Science:Math Exam Resources/Courses/MATH312/December 2010/Question 02
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Question 02 

Let and be the digit number where the digits 85 repeat n times. (a) Is a divisible by 9? (b) Is a divisible by 11? Explain your answers. 
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 hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

Remember divisibility rules. A number is divisible by 9 if the sum of its digits is divisible by 9 and it is divisible by 11 if the alternating sum of its digits is divisible by 11. 
Checking a solution serves two purposes: helping you if, after having used the hint, 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. Proceeding as stated in the hint, notice that the sum of the digits of a is
and this is clearly divisible by 9. Thus a is divisible by 9. Further, the alternating sum of the digits is
and this is clearly not divisible by 11. Thus a is not divisible by 11. 