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Problem 16

The Fibonacci sequence 1,1,2,3,5,8,13,21,…starts with two 1 , and each term afterwards is the sum of its two predecessors. Which one of the ten digits is the last to appear in the units position of a number in the Fibonacci sequence?

(A) 0 (B) 4 (C) 6 (D) 7 (E) 9

ANSWER:C

Problem 15

Chandra pays an online service provider a fixed monthly fee plus an hourly charge for connect time. Her December bill was $12.48, but in January her bill was $17.54 because she used twice as much connect time as in December. What is the fixed monthly fee?

(A) $2.53 (B) $5.06 (C) $6.24 (D) $7.42 (E) $8.77

ANSWER: D

Problem 14

Each day, Jenny ate 20% of the jellybeans that were in her jar at the beginning of that day. At the end of the second day, 32 remained. How many jellybeans were in the jar originally?

(A) 40 (B) 50 (C) 55 (D) 60 (E) 75

ANSWER: B

Problem 13

In the year 2021, Frost middle school will host a math competition. Let L,M, and N be distinct positive integers such that the product L*M*N=2001. What is the largest possible value of the sum L+M+N?

(A) 23 (B) 55 (C) 99 (D) 111 (E) 671

ANSWER: E

Problem 12

Teams A and B are playing in a basketball league where each game results in a win for one team and a loss for the other team. Team A has won 2/3 of its games and team B has won 5/8 of its games. Also, team B has won 7 more games and lost 7 more games than team A. How many games has team A played?

(A) 21 (B) 27 (C) 42 (D) 48 (E) 63

ANSWER： C

Problem 10

The three highest-placing teams in a high school debate tournament are the teams from F,G,H high schools. Each team has exactly two members. The individuals on these three teams are M,N,O,P,S,and T. The following is the case:

S is on the team from G high school.

T is on the second-place team.

M and P are not on the same team.

P’s team places higher than N’s team.

The team from G high school places higher than the team form H high school.

S’s teammate could be any one of the following except:

(A)M

(B)N

(C)O

(D)P

(E)T

ANSWER: B

Problem 9

A competition is being held to select a design for college’s new student union building. Each of six architects–G,J,L,M,P,and V–has submitted exactly one design. There are exactly six designs,and they are presented one at a time to the panel of judges, each design being presented exactly once, consistent with the following conditions:

M’s design is presented at some time before L’s and after P’s.

G’s design is presented either at some time before J’s or at some time after L’s, but not both.

V’s design is presented either at some time before G’s or at some point after P’s, but not both.

If J’s design is presented at some time before M’s, then each of the following could be true except:

(A) J’s design is presented second.

(B) P’s design is presented third.

(C) P’s design is presented fourth.

(D) J’s design is presented fifth.

(E) L’s design is presented fifth.

ANSWER:D

Problem 8

Five performers–T,W,X,Y,and Z–are recruited by three talent agencies–F Agency,P Agency,and S Agency.each performers signs with exactly one of the agencies and each agency signs at least one of the performers. The performers’ signing with the agencies is in accord with the following:

X sings with F Agency.

X and Y do not sign with the same agency as each other.

Z signs with the same agency as Y.

If T signs with S Agency,W also signs with S Agency.

Which one of the following could be a complete and accurate list of the performers who sign with each agency?

(A) F Agency: X P Agency:W S Agency: T,Y,Z

(B) F Agency: X P Agency:T,W S Agency: Y,Z

(C) F Agency: X P Agency:T,Y S Agency: W,Z

(D) F Agency: Y,Z P Agency:X S Agency: T,W

(E) F Agency: X,Y,Z P Agency:T S Agency: W

ANSWER:B