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Positive integer n is equal to the difference of the squares of x and

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Positive integer n is equal to the difference of the squares of x and [#permalink]

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New post 31 Jul 2017, 06:48
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Positive integer n is equal to the difference of the squares of x and y, where x and y are integers. If n is equal to 21, then which of the following could be the sum of x and y?

(A) 0

(B) 11

(C) -1

(D) -11

(E) 121
[Reveal] Spoiler: OA

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Positive integer n is equal to the difference of the squares of x and [#permalink]

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New post 31 Jul 2017, 07:01
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Bunuel wrote:
Positive integer n is equal to the difference of the squares of x and y, where x and y are integers. If n is equal to 21, then which of the following could be the sum of x and y?

(A) 0

(B) 11

(C) -1

(D) -11

(E) 121


n = \(x^2\) - \(y^2\) ; n=21

21= (x+y) * (x-y)

This means (x+y) should be an integer that divides 21. Or in other words a factor of 21.

The only value possible from the options is -1.

[Reveal] Spoiler:
C

Last edited by sarathgopinath on 31 Aug 2017, 20:00, edited 1 time in total.

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Re: Positive integer n is equal to the difference of the squares of x and [#permalink]

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New post 31 Jul 2017, 07:14
Bunuel wrote:
Positive integer n is equal to the difference of the squares of x and y, where x and y are integers. If n is equal to 21, then which of the following could be the sum of x and y?

(A) 0

(B) 11

(C) -1

(D) -11

(E) 121


x,y can take +10,-10,11,-11

Only Possible value of x+y is -1
C
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Re: Positive integer n is equal to the difference of the squares of x and [#permalink]

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New post 31 Jul 2017, 07:22
Answer is C -1, that's the only combination of 10,11 that sums up to and answer in the choices available. Sorry for my weird/simplistic explanation.


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Re: Positive integer n is equal to the difference of the squares of x and [#permalink]

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New post 01 Aug 2017, 10:16
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(x^2-y^2) = 21
=> (x+y)(x-y) = 21
Since x and y are integers
we can have following possibilities
7X3
3X7
21X1
1X21
-1X-21
-21X-1


out of the given options (-1) is the only value that fits into the solution.
Hence Option (C)

Kudos [?]: 1 [1], given: 0

Re: Positive integer n is equal to the difference of the squares of x and   [#permalink] 01 Aug 2017, 10:16
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