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# When n is divided by 6, the remainder is 2. What is the remainder when

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Math Expert
Joined: 02 Sep 2009
Posts: 47983
When n is divided by 6, the remainder is 2. What is the remainder when  [#permalink]

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28 Apr 2016, 04:55
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When n is divided by 6, the remainder is 2. What is the remainder when (n + 3)^2 is divided by 12?

A. 1
B. 2
C. 3
D. 4
E. 5

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Re: When n is divided by 6, the remainder is 2. What is the remainder when  [#permalink]

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28 Apr 2016, 10:25
1
Bunuel wrote:
When n is divided by 6, the remainder is 2. What is the remainder when (n + 3)^2 is divided by 12?

A. 1
B. 2
C. 3
D. 4
E. 5

Least possible value of n = 8

$$(n + 3)^2$$ = $$(8 + 3)^2$$ =>121

121 divided by 12 will have remainder 1, so answer will be (A)
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Re: When n is divided by 6, the remainder is 2. What is the remainder when  [#permalink]

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29 Apr 2016, 00:16
Bunuel wrote:
When n is divided by 6, the remainder is 2. What is the remainder when (n + 3)^2 is divided by 12?

A. 1
B. 2
C. 3
D. 4
E. 5

This question can easily be done by assuming values.

Assume n = 8
(n + 3)^2 = 11^2 = 121
Remainder of 121/12 = 1
Correct Option: A
Math Expert
Joined: 02 Aug 2009
Posts: 6549
Re: When n is divided by 6, the remainder is 2. What is the remainder when  [#permalink]

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29 Apr 2016, 02:06
1
Abhishek009 wrote:
Bunuel wrote:
When n is divided by 6, the remainder is 2. What is the remainder when (n + 3)^2 is divided by 12?

A. 1
B. 2
C. 3
D. 4
E. 5

Least possible value of n = 8

$$(n + 3)^2$$ = $$(8 + 3)^2$$ =>121

121 divided by 12 will have remainder 1, so answer will be (A)

Hi,
you are correct in answer and approach BUT least possible value of n is not 8..
positive least value is 2..
and with no restrictions it can go to anything example : -58 = 6*-10 +2.. here remainder is 2 again..
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: When n is divided by 6, the remainder is 2. What is the remainder when  [#permalink]

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20 Jan 2017, 12:29
n=6q+2 where q is a positive integer.

Also, (n+3)^2 when divided by 12 leaves a remainder, say r
Therefore, (n+3)^2
= (6q+2+3)^2
= (6q+5)^2
= 36q^2+25+60q

Now, consider each of the terms above separately to see what is the remainder when they are divided by 12.

36q^2 is divisible by 12 as 36 is divisible by 12. Hence remainder is 0
60q is divisible by 12 as 60 is divisible by 12.Hence remainder is 0
25 when divided by 12 leaves a remainder 1

Hence, remainder for (n+3)^2 is 1
Hence correct option is A
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Re: When n is divided by 6, the remainder is 2. What is the remainder when  [#permalink]

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21 Jan 2017, 23:52
N=8,14,20. (N+3)^2= 121,289,529. In all the cases the remainder is 1.
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When n is divided by 6, the remainder is 2. What is the remainder when  [#permalink]

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15 Mar 2018, 05:14
Bunuel wrote:
When n is divided by 6, the remainder is 2. What is the remainder when (n + 3)^2 is divided by 12?

A. 1
B. 2
C. 3
D. 4
E. 5

n = 2, 8, 14 etc.

Therefore we can start with n as "2", (2 + 3) ^2 = 25

Now 25/12 gives us remainder = 1

(A).
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When n is divided by 6, the remainder is 2. What is the remainder when &nbs [#permalink] 15 Mar 2018, 05:14
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