<p>The algebraic relationship is as follows:</p>
<p>HGC = Hours Good Clock
HBC = Hours Bad Clock
HE = Hours Elapsed</p>
<p>HGC = HE [Mod[/url</a>] 12
HBC = (HE / 3) Mod 12 (where 1/3 = 20 minutes Bad Clock/60 minute Good Clock)</p>
<p>Solve for HGC = HBC:
HE Mod 12 = (HE / 3) Mod 12</p>
<p>Because of the nature of the Mod operator, you don’t need to concern yourself with values of HE less than 12 for the HGC = HBC equality. Then the question is, what value of HE will satisfy the equation such that HE divided by 3 (and then divided by 12) results in the same remainder when HE is divided by 12? </p>
<p>Because the [url=<a href=“http://mathforum.org/library/drmath/view/51619.html]reverse”>http://mathforum.org/library/drmath/view/51619.html]reverse</a> of the mod function](<a href=“http://en.wikipedia.org/wiki/Modulo_operation]Mod[/url”>Modulo - Wikipedia) gives several possible values, the strategy at this point is to start evaluating the relationship with values starting at 12. To save time, use the values from the multiple choice answers:</p>
<p>For HE = 12, HE Mod 12 = (HE / 3) Mod 12 : 0 <> 4
For HE = 18, HE Mod 12 = (HE / 3) Mod 12 : 6 = 6 (this satisfies the equation)
…
For HE = 36, HE Mod 12 = (HE / 3) Mod 12 : 0 = 0 (this also satisfies the equation) (see [url=<a href=“http://talk.collegeconfidential.com/1063262570-post9.html]#9[/url”>http://talk.collegeconfidential.com/1063262570-post9.html]#9[/url</a>] for discussion on possible interpretations of the question)</p>