As promised, here is the answer to yesterday’s Challenge Problem!
Question
A certain club has exactly 5 new members at the end of its first week. Every subsequent week, each of the previous week’s new members (and only these members) brings exactly x new members into the club. If y is the number of new members brought into the club during the twelfth week, which of the following could be y?
(A)
(B)
(C)
(D)
(E)
Answer
At the end of the first week, there are 5 members. During the second week, 5x new members are brought in (x new members for every existing member). During the third week, the previous week’s new members (5x) each bring in x new members:
new members. If we continue this pattern to the twelfth week, we will see that 
new members join the club that week. Since y is the number of new members joining during week 12, 
.
If , we can set each of the answer choices equal to and see which one yields an integer value (since y is a specific number of people, it must be an integer value). The only choice to yield an integer value is (D):
Therefore x = 15.
Since choice (D) is the only one to yield an integer value, it is the correct answer.
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