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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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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

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-n-is-a-positive-integer-and-r-is-the-remainder-when-93364.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 27 Jul 2013, 12:48, edited 1 time in total.
Edited the question and added the OA.
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4+7n = 3q1 + r

St1:
n+1 is a multiple of 3. n+1 can be 3,6,9,12,... then n could be 2,5,8,11... For these values of n, the remainder r could be 0,1,1,0...etc. Insufficient.

St2:
n could be 22,23,24.... for these values of n, the remainder r could be 2,0,1... Insufficient.

Using both st1 and st2, n+1 could be 22,25,28... and n will then be 21,24,27...
For these values of n, r is 1. Sufficient.

Ans C
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forgmat 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


Please explain


Fact1
if n+1 is divisible by 3, n+4 must be divisible by 3 as well
Also, 4+7n can be re-written as 6n+n+4
n+4 is divisible by 3
6n is definitely divisible by 3 (get result of 2n)
therefore, r=0

Fact2
n>20 doesn't tell anything
let's say if n=21 then 4+7n = 151 and r = 1
if n = 22 then 4+7n = 158 and r = 2

so I would say "A"
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Re: If n is a positive integer and r is the remainder when 4+7n [#permalink]

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(1) suff

if n+1 is divisible by 3, n is not divisible by 3 and n/3 has a reminder of 2, so

(4+7n)/3 --> 4/3+7n/3 --> 1/3 (which is a remainder of 4/3) + 2/3 (remainder of 7n/3) = 3/3, hence r=0

(2) insuff.

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

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New post 27 Jul 2013, 12:48
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Re: If n is a positive integer and r is the remainder when 4+7n [#permalink]

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New post 27 Jul 2013, 12:52
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forgmat 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


Please explain


statmnt 1:
n+1 ==>div by 3
therefore 7(n+1) ==>div. by 3
(7n+4)+3 ==>div by ===>this means 7n+4 is div by 3
sufficient

statement 2:
n>20
let n=30==>7n+4=214==>when divided by 3 remainder i s1
let n=40==>7n+4=284==>when divided by 3 remainder i s2
hence not sufficient

hence A
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Re: If n is a positive integer and r is the remainder when 4+7n   [#permalink] 27 Jul 2013, 12:52
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