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If n is a positive integer, what is the remainder when

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Re: If n is a positive integer, what is the remainder when [#permalink]

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New post 30 May 2015, 20:57
by the method of exponents break the exp as (3^8n * 3^3) +2
now , we know cyclicity of 3 is 4 that means unit digit is 1 when 3^4 so,3^8n =1 (bcz 8n is divisible by 4)
=> exp becomes 27*3^8n + 2 => 27 *xxxx1 (since n can be any integer)+2 => xxx7+2=> xxx9 and now xxx9/5 leaves rem(5) .

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Re: If n is a positive integer, what is the remainder when [#permalink]

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New post 04 Jul 2016, 08:34
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Re: If n is a positive integer, what is the remainder when [#permalink]

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New post 03 Aug 2017, 10:21
Hello from the GMAT Club BumpBot!

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Re: If n is a positive integer, what is the remainder when [#permalink]

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New post 09 Aug 2017, 12:51
azule45 wrote:
If n is a positive integer, what is the remainder when 3^(8n+3) + 2 is divided by 5?

A. 0
B. 1
C. 2
D. 3
E. 4


We need to determine the remainder of:

3^8n x 3^3 + 2 when it is divided by 5.

We only need to know the units digit of the above expression to determine the remainder.

Let’s look at the pattern of units digits of powers of 3. Note that we are only concerned with the units digits, so, for example, for 3^3, we concern ourselves only with the units digit of 27, which is 7. Here is the pattern:

3^1 = 3

3^2 = 9

3^3 = 7

3^4 = 1

3^5 = 3

The repeating pattern is 3-9-7-1. Since the units digit pattern for a base of 3 is 3-9-7-1, we see that whenever 3 is raised to an exponent that is a multiple of 4, the units digit will be 1. Thus:

3^8n x 3^3 = units digit of 1 x units digit of 7 = units digit of 7

So, units digit of 7 + 2 = units digit of 9, and thus 9/5 has a remainder of 4.

Answer: E
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Re: If n is a positive integer, what is the remainder when   [#permalink] 09 Aug 2017, 12:51

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