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Triangle ACE, shown in the figure below, is isosceles with base . B lies on and D lies on . Segments and bisect AEC and CAE respectively. Which one of the following angle congruences is necessarily true?

(A) ∠CAE ≅ ∠BEC

(B) ∠CAD ≅ ∠AEC

(C) ∠CAE ≅ ∠ACE

(D) ∠AEC ≅ ∠ACE

(E) ∠BEC ≅ ∠DAE

Noreen recently took a job helping people register to vote. The job has a mandatory 10-day period of probation during which her success rate is strictly monitored. On her first day, she registered 30 people. Then, for each of the next 9 days, she registered 4 more people than she did on the previous day. How many people did she register altogether during her probationary period?

(F) 300(G) 340(H) 480(J) 560(K) 600

Correct Answer: H

In an elite marathon runner's training, total mileage consists of miles run at or faster than marathon pace and miles run slower than marathon pace. The table below shows miles run at or below marathon pace and total mileage for an elite marathon runner for each of 3 consecutive years.

In 2004, how many miles of the runner's total mileage were miles run slower than marathon pace?

(F) 1,012 (G) 2,972 (H) 3,368 (J) 3,832 (K) 3,850

Correct Answer: J

Mr. Dietz is a teacher whose salary is $22,570 for this school year, which has 185 days. In Mr. Dietz's school district, substitute teachers are paid $80 per day. If Mr. Dietz's takes a day off without pay and a substitute teacher is paid to teach Mr. Dietz's classes, how much less does the school district pay in salary by paying a substitute teacher instead of paying Mr. Dietz's for that day?

(F) $ 42

(G) $ 80

(H) $ 97

(J) $105

(K) $122

Correct Answer: F