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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

Problem 7

Detectives investigating a citywide increase in burglaries questioned exactly seven suspects–S,T,V,W,X,Y,and Z–each on a different one of seven consecutive days. Each suspect was questioned exactly once. Any suspect who confessed did so while being questioned. The investigation conformed to the following:

T was questioned on day three.

The suspect questioned on day four did not confess.

S was questioned after W was questioned.

Both X and V were questioned after Z was questioned.

No suspects confessed after W was questioned.

Exactly two suspects confessed after T was questioned.

Which one of the following could be true?

A. X was questioned on day one

B. V was questioned on day two

C. Z was questioned on day four

D. W was questioned on day five

E S was questioned on day six

ANSWER: B

Problem 6

Three short seminars–Goals, Objections, and Persuasion–and three long seminars–Humor, Negotiating, and Telemarketing–will be scheduled for a three-day sales training conference. On each day, two of the seminars will be given consecutively. Each seminar will be given exactly once. The schedule must conform to the following conditions:

Exactly one short seminar and exactly one long seminar will be given each day.

Telemarketing will not be given until both Goals and Objections have been given.

Negotiating will not be given until Persuasion has been given.

If Goals is given on the first day of the sales training conference, then which one of the following could be true?

A. Negotiating is given on the first day

B. Objections is given on the first day.

C. Persuasion is given on the first day.

D. Humor is given on the second day.

E. Telemarketing is given on the second day.

ANSWER: E

Problem 5



Workers at a water treatment plant open eight valves-G,H,I,K,L,N,O, and P-to flush out a system of pipes that needs emergency repairs. To maximize safety and efficiency, each valve is opened exactly once, and no two valves are opened at the same time. The valves are opened in accordance with the following conditions:

Which one of the following could be the order, from first to last, in which the valves are opened?

A. P,I,K,G,N,H,O,L

B. P,G,K,N,L,H,O,L

C. G,K,I,P,H,O,N,L

D. N,K,P,H,O,I,L,G

E. K,I,N,G,P,H,O,L

ANSWER : A