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Question
Hello Janet,

 Can you help me solve this question:

Q:  lf (3x)/8 has a remainder of 4 and (3y)/8 has a remainder of 2 then (xy)/8 has a remainder of_______

the answer is 0

  Thanks
   Thi

Answer
3x mod8 = 4, so there is an integer m such that
3x = 8m + 4
  = 4(m + 1)

4(m + 1) is divisible by 3.
Since 4 is not divisible by 3, (m + 1)/3 must be an integer.
Therefore, x is divisible by 4.

3y mod8 = 2, so there is an integer n such that
3y = 8n + 2
  = 2(4n + 1)

2(4n + 1) is divisible by 3.
Since 2 is not divisible by 3, (4n + 1)/3 must be an integer.
Therefore, y is divisible by 2.

xy is divisible by 42 = 8, so xy mod8 = 0
xy/8 has a remainder of 0.

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Janet Yang

Expertise

I can answer questions in Algebra, Basic Math, Calculus, Differential Equations, Geometry, Number Theory, and Word Problems. I would not feel comfortable answering questions in Probability and Statistics or Topology because I have not studied these in depth.

Experience

I tutor students (fifth through twelfth grades) and am a Top Contributor on Yahoo!Answers with over 24,000 math solutions.

Publications
Co-author of An Outline of Scientific Writing: For Researchers With English as a Foreign Language

Education/Credentials
I have a Bachelor's degree in Applied Mathematics from the University of California at Berkeley.

Past/Present Clients
George White Elementary School. Homework Help program at the Ridgewood Public Library, Ridgewood, NJ. Individual students.

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