $6.57

Two boxes of pudding mix = $0.73 ⇒ one box of pudding mix = $0.3650 1 box of cake mix = 2($0.73) = $1.46

따라서 3 boxes of pudding mix = 3 ×$0.3650 = $1.0950, 3 boxes of cake mix = 3×$1.46 = $4.38

두 값을 합하면 $5.48,

: 정답은 (D) :

14. Out of their annual net income, a couple spent 25 percent for food, 13.5 percent for

entertainment, 20 percent for housing, 8 percent for car expenses, 15 percent for clothing, and

saved the rest. What was the ratio of the amount saved to the amount spent for entertainment?

(A) 27

19 (B)

5

6 (C)

27

37 (D)

9

19 (E)

3

7

Income 중에서 25% + 13.% + 20% + 8% + 15% = 81.5% 을 쓰고 나머지 18.5%는 저축하는데,

저축

퍼센트와 entertainment에 쓴 돈의 ratio 을 구하는 문제네요.

18.5%: 13.5% = 27

37

135.0

185.0=

: 정답은 (C) :



15. Approximately how many minutes will it take a secretary who types at an average rate of 60

words per minute to type a 5-page report with 250 words per page?

(A) 4 (B) 12 (C) 21 (D) 30 (E) 75

1분에 60 words 을 치는 비서가 1,250 words ( 250 × 5 pages) 치는데 얼마나 걸리는가를

묻는 문제입니다.다.60 = X : 1,250 에서 X = 20. 8333 의 근사치는 21,

: 정답은 (C) :

16 If the speed of an airplane is 360 kilometers per hour, how many meters will it travel in one

second? (1 kilometer = 1,000 meters)

(A) 100 (B) 360 (C) 1,000 (D) 3,600 (E) 6,000

일단 360 kilometers을 meters로 바꾸면 360×1,000 = 360,000 meters

1 hours 을 one second으로 바꾸면 1 ×60 × 60 = 3600 seconds

360,000 meters을 3600 seconds로 나누면 1초에 가는 거리가 100 meters가 나옵니다.

: 정답은 ( A ) :

<High Level Questions 문제해설>

17. The total time required to transport rail freight from City X to City Y is 4 days, 15 hours.

If, by eliminating certain intermediate stops, the total time were reduced by 3

1, the total

transport time required would be

(A) 1 day, 3

15 hours

(B) 1 day, 13 hours

(C) 2 days, 3

210 hours

(D) 2 days, 3

215 hours

(E) 3 days, 2 hours

시간이 3

1만큼 감소 했기 때문에(be reduced by

3

1) 이제

3

2만큼의 시간이 소요됩니다.

)(743

2)(111 hourshours =×

( 4 days, 15 hours은 111시간 입니다. )

ÿ 답은 (E)입니다.



18. A small firm spent 4

1 of its annual budget during the first 2 months of its fiscal year and

spent 2

1 of its remaining budget during the next 5 months. What fraction of the annual

budget remained unspent at the end of the first 7 months?

(A) 16

3 (B)

4

1 (C)

16

5 (D)

8

3 (E)

12

5

새로운 회계연도가 시작하여 2개월이 지난 후 예산의 4

3이 남겨 졌으며, 그 후 5개월 동안

남겨진 예산의 2

1만큼이 집행 되었으므로 미집행된 예산은

8

3입니다.

: 답은 (D)입니다. :

19. Members of a social club met to address 280 newsletters. If they addressed 4

1 of the

newsletters during the first hour and 5

2 of the remaining newsletters during the second hour,

how many newsletters did they address during the second hour?

(A) 28 (B) 42 (C) 63 (D) 84 (E) 112

한 시간동안의 작업 후에 남은 회보는 210장

×= 280

4

3입니다. 이중

5

2가 두 번째 한 시

간동안에 작업이 이루어진 것 입니다.

: 답은 (D)입니다. :

20. In a certain used-car lot, there are 4 times as many blue cars as green cars and 3

1 as many

green cars as red cars. If there are q4 red cars in the lot, how many blue cars are in the lot?

(A) q12 (B) 3

16q (C) q3 (D)

3

4q (E)

4

3q

파란색 차가 녹색 차보다 4배가 많고 녹색차의 3

1만큼이 붉은색 차라고 합니다.(붉은색 차

가 녹색차보다 3배가 많다는 의미입니다.)

색상에 따른 자동차들간에 비율을 구하면 “파란색 : 녹색 : 붉은색 = 4 : 1 : 3” 입니다. 따라

서 파란색 자동차 대 붉은색 자동차간에 비율은 4:3입니다.

: 답은 (B)입니다. :



21. When Inez and Fernando purchased a property for $20,000. Fernando contributed 3

1 the

amount contributed by Inez for the purchase. If they sold the property for $40,000 and shared this amount in proportion to their respective contributions, how much was Fernando’s

share?

(A) $5,000 (B) $10,000 (C) $13,333 (D) $20,000 (E) $26,666

Inez와 Fernando는 $20,000에 부동산을 구입했다고 합니다. 부동산 구입을 위하여Fernando는

Inez가 지급한 돈의 3

1만큼을 지불 했다고 합니다. 이 부동산을 $40,000에 팔았을 때, 구입

시 기여한 비율 만큼의 돈을 각 사람에게 분배하면 Fernando가 받게 될 금액을 물어 보고

있습니다.

Fernando는 Inez가 지급한 돈의 3

1만큼을 지불 했다고 했으므로, Inez는 Fernando가 지급한

돈의 3배를 지급한 것 입니다. 따라서 Fernando와 Inez가 지불한 금액의 비율은 Fernando :

Inez = 1 : 3의 비율이 됩니다. $40,000을 받고 부동산을 팔았다고 했으므로 이 돈을 4등분하여

Fernando는 1부분 만큼의 돈을 갖게 됩니다.

식을 세워서 문제를 풀 수 도 있겠지만 percent, ratio와 관련된 문제들은 문제를 읽어 가면서

포인트를 파악해 가는 훈련을 쌓아 가는 것이 좋습니다.

: 답은 (B)입니다. :

22. Of Amy’s monthly salary, 4

1 goes to rent and

5

1 to food. If the remainder of her monthly

salary amounts to $990, what is Amy’s monthly salary?

(A) $1,042

(B) $1,273

(C) $1,800

(D) $1,980 (E) $2,200

월급의 4

1은 rent 비용으로,

5

1은 식료품 구입을 위해 사용한 후 남는 급여는 $990이라고 합

니다. 이 때 월급의 액수를 물어보고 있습니다.

전체 월급에서

+=

5

1

4

1

20

9만큼을 사용하고 남는 월급의

20

11에 해당하는 금액이 $990입

니다. 따라서 월급은 $1,800

×= 990$

11

20입니다.

: 답은 (C)입니다 :



23. When 9

2 of the votes on a certain resolution have been counted,

4

3 of those counted are in

favor of the resolution. What fraction of the remaining votes must be against the resolution

so that the total count will result in a vote of 2 to 1 against the resolution?

(A) 14

11

(B) 18

13

(C) 7

4

(D) 7

3

(E) 14

3

개표가 9

2만큼 이루어 졌을 때, 찬성표가

4

3이었습니다. 반대 대 찬성의 비율이 2 : 1이 되

기 위해서는 미개표된 표 중 얼마가 반대표여야 하는지 물어 보고 있습니다.

전체 투표의 9

2가 개표 되었을 때 찬성표가

4

3이었으므로 반대표는 전체 투표의

×=

4

1

9

2

18

1입니다. 반대 대 찬성의 비율이 2:1이기 위해서는 전체표의

18

12가 반대표이면

됩니다. 따라서 다음의 식에서 x 를 구해 주면 됩니다. 18

11

9

7=× x

: 답은 (A)입니다 :

24. In a certain population, there are 3 times as many people aged twenty-one or under as there

are people over twenty-one. The ratio of those twenty-one or under to the total population is

(A) 1 to 2

(B) 1 to 3

(C) 1 to 4

(D) 2 to 3

(E) 3 to 4

의미만 정확히 파악하면 쉬운 문제입니다. 21세 이하의 사람이(people aged twenty-one or under-

이런 표현들을 잘 기억해 두면 좋습니다.) 22세 이상의 사람의(people over twenty-one – 21세

는 포함되지 않습니다.) 3배라고 합니다. 21세 이하 사람 대비 전체 인원비율은 3 : 4가 됩니

다.

: 답은 (E)입니다. :



25. Last year Department Store X had a sales total for December that was 4 times the average (arithmetic mean) of the monthly sales totals for January through November. The sales total

for December was what fraction of the sales total for the year?

(A) 4

1

(B) 15

4

(C) 3

1

(D) 11

4

(E) 5

4

12월 한 달간의 판매량이 1월부터 11월 사이의 월평균 판매량의 4배일 때, 12월 판매량 대

1년 동안의 판매량의 비율을 물어 보고 있습니다.

1월부터 11월 사이의 월평균판매량을 q 라 하면 12월의 판매량은 q4 입니다. 따라서 1년간

의 총판매량은 q15 가 됩니다.

:: 답은 (B)입니다. ::

26. Millie and Rick addressed 150 invitations. If Millie addressed 2

11 times as many as Rick

addressed, how many of the invitations did Rick address?

(A) 30

(B) 60

(C) 75

(D) 90

(E) 100

Millie와 Rick은 초청장 150장을 보냈다고 합니다. Mille이 발송한 초청장이 Rick이 발송한

초청장 수의 2

11 배일 때, Rick이 보낸 초청장 수를 물어 보고 있습니다.

Rick이 보낸 초청장 수를 R 이라 하면 다음과 같이 식을 세워 문제를 풀 수 있습니다.

1502

11 =+ RR

하지만 문제를 보다 빨리 풀기 위해서는 Millie이 발송한 초청장이Rick이 발송한 초청장보다

2

11 배라는 것을 읽으면서 Millie이 보낸 초청장 수가 Rick이 보낸 초청장 수보다 50%가 많

다는 사실을 파악하여 보기로 부터 답을 찾는 것 입니다.

:: 답은 (B)입니다 ::



27. In 1990 a total of x earthquakes occurred worldwide, some but not all of which occurred in

Asia. If m of these earthquakes occurred in Asia, which of the following represents the

ratio of the number of earthquakes that occurred in Asia to the number that did not occur in

Asia?

(A) m

x (B)

x

m (C)

mx

m

− (D)

mx

x

− (E)

x

m−1

아시아에서 일어난 지진 횟수 대 아시아이외 지역에서 일어난 지진의 비율을 물어 보고 있

습니다.

:: 답은 (C)입니다. ::

28. The ratio of two quantities is 3 to 4. If each of the quantities is increased by 5, what is the

ratio of these two new quantities?

(A) 4

3

(B) 9

8

(C) 19

18

(D) 24

23

(E) It cannot be determined from the information given.

두 분량의 비율이 3 : 5이며 각각의 분량이 5 만큼씩 증가할 때 새로운 분량의 비율을 물어

보고 있습니다. 원래 있던 분량이 얼마인지 알 수 없기 때문에 새로 추가되는 5가 두 분량

간의 비율을 어떻게 변화시킬지 알 수 없습니다. .

예) 300 : 500 ⇒ 305 : 505, 30 : 50 ⇒ 35 : 55

:: 답은 (E)입니다. ::

29. Of the people who responded to a market survey, 120 preferred Brand X and the rest

preferred Brand Y . If the respondents indicated a preference for Brand X over Brand

Y by a ratio of 3 to 1, how many people responded to the survey? (A) 80 (B) 160 (C) 240 (D) 360 (E) 480

X 브랜드를 선호한다고 답변한 사람이 120명이었으며 X 브랜드 대 Y 브랜드를 선호하는

사람의 비율이 3 : 1이라고 합니다. 이 때 설문조사에 응한 전체 응답자 수를 물어 보고 있

습니다.

X 브랜드를 선호한다는 응답자의 수가 120명이었으므로 Y 브랜드를 선호한다고 응답한 사

람은 40명입니다.

:: 답은 (B)입니다. ::



30. Orange juice of normal strength is prepared by adding three 6-ounce cans of water to the

contents of a 6-ounce can of orange juice concentrate. If 1 ounce of the can of concentrate

was already used for some other purpose, how many 6-ounce cans of water should be added to

the remainder of the concentrate to prepare juice of normal strength?

(A) 3

21

(B) 2

(C) 3

12

(D) 2

12

(E) 6

52

일반농도의 오렌지 쥬스는 6-ounce 오렌지 농축액 한 개의 can과 6-ounce 물 세 개의can을

섞어서 만든다고 합니다. 1-ounce 오렌지 농축액이 다른 용도로 사용 되었을 때, 일반농도의

오렌지쥬스를 만들기 위해 몇 can의 물이 사용되는지 물어 보고 있습니다.

오렌지 농축액 6 ounce와 물 18ounce를 혼합하여 일반농도를 만들므로 “오렌지 농축액 : 물=

1 : 3 ”입니다. 5 ounce만큼의 오렌지 농축액이 남아 있으므로 15ounce만큼의 물이 필요합니다.

:: 답은 (D)입니다. ::

31. A coffee merchant makes a house blend of coffee using 4 pounds of Arabian beans costing $3

per pound, 2 pounds of Java beans costing $4 per pound, and 4 pounds of Brazilian beans

costing $1 per pound. If the merchant sold all of the blend for 50 percent more than the total

cost of the beans used, at what price per pound was the blend sold?

(A) $1.20

(B) $2.40

(C) $3.00

(D) $3.60

(E) $4.50

파운드 당 $3하는 Arabian산 커피 4파운드(총 $12) , 파운드 당 $4하는 Java산 커피 2파운드

(총 $8), 파운드 당 $1하는 Brazil 커피 4파운드(총 $4)를 이용하여 브랜드커피를 만듭니다.

판매가격은 브랜드커피를 만들기 위해 구입한 커피의 비용보다 50%가 높을 때 1파운드 당

가격을 물어 보고 있습니다.

10파운드의 커피를 구입하는데 총 $24이 소요 되었습니다. 1파운드 당 $2 4가 소요된 것이며

판매가격은 $ 2.4보다 50% 많으므로 $3.6입니다.

:: 답은 (D)입니다. ::



32. The current ratio of men to women on a certain board of trustees is 2 to 5. If 4 men were

added to the board, the ratio of men to women would be 2 to 3. How many men are currently

on the board?

(A) 2

(B) 4

(C) 5 (D) 6

(E) 8

남성 대 여성의 비율이 2 : 5라고 합니다. 위원회에 남성이 4명 더 참가하면 남성 대 여성의

비율이 2 : 3으로 바뀐다고 합니다. 현재 몇 명의 남성이 위원회에 있는지 물어 보고 있죠.

남성의 수를 m , 여성의 수를 f 라 하면 5:2: =fm 입니다. 남성이 4명 참가 하면

3:2:4 =+ fm 이 됩니다. 따라서 두 식을 연립하여 계산하면 남성의 수를 구할 수 있죠.

:: 답은 (D)입니다. ::

33. A custom blend of paint is made by mixing red, yellow, and black paints in the ratio of 12 to 11

to 1. If all of the paints are sold only in pint-sized containers, how many containers of yellow

are used in preparing 6 gallons of the blend? (8 pints = 1 gallon)

(A) 2 (B) 3

(C) 11

(D) 22

(E) 24

붉은색, 노란색, 검은색을 12:11:1의 비율로 혼합하여a custom blend of paint를 만든다고 합니다.

모든 페인트가 파인트(pint : 1/8gallon) 단위의 용기에 담겨져 팔릴 때, 6 gallon의 blend을 준비

하기 위해서 노란색 페인트 몇 통을 사용해야 하는지 물어 보고 있습니다.

< 풀이1 >

A custom blend of paint에서 노란색이 차지하는 비율은 24

11입니다. 노란색의 페인트는

2.75gallon

×=

24

116gallon 이 필요합니다. 따라서 노란색 22 ( )875.2 ×= gallon 파인트가 필

요합니다.

< 풀이 2 >

6gallon은 48파인트 입니다. 48파인트의 24

11은 22파인트입니다.

:: 답은 (D)입니다. ::



34. A rectangular office floor is 28 meters by 20 meters. A custodian, working at a constant rate,

waxes a section of the floor that is 5 meters by 20 meters in 4

3 hour. How many hours does

it take the custodian, working at this same constant rate, to wax the entire floor?

(A) 2.52 (B) 3 (C) 3.45 (D) 4.2 (E) 7

4

3시간 동안 5 meters by 20 meters만큼씩 마루바닥을 닦을 때, 28 meters by 20 meters 크기의 직

사각형 바닥을 닦는데 얼마만큼의 시간이 소요될지 물어 보고 있습니다.

28 meters by 20 meters크기의 직사각형 바닥은 4

3시간 동안에 닦을 수 있는 5 meters by 20

meters크기의 5.6배 입니다.

=

××

6.5205

2028 따라서 시간도 5.6배 만큼 소요됩니다.

:: 답은 (D)입니다. ::

35. A glucose solution contains 15 grams of glucose per 100 cubic centimeters of solution. If 45

cubic centimeters of the solution were poured into an empty container, how many grams of

glucose would be in the container?

(A) 3.00 (B) 5.00 (C) 5.50 (D) 6.50 (E) 6.75

포도당 용액은 물 100 cubic centimeter당 15그램의 포도당을 포함하고 있다고 합니다. 이 때

포도당 용액 45 cubic centimeter내에 포함되어 있는 포도당의 질량을 물어 보고 있습니다.

75.615100

45=×

:: 답은 (E) 입니다 ::

36. Dan bought x pencils, some at 10 cents each and the rest at 6 cents each. For the same

amount of money that he spent on these pencils, he could have bought x pencils at 9 cents

each. What is the ratio of the number of 10-cent pencils purchased to the number of 6-cent

pencils purchased?

(A) 1 : 1 (B) 2 : 1 (C) 3 : 1 (D) 4 : 1 (E) 5 : 1

Dan은 x개의 연필을 구입했고 구입한 연필 중 일부는 한 자루 당 가격이10cent 였으며 나

머지는 6cent였다고 합니다. 연필을 구입하는데 지불한 동일한 금액 만큼을 가지고 한 자루

당 9cent하는 연필을 x자루 살 수 있다고 합니다. 10 cent연필과 6cent 연필의 비율을 물어

보고 있습니다.

연필을 구입하는데 지불한 동일한 금액 만큼을 가지고 한 자루 당 9cent하는 연필을 x자루

살 수 있다고 했으므로, 구입한 연필의 한 자루 당 평균금액이 9cent라는 것을 의미합니다.



평균금액이 9cent가 되기 위해서는 6cent 연필 한 자루 당10 cent연필이 3자루씩 있어야 합니

다. 따라서 10 cent 연필 대 6 cent 연필의 비율은 3:1입니다.

:: 답은 (C)입니다. ::

37. A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black

paint. If 2 gallons of the mixture is needed and the individual colors can be purchased only in

one-gallon or half-gallon cans, what is the least amount of paint, in gallons, that must be

purchased in order to measure out the portions needed for the mixture?

(A) 2

(B) 2

12

(C) 3

(D) 2

13

(E) 4

특정농도의 회색 페인트는 흰색 페인트를 3, 검은색 페인트는 5만큼 혼합하여 만든다고 합

니다. 2 gallon의 회색페인트가 필요하며 개별 색은 1 gallon 또는 2

1gallon씩 구입 할 수 있을

때, 회색페인트를 만들기 위해 구입해야 하는 페인트의 최소량을 물어 보고 있습니다.

회색페인트를 만들기 위해 필요한 검은색 페인트는 전체 페인트 양의 8

5입니다.

8

5는

2

1

보다는 크지만 1보다는 작습니다. 따라서 검은색 페인트가 1.5gallon이 필요하다는 것을 알

수 있습니다.

물론 1.5gallon이 모두 필요한 것은 아니죠. 다만 페인트를 구입할 수 있는 단위가 1 gallon

또는 2

1gallon이기 때문에 1.5gallon을 구입하여 1.25gallon만큼을 사용하게 됩니다. 흰색페인

트는 전체 페인트 양의 8

3이 필요합니다.

8

3은 ( )25.0

4

1= 보다

2

1보다는 작습니다. 따라서

1gallon만큼 구입하면 됩니다.(실재 사용량은 0.75 gallon

×=

8

32 입니다.)

:: 답은 (B)입니다. ::



38. Working alone, printers X , Y , and Z can do a certain printing job, consisting of a large

number of pages, in 12, 15, and 18 hours, respectively. What is the ratio of the time it takes

printer X to do the job, working alone at its rate, to the time it takes printers Y and Z to do the job, working together at their individual rates?

(A) 11

4 (B)

2

1 (C)

22

15 (D)

15

22 (E)

4

11

프린터 X , Y , Z 가 특정 인쇄작업을 하는 데 각각 12시간, 15시간, 18시간이 소요된다고

합니다. 프린터 X 가 특정 작업을 완수하는데 소요되는 시간 대 프린터 Y , Z 가 동시에

작업을 하여 일을 끝내는데 소요되는 시간의 비율을 구하는 문제입니다.

프린터 Y , Z 가 동시에 한 시간 내에 할 수 있는 작업의 양은 90

11

+=

18

1

15

1입니다.

따라서 작업을 완수하는데 11

90시간이 소요됩니다. 시간은 비율은

11

9012 입니다.

:: 답은 (D)입니다. ::

39. The ratio, by volume, of soap to alcohol to water in a certain solution is 2:50:100. The

solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to

water is halved. If the altered solution will contain 100 cubic centimeters of alcohol, how

many cubic centimeters of water will it contain?

(A) 50 (B) 200 (C) 400 (D) 625 (E) 800

비누 : 알코올 : 물 = 2 : 50 : 100 일 때, 알코올에 대한 비누의 비율은 2배가 되도록 물에 대

한 비누의 비율은 1/2배가 되도록 용액이 변했다고 합니다. 변화된 용액에서 알코올이 100

cubic centimeters ( )3Cm 일 때, 물은 몇 cubic centimeters인지 물어 보고 있습니다.

원래 용액에서의 비누의 비율 대 알코올의 비율은 2 : 50

=

50

2입니다. 비율이 두 배가 되

기 위해서는 현재 보다 비누의 양이 2배로 증가

⋅

50

22 하면 됩니다. 비누의 비율 대 물의

비율이 1/2배가 되기 위해서는 물의 양은 2배가 증가해야 됩니다. 비누의 비율 대 알코올의

비율이 2 배가 되기 위해서 이미 비누의 양이 두 배가 증가 했기 때문에 물의 양은 4배가

증가해야 합니다.

=

××

→100

1

4100

22

100

2 새로운 용액에서의 비율은 “비누 : 알코올 : 물

= 4 : 50 : 400”입니다. 알코올이 100 cubic centimeters이므로 물은 800cubic centimeters입니다.

:: 답은 (E)입니다 ::



40. Tom and Carlos begin to play a series of four games with 400 chips each. At the end of each

game, there is a loser who must surrender half of his chips to the winner. If Tom wins only

the first and third games, how many chips does he have after the pay-off at the end of the

fourth game?

(A) 200 (B) 275

(C) 400

(D) 525

(E) 550

Tom과 Carlos는 각자 400개의 칩을 가지고 4경기를 시작합니다. 매 경기 패자가 승자에게

자신이 가진 칩의 절반을 줄 때, Tom이 첫 번째, 세 번째 게임만을 이겼을 경우 Tom이 4

경기가 끝난 후 갖게 되는 칩의 개수를 물어 보고 있습니다.

Tom이 매 경기 후 갖게 되는 칩의 개수는 다음과 같습니다.(두 사람이 가지고 있는 칩의 개

수는 총 800개 입니다. 따라서 “800 – Tom이 갖고 있는 칩의 개수”가 Carlos가 가지고 있는

칩의 개수 입니다.)

첫 번째 경기 두 번째 경기 세 번째 경기 네 번째 경기

600개 300개 550개 275개

+ 200(승리) -300(패배) +250(승리) -275(패배)

:: 답은 (B)입니다 ::

gre math 강좌 set 4

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