DS-1：

2. 86-!-item-!-187;#058&000002

Of the students who eat in a certain cafeteria, each student either likes or dislikes lima beans and each student
either likes or dislikes brussels sprouts. Of these students,

2
dislike lima beans;
3 and of those who dislike lima beans,
 3
5
also dislike brussels sprouts. How many of the students like brussels sprouts but dislike lima beans?
(1) 120 students eat in the cafeteria.
(2) 40 of the students like lima beans.
D

10. 719-!-item-!-187;#058&000515
Of the 800 students at a certain college, 250 students live on campus and are more than 20 years old. How many
of the 800 students live on campus and are 20 years old or less?
(1) 640 students at the college are more than 20 years old.
(2) 60 students at the college are 20 years old or less and live off campus.
E-C

12. 1013-!-item-!-187;#058&000609
Of the 25 cars sold at a certain dealership yesterday, some had automatic transmission and some had antilock
brakes. How many of the cars had automatic transmission but not antilock brakes?
(1) All of the cars that had antilock brakes also had automatic transmission.
(2) 2 of the cars had neither automatic transmission nor antilock brakes.
E
20. 1491-!-item-!-187;#058&000755
A certain one-day seminar consisted of a morning session and an afternoon session. If each of the 128 people
attending the seminar attended at least one of the two sessions, how many of the people attended the morning
session only?
(1)

3
4
of the people attended both sessions.
(2)
 7
8
of the people attended the afternoon session.
E-B
(2)并没有说是只参加下午的人
22. 1599-!-item-!-187;#058&000810
Of the 800 sweaters at a certain store, 150 are red. How many of the red sweaters at the store are made of pure
wool?
(1) 320 of the sweaters at the store are neither red nor made of pure wool.
(2) 100 of the red sweaters at the store are not made of pure wool.
E-B

23. 1653-!-item-!-187;#058&000843
At least 100 students at a certain high school study Japanese. If 4 percent of the students at the school who study
French also study Japanese, do more students at the school study French than Japanese?
(1) 16 students at the school study both French and Japanese.
(2) 10 percent of the students at the school who study Japanese also study French.
C-B

37. 3184-!-item-!-187;#058&003224
When 1,000 children were inoculated with a certain vaccine, some developed inflammation at the site of the
inoculation and some developed fever. How many of the children developed inflammation but not fever?
(1) 880 children developed neither inflammation nor fever.
(2) 20 children developed fever.
C

61. 5157-!-item-!-187;#058&004472
Of the 60 animals on a certain farm,

2
3
are either pigs or cows. How many of the animals are cows?
(1) The farm has more than twice as many cows as it has pigs.
(2) The farm has more than 12 pigs.
A-C

64. 5320-!-item-!-187;#058&004563
Are at least 10 percent of the people in Country X who are 65 years old or older employed?
(1) In Country X, 11.3 percent of the population is 65 years old or older.
(2) In Country X, of the population 65 years old or older, 20 percent of the men and 10 percent of the women are
employed.
E-B
78. 6841-!-item-!-187;#058&005248
For each customer, a bakery charges p dollars for the first loaf of bread bought by the customer and charges q
dollars for each additional loaf bought by the customer. What is the value of p ?
(1) A customer who buys 2 loaves is charged 10 percent less per loaf than a customer who buys a single loaf.
(2) A customer who buys 6 loaves of bread is charged 10 dollars.
C
86. 7767-!-item-!-187;#058&005660
Each of the students in a certain class received a single grade of P, F, or I. What percent of the students in the class
were females?
(1) Of those who received a P, 40 percent were females.
(2) Of those who received either an F or I, 80 percent were males.
E
120. 12140-!-item-!-187;#058&008146
How many of the students in a certain class are taking both a history and a science course?
(1) Of all the students in the class, 50 are taking a history course.
(2) Of all the students in the class, 70 are taking a science course.
E

121. 12343-!-item-!-187;#058&008383
Pat bought 5 pounds of apples. How many pounds of pears could Pat have bought for the same amount of money?
(1) One pound of pears costs $0.50 more than one pound of apples.
(2) One pound of pears costs 1
 1
2
times as much as one pound of apples.
C-B
140. 14319-!-item-!-187;#058&009938
At a certain pet shop,
 1
of the
3
pets are dogs and
 1
5
of the pets are birds. How many of the pets are dogs?
(1) There are 30 birds at the pet shop.
(2) There are 20 more dogs than birds at the pet shop.
D
162. 16257-!-item-!-187;#058&010730
What fraction of this year's graduating students at a certain college are males?
(1) Of this year's graduating students, 33 percent of the males and 20 percent of the females transferred from
another college.
(2) Of this year's graduating students, 25 percent transferred from another college.
C
164. 16412-!-item-!-187;#058&010774
At a two-day seminar, 90 percent of those registered attended the seminar on the first day. What percent of those
registered did not attend the seminar on either day?
(1) A total of 1,000 people registered for the two-day seminar.
(2) Of those registered, 80 percent attended the seminar on the second day.
E
165. 16466-!-item-!-187;#058&010795
Of the 1,400 college teachers surveyed, 42 percent said that they considered engaging in research an essential goal.
How many of the college teachers surveyed were women?
(1) In the survey, 36 percent of the men and 50 percent of the women said that they considered engaging in
research an essential goal.
(2) In the survey, 288 men said that they considered engaging in research an essential goal.
C-A
179. 17750-!-item-!-187;#058&011285
A manufacturer conducted a survey to determine how many people buy products P and Q. What fraction of the
people surveyed said that they buy neither product P nor product Q ?
(1)

1
3
of the people surveyed said that they buy product P but not product Q.
(2)
 1
2
of the people surveyed said that they buy product Q.
------------------------------------------------------------------------------------------------------------------------------------
C
192. 18939-!-item-!-187;#058&011984
Of the 75 houses in a certain community, 48 have a patio. How many of the houses in the community have a
swimming pool?
(1) 38 of the houses in the community have a patio but do not have a swimming pool.
(2) The number of houses in the community that have a patio and a swimming pool is equal to the number of
houses in the community that have neither a swimming pool nor a patio.
C-B

DS-2：
9. 617-!-item-!-187;#058&000317
Each of the 105 students in a certain club is either a freshman, a sophomore, or a junior. How many of the students
in the club are sophomores?
(1) The ratio of the number of freshmen to the number of sophomores is 1 to 2.
(2) The ratio of the number of freshmen to the number of juniors is 1 to 4.
C
44. 3524-!-item-!-187;#058&003319
How many people received a certain survey?
(1) Six-tenths of those who received the survey responded.
(2) Of those who received the survey, 42 responded.
C
46. 3927-!-item-!-187;#058&003647
Three thousand families live in a certain town. How many families who live in the town own neither a car nor a
television set?
(1) Of the families who live in the town, 2,980 own a car.
(2) Of the families who live in the town, 2,970 own both a car and a television set.
E
72. 6868-!-item-!-187;#058&005029
Of the 4,800 voters who voted for or against Resolution K, 1800 were Democrats and 3,000 were Republicans.
What was the total number of female voters who voted for Resolution K ?
(1)

3
of
4
the Democrats and
 2
3
of the Republicans voted for Resolution K.
2)
 1
of the Democrats
3
who voted for Resolution K and
 1
2
of the Republicans who voted for Resolution K were females.
C
86. 7962-!-item-!-187;#058&005867
Do more than 50 percent of the children in a certain group have brown hair?
(1) 70 percent of the boys in the group have brown hair.
(2) 30 percent of the children in the group are girls with brown hair.
C-E
119. 11954-!-item-!-187;#058&008495
At a two-candidate election for mayor,
 3
4
of the registered voters cast ballots. How many registered voters cast ballots for the winning candidate?
(1) 25,000 registered voters did not cast ballots in the election.
(2) Of the registered voters who cast ballots, 55 percent cast ballots for the winning candidate.
E-C
127. 13762-!-item-!-187;#058&010132
If
 2
5
of the students at College C are business majors, what is the number of female students at College C ?
(1)
 2
5
of the male students at College C are business majors.
(2) 200 of the female students at College C are business majors.
E-C
141. 14664-!-item-!-187;#058&010407
Of the 20 people who each purchased 2 tickets to a concert, some used both tickets, some used only 1 ticket, and
some used neither ticket. What percent of the tickets that were purchased by the 20 people were used by those
people?
(1) Of the 20 people, 10 used only 1 ticket.
(2) Of the 20 people, 4 used neither ticket.
C
163. 16419-!-item-!-187;#058&011075
In a certain election, 240 men and 280 women voted for the winning candidate. What was the total number of men
and women who voted in the election?
(1) The number of women who voted was
 7
the number of men who voted.
8
(2) Of the men and women who voted, 30 percent of the men and 40 percent of the women voted for the winning
candidate.
B
181. 17723-!-item-!-187;#058&011591
Rasheed bought two kinds of candy bars, chocolate and toffee, that came in packages of 2 bars each. He handed
out
 2
of the
3
chocolate bars and
 3
5
of the toffee bars. How many packages of chocolate bars did Rasheed buy?
(1) Rasheed bought 1 fewer package of chocolate bars than toffee bars.
(2) Rasheed handed out the same number of each kind of candy bar.
E-C

185. 17987-!-item-!-187;#058&011677
Of the 200 members of a certain association, each member who speaks German also speaks English, and 70 of the
members speak only Spanish. If no member speaks all three languages, how many of the members speak two of
the three languages?
(1) 60 of the members speak only English.
(2) 20 of the members do not speak any of the three languages.
A-C
211. 20614-!-item-!-187;#058&013294
A certain economics class consists of 50 women and 30 men. How many of the men in the class are business
majors?
(1) 40 percent of the women in the class are business majors.
(2) 50 percent of all the people in the class are business majors.
C
GWD-2:
Q28:
Of the goose eggs laid at a certain pond, 2/3 hatched, and 3/4 of the geese that
hatched from those eggs survived the first month. Of the geese that survived the first
month, 3/5 did not survive the first year. If 120 geese survived the first year and if no
more than one goose hatched from each egg, how many goose eggs were laid at the
pond?

A. 280
B. 400
C. 540
D. 600
E. 840
Answer:
GWD-5:
Q19:
In a survey of 200 college graduates, 30 percent said they had received student loans during their
college careers, and 40 percent said they had received scholarships. What percent of those
surveyed said that they had received neither student loans nor scholarships during their college
careers?
(1) 25 percent of those surveyed said that they had received scholarships but no loans.
(2) 50 percent of those surveyed who said that they had received loans also said that they
had received scholarships.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Answer: D
GWD-6:
Q14:
A total of 30 percent of the geese included in a certain migration study were male. If some of the
geese migrated during the study and 20 percent of the migrating geese were male, what was the
ratio of the migration rate for the male geese to the migration rate for the female geese?
[Migration rate for geese of a certain sex = (number of geese of that sex migrating) / (total number
of geese of that sex)]

A. 1/4
B. 7/12
C. 2/3
D. 7/8
E. 8/7
Answer: C-B
GWD-9:
Q20:

Favorable Unfavorable Not Sure

Candidate M 40 20 40
Candidate N 30 35 35

The table above shows the results of a survey of 100 voters each responded “favorable” or
“unfavorable” or “not sure” when asked about their impressions of candidate M and of candidate
N. What was the number of voters who responded “favorable” for both candidates?
(1) The number of voters who did not respond “favorable” for either candidate was 40.
(2) The number of voters who responded “unfavorable” for both candidates was 10.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Answer:
GWD-14:
Q14:

Of all the students in a certain dormitory, are first-year students and the rest are second-year

students. If of the first-year students have not declared a major and if the fraction of second-

year students who have declared a major is 3 times the fraction of first-year students who have
declared a major, what fraction of all the students in the dormitory are second-year students who
have not declared a major?

A.

B.

C.

D.

E.

Answer:
Q37:
Of the 500 business people surveyed, 78 percent said that they use their laptop computers at home,
65 percent said that they use them in hotels, and 52 percent said that they use them both at home
and in hotels. How many of the business people surveyed said that they do not use their laptop
computers either at home or in hotels?

A. 45
B. 55
C. 65
D. 95
E. 130
Answer: A
GWD-15:
Q35:
For what percent of those tested for a certain infection was the test accurate; that is, positive for
those who had the infection and negative for those who did not have the infection?

(1) Of those who tested positive for the infection, did not have the infection.

(2) Of those tested for the infection, 90 percent tested negative.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Answer: A-E
GWD-17:
Q19:
Of the people who attended a workshop, 60 percent were teachers and some of the teachers were
teachers of language arts. What percent of the people who attended the workshop were teachers of
language arts?
(1) 200 people attended the workshop.
(2) 72 of the teachers who attended the workshop were not teachers of language arts.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Answer: B-C
GWD-18:
Q33:

If Diana’s stamp collection, of the stamps are Canadian, and of the Canadian stamps were
issued before 1940. If 192 stamps in Diana’s collection are Canadian stamps that were issued in
1940 or later, how many stamps in her collection are not Canadian?

A. 84
B. 88
A. 96
B. 104
C. 112
Answer: A
GWD-19:
Q12:
Each person who attended a company meeting was either a stockholder in the company, an
employee of the company, or both. If 62 percent of those who attended the meeting were
stockholders and 47 percent were employees, what percent were stockholders, who were not
employees?

A. 34%
B. 38%
C. 45%
D. 53%
E. 62%
Answer:
Q37:
A club with a total membership of 30 has formed 3 committees, M, S, and R, which have 8, 12,
and 5 members, respectively. If no member of committee M is on either of the other 2
committees, what is the greatest possible number of members in the club who are on none of the
committees?

A. 5
B. 7
C. 8
D. 10
E. 12
Answer: C
GWD-21:
Q20:

Of the 60 animals on a certain farm, are either pigs or cows. How many of the animals are

cows?
(1) The farm has more than twice as many cows as it has pigs.
(2) The farm has more than 12 pigs.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Answer: E-C
Q23:
On a certain transatlantic crossing, 20 percent of a ship’s passengers held round-trip tickets and
also took their cars abroad the ship. If 60 percent of the passengers with round-trip tickets did not
take their cars abroad the ship, what percent of the ship’s passengers held round-trip tickets?

A. 33 %

B. 40%
C. 50%
D. 60%

E. 66 %

Answer: C
QX:
On a certain transatlantic crossing, 20 percent of a ship’s passengers held round-trip tickets and
also took their cars abroad the ship. If 60 percent of the passengers with round-trip tickets did not
take their cars abroad the ship, what percent of the ship’s passengers held round-trip tickets?

A. 20
D. 30
B. 50
C. 65
D. 70
Answer:
GWD-22:
Q32:

Number Studying Number Not Total

Biology Studying Biology
Number 18
of Boys
Number
of Girls
Total 26

The table above shows the number of students in a certain high school class who are boys and the
number of students in the class who are studying biology. What is the total number of students in
the class?
 (1) Of the boys in the class, 15 are studying biology.
(2) The number of girls in the class is twice the number of students in the class who are not
studying biology.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Answer: C-B
GWD-23:
Q25:
Of the high school students who participated in a recent survey, 110 had taken a course in biology
and 230 had taken a course in history. How many students participated in the survey?
(1) Of the students who participated in the survey, 120 had taken neither a course in biology
nor a course in history.
(2) Of the students who participated in the survey, 60 had taken both a course in biology
and a course in history.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Answer: C
Q37:

Of the goose eggs laid at a certain pond, hatched, and of the geese that hatched from those

eggs survived the first month. Of the geese that survived the first month, did not survive the

first year. If 120 geese survived the first year and if no more than one goose hatched from each
egg, how many goose eggs were laid at the pond?

A. 280
B. 400
C. 540
D. 600
E. 840
Answer: D
GWD-26:
Q27:
In a survey, 2,500 executives were each asked whether they read Newsletter A or Newsletter B.
According to the survey, 55 percent of the executives read Newsletter A, 62 percent read
Newsletter B, and 37 percent read both Newsletter A and Newsletter B. How many of the
executives surveyed read neither Newsletter A nor Newsletter B?

A. 425
B. 500
C. 600
D. 675
E. 750
Answer: B
GWD-27:
Q33:

Favorable Unfavorable Not Sure

Candidate M 40 20 40
Candidate N 30 35 35

The table above shows the results of a survey of 100 voters each responded “favorable” or
“unfavorable” or “not sure” when asked about their impressions of candidate M and of candidate
N. What was the number of voters who responded “favorable” for both candidates?
(1) The number of voters who did not respond “favorable” for either candidate was 40.
(2) The number of voters who responded “unfavorable” for both candidates was 10.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Answer: D-A
FEIFEI 第一部分:
12、共有 200 人，其中买 A 产品的有 50 人，买 B 的有 40 人，买 C 的 75 人，买 D 的 60 人，买 E 的 85 人，已
经既买 A 又买 B 的是 15，求既不是 A 又不是 B 的人数？

【答案】125
【思路】200- (50+40-15) = 125
20、有 350 个人，不是研究生就是本科生，从中任取一个，是女研究生的概率？
（1）研究生有 187；
（2）女的有 247；

【答案】：E
【思路】：古典概率，但不知道女研究生的人数，所以选 E
23、两个班 A，B，在某次考试中的分数如下：问 A 和 B 在一起的 average>median ?
班级 median score average score
A 80 82
B 78 74

（1）A 37 人，B40 人；
（2）A+B 77 人；

【答案】a
【思路】
ave(a+b)≈77.8
a37→a(19)≥80
b40→b(20)≥78；b(21) ≥78
median(a+b)=(a+b)39≥78>ave(a+b)
选a

第二部分:
1、一个班总共有 60 个字生，他们要么学习西班牙语，要么学法语，或两者都学。学西班牙语的有 36 人，其中包括 6 个学两
种语言的。问学法语的有多少人？

【答案】：30
【思路】
根据集合定律：AUB=A+B-AB 交集,设学法语的为 X 人--->60=X+36-6-->X=60-36+6=30
11、一个有 200 人的小组中，选 P 的有 125 人，选 S 的有 81 人，求既不选 P 也不选 S 的人有多少？
（1）选 S 的人中有 20%的人选了 P；
（2）选 P 的人中有 56 人没有选 S；

【答案】D
【思路】I=p+s-ps+非 p 非 s（I 代表全集）， 所以只要求出 ps 即可！（1）和（2）分别可以求出即选了 p 又选了 s 的
人数。所以答案是 D
18、300 个病人有 3 种症状 A、B、C（每人至少有一各症状），A 为 35%，B 为 45%，C 为 40%，有且仅有两
种症状的为 10%，问有且仅有一种症状的为多少人？(0025 录音)

【答案】255
【思路】假设同时有三种症状的百分比为 X, 而有且仅有一种症状的百分比为 Y
则 35%+45%+40%-(10%+3X)+X=1---->X=5%
Y=1-10%-5%=85%----->有且仅有一种症状的人为 300×85％＝255

1=A+B+C-AB-BC-AC+ABC
25、某地 150000 个家庭，其中 80%有 CableTV，60%有 CassetteVIDIO，问既有 CABLE 又有
CASSETTE 的家庭可能数？

【答案】40%~60%的家庭两者都有，可能数为 60000~90000
【思路】最大的交集在于所有的 CassetteVIDIO 用户都拥有 CableTV，最小的可能性是为(0.8+0.6)-1=0.4
第四部分：
2、一个班有 18 个男生，全班有 26 人选修生物课，问全班人数？
（1）男生中选修生物课的有 15 人；
（2）女生人数是没有选修生物课的人数的 2 倍；

【答案】B
【思路】设全班人数为 X，则女生人数为 X-18，没选修的人数为 X-26，只有条件二可解 X。
3、There are 100 students in the class. Each student must choose at least one course of
English, French, and German. But no student can choose all the three class. There are
30 students learn E, and 60 students learn French, and 15 students learning German
also learn English. How many students learn German? (students learning E do not
learn French and F not G)

【答案】25
【思路】100-30-60+15=25，学 E 不学 F，也就是 E 与 F 的交集为 0，同理 F 与 G 的交集也为 0，那么只有 E
与 G 有交集为 15，则学 E 学 G 的人为 60+30-15，现在要求 F 只要把学 E 学 G 的减掉即可。
16 、 There are 1200 respondents to a poll, each favoring their preference for
candidates A, B, and C. 54% favored A, 48% favored B, and 42% favored C, and
there is 30% favored both A and B. What’s the largest possible number of respondents
favoring C, but not C & B, nor C &A.

【答案】1200×0.28＝336
【思路】题目问只选 C 的最大可能数是多少，要使这个数最大，就要满足所有选 C 的人，都不会同时选 A 或者 B。即
P(c)=1-P(A+B)=1-[P(A)+P(B)-P(AB)]=1-(0.54+0.48-0.3)=0.28。
第六部分：
1、In an insurance company, each policy has a paper record or an electric record, or
both of them. 60 percent of the policies having incorrect paper record have incorrect
electric record and 75 percent of the policies having incorrect electric record have
incorrect paper record. 3 percent of all the policies have both incorrect paper and
incorrect electric records. If we randomly pick out one policy, what is the probability
that it is one having both correct paper and correct electric record?

【答案】94%
【思路】
设总数为 X policies，则既有非 P 又有非 E 为 3%X；60%的非 P 中为非 E，则非 P 为 3%X/60%；75%的
非 E 为非 P，则非 E 为 3%/75%，那么非 P 与非 E 一共有（3%X/60%+3%X/75%-3%X） ，那么 P 与
E 一 共 有 X- （ 3%X/60%+3%X/75%-3%X ） ， 则 其 概 率 为 [X- （ 3%X/60%+3%X/75%-
3%X）]/X=94%