Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Question 1
A club consists of 8 women and 8 men.
The club has a president and a vice president.
No club member can hold more than one position.
| Quantity A | Quantity B |
|
The number of possible assignments such that a woman is president and a man is vice president |
The number of possible assignments such that both the president and vice president positions are filled by women |
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Question 2
Given an alphabet of 26 letters, with 21 consonants, and 5 vowels, approximately how many three-letter words can be formed with a vowel as the middle letter and a consonant as the last letter?
1000
1500
2500
3500
4000
Question 3
Of the 100 eighth-graders at Easton Junior High, 60 students take gym, 40 take a foreign language, and 30 take both gym and a foreign language.
| Quantity A | Quantity B |
| 30 |
The number of students taking neither gym nor a foreign language |
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Question 4
Graham’s Catering Service currently employs three chefs and offers three different meals. For an upcoming event, the catering service must provide three meals, with each chef cooking one of the meals.
| Quantity A | Quantity B |
|
The number of assignments of chefs to meals if each chef must cook a different meal |
The number of assignments of chefs to meals if each chef may cook any of the three meals |
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Question 5
A certain password must contain 3 distinct digits followed by 2 distinct capital letters. Given ten digits and 26 capital letters, how many different passwords are possible?
Question 6
190 students go to a school bake sale. 95 buy a chocolate chip cookie, 75 buy a peanut butter cookie, and at least 12 buy both. What is the least number of students who could have bought neither type of cookie?
10
24
30
32
45
Question 7
Geoff is setting up an aquarium and must choose 4 of 6 different fish and 2 of 3 different plants. How many different combinations of fish and plants can Geoff choose?
8
12
18
45
90
Question 8
If the current day and time is 9:30 p.m. on Tuesday, what time will it be (to the nearest minute) 100,000 seconds from now?
1:17 a.m., Wednesday
3:47 p.m., Wednesday
1:10 a.m., Thursday
1:17 a.m., Thursday
2:17 a.m., Thursday
Question 9
What is the difference between the number of three-member committees that can be formed from a group of nine members and the total number of ways there are to arrange the members of such a committee?
0
84
252
420
504
Question 10
Six students compete in a table tennis tournament. Each student plays each of the other students four times. What is the total number of games played in the tournament?
Question 11
A four-person leadership committee is to be chosen from a student council that consists of seven juniors and five seniors. Q is the total number of different leadership committees that include three seniors and one junior.
| Quantity A | Quantity B |
| Q | 75 |
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Question 12
Contestants at a baking contest must use between 5 and 8 of 10 possible ingredients.
| Quantity A | Quantity B |
|
The number of ingredients that must be used to get the smallest possible number of different combinations |
The number of ingredients that must be used to get the largest possible number of different combinations |
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Question 13
Depending on the night, a pizza restaurant offers anywhere from seven to nine different choices of toppings. Sam wants a pizza with three toppings. Which of the following could be the number of different ways that Sam can order his pizza with three different toppings?
Indicate all such values.
35
42
56
84
210
252
504
Question 14
Depending on the day, an ice cream shop offers seven to nine possible ice cream flavors and three to four possible sauces. A Deluxe Sundae consists of two different types of ice cream and two different sauces. Which of the following could be the number of different Deluxe Sundaes that Eva can order?
Indicate all such values.
36
54
84
216
432
864