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What is the remainder when x^2 - y^2 is divided by 3?

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What is the remainder when x^2 - y^2 is divided by 3? [#permalink] New post 29 Apr 2013, 11:05
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Question Stats:

86% (01:48) correct 13% (01:08) wrong based on 88 sessions
What is the remainder when x^2 - y^2 is divided by 3?

(1) x^2 is divisible by 6.
(2) y^2 is divisible by 9.
[Reveal] Spoiler: OA

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Last edited by Bunuel on 29 Apr 2013, 12:08, edited 1 time in total.
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Re: What is the remainder when x^2 - y^2 is divided by 3? [#permalink] New post 29 Apr 2013, 12:11
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What is the remainder when x^2 - y^2 is divided by 3?

(1) x^2 is divisible by 6. No info about y. Not sufficient.
(2) y^2 is divisible by 9. No info about y. Not sufficient.

(1)+(2) x^2 - y^2 = (multiple of 3) - (multiple of 3) = (multiple of 3), thus the remainder is zero. Sufficient.

Answer: C.
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Re: What is the remainder when x^2 - y^2 is divided by 3? [#permalink] New post 29 Apr 2013, 13:11
Such a simple way to solve it .. thanks Bunuel!
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What is the remainder when x^2 - y^2 is divided by 3? [#permalink] New post 25 Oct 2013, 13:20
What is the remainder when x^2 - y^2 is divided by 3?

(1) x^2 is divisible by 6.

(2) y^2 is divisible by 9.


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Re: What is the remainder when x^2 - y^2 is divided by 3? [#permalink] New post 25 Oct 2013, 13:23
Expert's post
avohden wrote:
What is the remainder when x^2 - y^2 is divided by 3?

(1) x^2 is divisible by 6.

(2) y^2 is divisible by 9.


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Merging similar topics. Please refer to the solution above.
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Re: What is the remainder when x^2 - y^2 is divided by 3? [#permalink] New post 01 Nov 2013, 03:02
Bunuel wrote:
What is the remainder when x^2 - y^2 is divided by 3?

(1) x^2 is divisible by 6. No info about y. Not sufficient.
(2) y^2 is divisible by 9. No info about y. Not sufficient.

(1)+(2) x^2 - y^2 = (multiple of 3) - (multiple of 3) = (multiple of 3), thus the remainder is zero. Sufficient.

Answer: C.


Why do we need information about y for 2)? Don't we need information about x^2 to determine the answer in (2)?
(x^2 - y^2)%3 = ((x^2)%3-(y^2)%3)%3
1) (0 - (y^2)%3)%3 = -(y^2)%3 | NS
2)((x^2)%3-0)%3 = (x^2)%3 | NS
(1)+(2): 0

Last edited by TooLong150 on 02 Nov 2013, 05:31, edited 1 time in total.
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Re: What is the remainder when x^2 - y^2 is divided by 3? [#permalink] New post 01 Nov 2013, 22:58
Official Explantion

Answer: C
- Each of the statements are insufficient on their own; we're looking for something concerning an expression with two variables, and each statement concerns only one of the variables.

Taken together, the statements are sufficient. If x^2 is divisible by 6, it is also divisible by all the factors of 6, including 3. The same reasoning applies to y^2. Since both x^2 and y^2 are divisible by 3, the difference between them is also divisible by 3, so the remainder is 0. Choice (C) is correct.
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Re: What is the remainder when x^2 - y^2 is divided by 3?   [#permalink] 01 Nov 2013, 22:58
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