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Really Tricky Remainder Theorem

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Really Tricky Remainder Theorem

by ronnie1985 » Wed May 23, 2012 10:38 am
If q is a positive integer less than 17 and r is the remainder when 17 is divided by q, what is the value of r?
1. q>10
2. q=2^k, where k is a positive integer
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by neelgandham » Wed May 23, 2012 10:50 am
If q is a positive integer less than 17 and r is the remainder when 17 is divided by q, what is the value of r?
1. q>10
If q = 11, then 17/11 leaves a remainder 6.
If q = 16, then 17/16 leaves a remainder 1.
Two different answers. So, statement 1 is insufficient to answer the question.
2. q=2^k, where k is a positive integer
The value of q can be 2,4,8,16.
If q = 2, then 17/2 leaves a remainder 1.
If q = 4, then 17/4 leaves a remainder 1.
If q = 8, then 17/8 leaves a remainder 1.
If q = 16, then 17/16 leaves a remainder 1.
One single answer! So, statement 2 is sufficient to answer the question.

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