Question 275093
Suppose n is divisible by 8 but not by 3. Then which of the following CANNOT be an integer?

A n/2  B n/4  C n  D  n/6 
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This problem is solved by this theorem:

<i>If n is divisible by r, and r is divisible by s, then n is divisible by s.</i>

The correct answer cannot be A, B, or C because of the above theorem
since 8 is divisible by 2, 4 and 1.  (Note that n means n/1) 

So that only leaves D.  But let's see why n/6 CANNOT be an integer.

If n/6 were an integer, then n would have to be divisible by 3, 
by the above theorem since 6 is divisible by 3.  But this 
contradicis the given statement that n is not divisible by 3. Thus
the assumption that n/6 is an integer is false.

Edwin</pre>