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whats the remainder when 2^k is divided by 10. 1. k is

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whats the remainder when 2^k is divided by 10. 1. k is [#permalink] New post 09 Sep 2004, 09:18
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whats the remainder when 2^k is divided by 10.
1. k is divisible by 10
2. k is divisible by 4
Manager
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 [#permalink] New post 09 Sep 2004, 09:36
B.

1) Insufficient - when k is divisible by 10, it can be 10,20,..
2^10 and 2^20 have different unit digits

2) sufficient - when k is divisible by 4, it can be 4,8,12, ...
2^4 or 2^8 have the same unit digit.
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 [#permalink] New post 09 Sep 2004, 10:05
B is true only if k is positive.

If k is negative, the numbers are: 2^(-4), 2^(-8), and so on.

This corresponds to: 1/16, 1/256, 1/4096.

Divide them by 10 (i.e., 10 times 0 is 0 and then the remainder), and your remainders are 1/16, 1/256, 1/4056, which are all different.:)
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 [#permalink] New post 11 Sep 2004, 10:12
intr3pid wrote:
B is true only if k is positive.

If k is negative, the numbers are: 2^(-4), 2^(-8), and so on.

This corresponds to: 1/16, 1/256, 1/4096.

Divide them by 10 (i.e., 10 times 0 is 0 and then the remainder), and your remainders are 1/16, 1/256, 1/4056, which are all different.:)


For the above series, where k is negative, I guess the reminders should be all ones!

Last edited by hardworker_indian on 11 Sep 2004, 15:56, edited 1 time in total.
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 [#permalink] New post 11 Sep 2004, 12:19
ALL, can we consider the case when 'k" = 0...........I would say 0 is divisible by 4 but 2^0 = 1 and hence when divided by 4 would yield remainder 1.........wotsay everyone??
  [#permalink] 11 Sep 2004, 12:19
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