TEST PROBLEMS / SOLUTIONS 
1. Theresa's parents have agreed to buy her tickets to see her favorite band if she spends an average of 10 hours per week helping around the house for 6 weeks. For the ¯rst 5 weeks she helps around the house for 8, 11, 7, 12 and 10 hours. How many hours must she work during the ¯nal week to earn the tickets? (A) 9 (B) 10 (C) 11 (D) 12 (E) 13
(D) The ¯rst 5 weeks Theresa works a total of 8+11+7+12+10 = 48 hours. She has promised to work 6£10 = 60 hours. She must work 60¡48 = 12 hours during the ¯nal week.
2. What is the sum of the two smallest prime factors of 250? (A) 2 (B) 5 (C) 7 (D) 10 (E) 12
(C) The prime factorization of 250 is 2 ¢ 5 ¢ 5 ¢ 5. The sum of 2 and 5 is 7.
3. A haunted house has six windows. In how many ways can Georgie the Ghost enter the house by one window and leave by a di®erent window? (A) 12 (B) 15 (C) 18 (D) 30 (E) 36
(D) Georgie has 6 choices for the window in which to enter. After entering, Georgie has 5 choices for the window from which to exit. So altogether there are 6£5 = 30 di®erent ways for Georgie to enter one window and exit another.
4. Chandler wants to buy a $500 mountain bike. For his birthday, his grandparents send him $50, his aunt sends him $35 and his cousin gives him $15. He earns $16 per week for his paper route. He will use all of his birthday money and all of the money he earns from his paper route. In how many weeks will he be able to buy the mountain bike? (A) 24 (B) 25 (C) 26 (D) 27 (E) 28
(B) For his birthday, Chandler gets 50 + 35 + 15 = 100 dollars. Therefore, he needs 500 ¡ 100 = 400 dollars more. It will take Chandler 400 ¥ 16 = 25 weeks to earn 400 dollars, so he can buy his bike after 25 weeks.
