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# If n is an integer, what is the remainder when (n 3)^2 is

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If n is an integer, what is the remainder when (n 3)^2 is  [#permalink]

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31 Mar 2011, 06:40
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Question Stats:

65% (01:47) correct 35% (01:36) wrong based on 75 sessions

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174. If n is an integer, what is the remainder when (n – 3)^2 is divided by 4?
(1) n is divisible by 2.
(2) n is divisible by 4.

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Re: If n is an integer  [#permalink]

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31 Mar 2011, 07:09
2
(1) n = 2k

(2k-3)^2 = 4k^2 - 12k + 9 = 4k^2 - 12k + 8 + 1

So remainder = 1 on division by 4

(1) is sufficient

(2) n = 4k

which is same as above

(4k - 3)^2 = 16k^2 - 24k + 9 = 16k^2 - 24k + 8 + 1

So remainder = 1 on division by 4

(2) is sufficient

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Re: If n is an integer  [#permalink]

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31 Mar 2011, 07:16
2
Pkit wrote:
174. If n is an integer, what is the remainder when (n – 3)^2 is divided by 4?
(1) n is divisible by 2.
(2) n is divisible by 4.

Square of an odd integer will leave a remainder of 1 when divided by 4.
Square of an even integer will leave a remainder of 0 when divided by 4.

Q: What is (n-3), even or odd?

(1) n is even.
n-3 = even-odd=odd
Remainder 1.
Sufficient.

(2) n is even.
n-3 = even-odd=odd
Remainder 1.
Sufficient.

Ans: "D"
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Re: If n is an integer  [#permalink]

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05 Apr 2011, 07:08
174. If n is an integer, what is the remainder when (n – 3)^2 is divided by 4?
(1) n is divisible by 2.
(2) n is divisible by 4.
1)
n=2;
n-3=2-3=-1 ===>(-1)^2=1; reminder=1;
n=6;
n-3=6-3=3 ====>(3)^2=9 ;reminder=1;
SUFFICIENT

2)
n=4;
n-3=4-3=1; ===>(1)^2=1;reminder=1
n=8;
n-3=8-3=5 ====>(5)^2=25;reminder=1
SUFFICIENT

THEREFORE, D is correct
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Re: If n is an integer, what is the remainder when (n 3)^2 is  [#permalink]

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02 Sep 2017, 11:48
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Re: If n is an integer, what is the remainder when (n 3)^2 is   [#permalink] 02 Sep 2017, 11:48
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