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The remainder when n is divided by 8 is 1. What is the

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The remainder when n is divided by 8 is 1. What is the [#permalink] New post 03 May 2006, 11:52
The remainder when n is divided by 8 is 1. What is the remainder when 3n is divided by 8?

n=8k+1
3n=3*8k+3

....so remainder is 3

If the above is true, help me understand this one:

The remainder when n is divided by 2 is 1. What is the remainder when 3n is divided by 2?

n=2k+1
3n=3*2k+3

....the answer I was given for the remainder is 1? Why is that?
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 [#permalink] New post 03 May 2006, 12:58
I plug in values for these.. because i tend to make mistakes easily if i dont plug in..

i try out 3-4 numbers.
9/8, 17/8, 25/8

And check out with 3n/8 now
27/8, 51/8, 75/8
also try negative values if you want!
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 [#permalink] New post 03 May 2006, 15:35
sideslip - This is because when you are diviging a number by 8, remainders can be 0,1,2,3,4...7

But when you are dividing a number by 2, remainder can only be 0 or 1

So here:
n=2k+1
3n=3*2k+3

remainder is 3 (per the example above), but 3 is divisible by 2 with a remainder of 1

Hence the answer is 1
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 [#permalink] New post 03 May 2006, 16:59
For the first part,

n can be written as n = 8x + 1 where x is any integer. Therefore, 3n = 24x + 3.

3n/8 = (24x+3)/8 = 3x + R3.

For the second part,

n can be written as n = 2x + 1 where x is any integer. Therefore 3n = 6x + 3.

3n/2 = (6x+3)/2 = (3x + 1) + R1.
  [#permalink] 03 May 2006, 16:59
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