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If 5^18 + 2 is divided by 4, the remainder is 1. 0 2. 1

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Manager
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If 5^18 + 2 is divided by 4, the remainder is 1. 0 2. 1 [#permalink] New post 25 Oct 2004, 05:31
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If 5^18 + 2 is divided by 4, the remainder is

1. 0
2. 1
3. 2
4. 3
5. none of these

How do you really go about solving questions like these, besides trying numbers here and there?

Also, check Manhattan's Challenge Problem of the week on this site:

http://www.manhattangmat.com/

Is there a time-saving strategy for these?
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Senior Manager
Senior Manager
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Joined: 19 May 2004
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 [#permalink] New post 25 Oct 2004, 05:55
R=3.
Remainder questions are often solved by looking for patterns.

What you can do is check a few numbers you know like:
(5^1 + 2) / 4 => Remainder = 3
(5^2 + 2) / 4 => Remainder = 3
(5^3 + 2) / 4 => Remainder = 3
And you can see that it's going to work with 5^18 as well.

The reason is that the remainder of 5/4 is 1, so the remainder of
5^n where n is a positive integer will also be 1.
Add 2 to that remainder and get the total remainder of 3.
Manager
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 [#permalink] New post 25 Oct 2004, 10:28
Got the same aswner as well. remainder should be 3.
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 [#permalink] New post 25 Oct 2004, 12:55
Agree w/ 3 as the remainder,

5^(anything) will yield a 5 at the units place and if you add 2 gives you 7 at the units place and the pattern is that truncating at the units place is divisble by 4 so the remainder is 3.
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 [#permalink] New post 25 Oct 2004, 22:04
Thanks guys. So I take it that in problems like these, we have to spend some time trying few numbers and see the pattern.
  [#permalink] 25 Oct 2004, 22:04
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If 5^18 + 2 is divided by 4, the remainder is 1. 0 2. 1

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