If n is a positive integer and r is the remainder when 4+7n : DS Archive
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# If n is a positive integer and r is the remainder when 4+7n

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If n is a positive integer and r is the remainder when 4+7n [#permalink]

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01 Oct 2005, 10:30
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If n is a positive integer and r is the remainder when 4+7n is divided by 3, what is the value of r?

1. n+1 is divisible by 3
2. n>20
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01 Oct 2005, 10:49
I get A)

1) n + 1 is divisible by 3
4+7n can be written as 7n + 7 - 3 => 7(n+1)-3
Since, 7(n+1) is divisible by 3, and 3 is divisible by 3 => 4+7n is divisible by 3 with a remainder r=0

2) n>20 insuff. Depending on the value of n .. r can take multiple values.
e.g. when n = 21, remainder is 1 (4+7n = 151) and when n=23 (4+7n=165), remainder is 0.
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-Vikram

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04 Oct 2005, 02:33
gsr wrote:
If n is a positive integer and r is the remainder when 4+7n is divided by 3, what is the value of r?

1. n+1 is divisible by 3
2. n>20

4 + 7n can be written as (6n + 6) + (n-2), if n+1 is divisible by 3, 6n+6 is also divisible by 3.
And, if n+1 is divisible by 3, then (n-2) is also divisible by 3. Hence 4+7n is divisible by 3, and the remainder is zero.

From st2
N can take different numbers greater than 20, and will not help.

Re: DS - Divisibility   [#permalink] 04 Oct 2005, 02:33
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