1. Among the [latex]9,000[latex] people attending a football game at College [latex]C[latex], there were [latex]x[latex] students from College [latex]C[latex] and [latex]y[latex] students who were not from College [latex]C[latex].
| Quantity A | Quantity B |
| The number of people attending the game who were not students | [latex]9000-x-y[latex] |
2. In a survey of [latex]250[latex] European travelers, [latex]93[latex] have traveled to Africa, [latex]155[latex] have traveled to Asia, and of these two groups, [latex]70[latex] have traveled to both continents, as illustrated in the Venn diagram above.
(a) How many of the travelers surveyed have traveled to Africa but not to Asia?
(b) How many of the travelers surveyed have traveled to at least one of the two continents of Africa and Asia?
(c) How many of the travelers surveyed have traveled neither to Africa nor to Asia?
3. In a graduating class of [latex]236[latex] students, [latex]142[latex] took algebra and [latex]121[latex] took chemistry. What is the greatest possible number of students that could have taken both algebra and chemistry?
4. Set [latex]A[latex] consists of [latex]40[latex] integers, and set [latex]B[latex] consists of [latex]150[latex] integers. The number of integers that are in both set [latex]A[latex] and set [latex]B[latex] is [latex]20[latex].
| Quantity A | Quantity B |
| The total number of integers that are in set A or set B, or both | [latex]170[latex] |
5. Set [latex]S[latex] consists of [latex]5[latex] objects
| Quantity A | Quantity B |
| The number of subsets of set [latex]S[latex] that consist of [latex]1[latex] object | The number of subsets of set [latex]S[latex] that consist of [latex]4[latex] object |
6. In a factory, there are workers, executives and clerks. [latex]59[latex]% of the employees are workers, [latex]460[latex] are executives, and the remaining [latex]360[latex] employees are clerks. How many employees are there in the factory?
(A) [latex]1500[latex]
(B) [latex]2000[latex]
(C) [latex]2500[latex]
(D) [latex]3000[latex]
(E) [latex]3500[latex]
7. In the town of Windsor, [latex]250[latex] families have at least one car while [latex]60[latex] families have at least two cars. How many families have exactly one car?
(A) [latex]30[latex]
(B) [latex]190[latex]
(C) [latex]280[latex]
(D) [latex]310[latex]
(E) [latex]420[latex]
8. Ana is a girl and has the same number of brothers as sisters. Andrew is a boy and has twice as many sisters as brothers. Ana and Andrew are the children of Emma. How many children does Emma have?
(A) [latex]2[latex]
(B) [latex]3[latex]
(C) [latex]5[latex]
(D) [latex]7[latex]
(E) [latex]8[latex]
9. A trainer on a Project Planning Module conducts batches of soft skill training for different companies. The trainer sets the batch size (the number of participants) of any batch such that he can make groups of equal numbers without leaving out any of the participants. For a particular batch he decides that he should be able to make teams of [latex]3[latex] participants each, teams of [latex]5[latex] participants each, and teams of [latex]6[latex] participants each, successfully without leaving out anyone in the batch. Which one of the following best describes the batch size (number of participants) that he chooses for the program?
(A) Exactly [latex]30[latex] participants.
(B) At least [latex]30[latex] participants.
(C) Less than [latex]30[latex] participants.
(D) More than [latex]30[latex] participants.
(E) Participants in groups of [latex]30[latex] or its multiples
10. In a multi-voting system, voters can vote for more than one candidate. Two candidates [latex]A[latex] and [latex]B[latex] are contesting the election. [latex]100[latex] voters voted for [latex]A[latex]. Fifty out of [latex]250[latex] voters voted for both candidates. If each voter voted for at least one of the two candidates, then how many candidates voted only for [latex]B[latex]?
(A) [latex]50[latex]
(B) [latex]100[latex]
(C) [latex]150[latex]
(D) [latex]200[latex]
(E) [latex]250[latex]
11. There are [latex]750[latex] male and female participants in a meeting. Half the female participants and one-quarter of the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female?
(A) [latex]75[latex]
(B) [latex]100[latex]
(C) [latex]125[latex]
(D) [latex]175[latex]
(E) [latex]225[latex]
12. In a school of [latex]150[latex] students, [latex]75[latex] take Latin, [latex]110[latex] take Spanish, and [latex]11[latex] take neither.
| Quantity A | Quantity B |
| The number of students who take only Latin | [latex]46[latex] |
13. In a class of [latex]25[latex] students, every student takes either Spanish, Latin, or French, or two of the three, but no students take all three languages. [latex]9[latex] take Spanish, [latex]7[latex] take Latin and [latex]5[latex] take exactly two languages.
| Quantity A | Quantity B |
| The number of students who take French | [latex]14[latex] |
14. A baby has [latex]x[latex] total toys. If [latex]9[latex] of the toys are stuffed animals, [latex]7[latex] of the toys were given to the baby by its grandmother, [latex]5[latex] of the toys are stuffed animals given to the baby by its grandmother, and [latex]6[latex] of the toys are neither stuffed animals nor given to the baby by its grandmother, what is the value of [latex]x[latex]?
15. At Lexington High School, everyone takes at least one language — Spanish, French, or Latin — but no one takes all three languages. If [latex]100[latex] students take Spanish, [latex]80[latex] take French, [latex]40[latex] take Latin, and [latex]22[latex] take exactly two languages, how many students are there?
(A) [latex]198[latex]
(B) [latex]220[latex]
(C) [latex]242[latex]
(D) [latex]264[latex]
(E) [latex]286[latex]
Answer:
1 C
2 (a) 23 travelers, (b) 178, (c) 72
3 121
4 C
5 C
6 B
7 B
8 D
9 E
10 C
11 C
12 B
13 C
14 17
15 A
