A high school sells tickets to a basketball game. Adult tickets cost $9 and student tickets cost $5. If tickets are sold for a total revenue of $927, how many possible values are there for ?

A. 18

B. 19

C. 20

D. 21

E. 22

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A high school sells tickets to a basketball game. Adult tickets cost $9 and student tickets cost $5. If tickets are sold for a total revenue of $927, how many possible values are there for ?

A. 18

B. 19

C. 20

D. 21

E. 22

The mean of a set of consecutive positive integers is . One of the integers is removed from the set to create a new set of positive integers with a mean of . Is even?

(1)

(2) The least element of the original set of integers is odd.

What is the sum of the digits of positive integer ?

(1) The sum of the digits of is an element of the set

(2) for some positive integer .

A woman who has two sons enrolled in an elementary school brings a batch of cookies to the school. Her youngest son is in a class with 10 other students and her oldest son is in a class with 7 other students. If she divides the cookies evenly among the students in her youngest son’s class there will be 5 left over. If she divides the cookies evenly among the students in her oldest son’s class there will be 7 left over. If she has more than 200 cookies, which of the following is the sum of the digits of the smallest possible value of ?

A. 9

B. 11

C. 13

D. 17

E. 23

Two farmers, and , each surround a triangular plot of land with a fence on their respective properties. Farmer requires 240 meters of fencing and farmer requires 60 meters of fencing. If the ratios of the lengths of the corresponding sides of the triangular plots of land are all equal to , then the area of the triangular plot of land on farmer ‘s property is how many times bigger than the area of the triangular plot of land on Â farmer ‘s property?

A.

B.

C.

D.

E. Â

How many distinct factors does have?

A. 2592

B. 2718

C. 3142

D. 3654

E. 3660

A group of burglars is trying to decide whether to target the houses in a particular neighborhood in which there are 100 households. Â of the households own a high-definition television, of the households own a valuable piece of artwork, of the households own a luxury car, and all of the households own at least one of these items. The burglars will target the houses in the neighborhood unless the probability of any given household owning all three items exceeds 50%, as this is correlated with tighter security. If , do the burglars target the houses in the neighborhood?

(1)

(2)

If and , what is the value of ?

A.

B.

C.

D.

E. Â 7

Four families of three are lining up for a photo. How many ways can they line up if all of the members in each family must stand together?

A.

B.

C.

D.

E.

Andy and Bob play a game in which a computer randomly selects two real numbers between 0 and 10. Andy’s score is the sum of the numbers and Bob’s score is one more than the product of the numbers. If the person with the Â higher score wins the game, what is the probability that Bob wins?

A. 18%

B. 19%

C. 68%

D. 82%

E. 90%