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If n is a positive integer, what is the remainder when 2n is divided

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If n is a positive integer, what is the remainder when 2n is divided  [#permalink]

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New post 28 Jul 2017, 00:41
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If n is a positive integer, what is the remainder when 2n is divided by 8?

(1) n, when divided by 6, leaves remainder 5.
(2) 3n, when divided by 6, leaves remainder 3.

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Re: If n is a positive integer, what is the remainder when 2n is divided  [#permalink]

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New post 28 Jul 2017, 01:10
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Bunuel wrote:
If n is a positive integer, what is the remainder when 2n is divided by 8?

(1) n, when divided by 6, leaves remainder 5.
(2) 3n, when divided by 6, leaves remainder 3.


It should be E

Statement 1: Insufficient

\(n = 6q + 5\)

This set has values \(5, 11, 17, 23\)... These have remainder of \(5, 3, 1, 7\) respectively when divided by 8. If we multiply them by \(2\), we get \(10,22,34,46,\) remainder when divided by 8 is 2,6,2,6 so not a singular value.

Statement 2: Insufficient

3n = 6r + 3

This set has values \(3, 9, 15, 21, 27\) and so on. Since this is \(3n\), n would be \(1,3,5,7,9,11,13,15,17\) and so on. \(2n\) would be \(2,6,10,14,18,22\) and so on. Remainder when \(2n\) is divided by \(9\) is, \(2, 6, 2, 6\).

Statement 1+2:

In both set of values of n from statements 1 and 2, we see \(5,11,17,23\) as common. \(2n\) would be \(10,22,34\) and \(46\). However remainder when divided by 8 is again not a singular value.
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Re: If n is a positive integer, what is the remainder when 2n is divided  [#permalink]

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New post 28 Jul 2017, 01:18
Bunuel wrote:
If n is a positive integer, what is the remainder when 2n is divided by 8?

(1) n, when divided by 6, leaves remainder 5.
(2) 3n, when divided by 6, leaves remainder 3.


2n = 8x + r ..r?

(1) n can take 5, 11, 17, 23, 29.....
2n becomes 10, 22, 34, 46, 58
when divided by 8 r is 2, 6, 2, 6, 2

Not sufficient

(2) 3n takes 3, 9, 15, 21, 27, 33, 39, 45
n becomes 1, 3, 5, 7, 9, 11, 13, 15
2n becomes 2, 6, 10, 14, 18, 22, 26, 30
when divided by 8 r is 2, 6, 2, 6, 2, 6, 2
Not sufficient

On combining also we have two value of r (2 and 6)

Not Sufficient
E
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Re: If n is a positive integer, what is the remainder when 2n is divided  [#permalink]

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New post 15 Dec 2017, 10:55
Bunuel wrote:
If n is a positive integer, what is the remainder when 2n is divided by 8?

(1) n, when divided by 6, leaves remainder 5.
(2) 3n, when divided by 6, leaves remainder 3.


We need to determine the remainder when 2n is divided by 8.

Statement One Alone:

n, when divided by 6, leaves remainder 5.

Thus, we see n can be a number such as 5, 11, 16, 21, 26, 31, 35, etc.

When 2(5) = 10 is divided by 8, the remainder is 2.

When 2(11) = 22 is divided by 8, the remainder is 6.

Statement one alone is not sufficient to answer the question.

Statement Two Alone:

3n, when divided by 6, leaves remainder 3.

Thus, we see that 3n can be a number such as 3, 9, 15, 21, 28, etc.

When 3n is 3, n is 1; when 3n is 9, n is 3; when 3n is 15, n is 5; etc.

In other words n will always be an odd number: 1, 3, 5, 7, ...

When 2(1) = 2 is divided by 8, the remainder is 2.

When 2(3) = 6 is divided by 8, the remainder is 6.

Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using our two statements, we see the first value for n that satisfies both statements is 5. We also see that in statement two, n can be any odd number. So, another number that would match is n = 11.

When 2(5) = 10 is divided by 8, the remainder is 2.

When 2(11) = 22 is divided by 8, the remainder is 6.

We see that the statements together are still not sufficient to answer the question.

Answer: E
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Re: If n is a positive integer, what is the remainder when 2n is divided   [#permalink] 15 Dec 2017, 10:55
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