Science:Math Exam Resources/Courses/MATH312/December 2005/Question 06
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Question 06 

Multiple Choice days from today it will be
Assume that the original exam was written on a Monday. 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

Note that 7 days from now, we are at the same day we were at today. So it suffices to compute this number modulo 7 then count that many days from today (Monday). 
Hint 2 

Euler's Formula will help a lot. 
Checking a solution serves two purposes: helping you if, after having used all the hints, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. The answer is d = Wednesday Proceeding as in the hints, we need to compute
We use Euler's formula which states that
Next, notice that is not divisible by 6 (the sum of the digits is not divisible by 3 so the number is not divisible by 3). However is divisible by 6 and thus, is divisible by 6 (here we let s be an integer). Hence
and thus, two days from Monday is a Wednesday. 