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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.


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