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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42 GPA: 3.82
If x and y are positive integers and (x-y)^2+y^2=25, which of the foll  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 78% (01:46) correct 22% (02:57) wrong based on 36 sessions

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[GMAT math practice question]

If $$x$$ and $$y$$ are positive integers and $$(x-y)^2+y^2=25$$, which of the following could be the value of $$x$$?

$$A. 6$$
$$B. 7$$
$$C. 8$$
$$D. 9$$
$$E. 10$$

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Re: If x and y are positive integers and (x-y)^2+y^2=25, which of the foll  [#permalink]

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MathRevolution wrote:
[GMAT math practice question]

If $$x$$ and $$y$$ are positive integers and $$(x-y)^2+y^2=25$$, which of the following could be the value of $$x$$?

$$A. 6$$
$$B. 7$$
$$C. 8$$
$$D. 9$$
$$E. 10$$

From the question we know:

$$(x-y)^2$$ and $$y^2$$ will be positive. Also, we can treat these two to be a part of Pythagorean triplets. Hence we can conclude:

$$4^2+3^2=5^2$$

=> $$(x-y)^2=4^2$$
& $$(y)^2=3^2$$

=> y=3 and x=7

Hence B is the correct answer.
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Re: If x and y are positive integers and (x-y)^2+y^2=25, which of the foll  [#permalink]

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MathRevolution wrote:
[GMAT math practice question]

If $$x$$ and $$y$$ are positive integers and $$(x-y)^2+y^2=25$$, which of the following could be the value of $$x$$?

$$A. 6$$
$$B. 7$$
$$C. 8$$
$$D. 9$$
$$E. 10$$

Identify two perfect squares that sum to 25:
1, 4, 9, 16...
The two values in blue sum to 25.
If y=3 and x=7, then (x-y)² = (7-3)² = 16 and y² = 9, with the result that (x-y)² + y² = 25.

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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8003
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: If x and y are positive integers and (x-y)^2+y^2=25, which of the foll  [#permalink]

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=>

The possible values of the pair $$(x-y,y)$$, with $$x$$ and $$y$$ positive, are $$(0,5), (3,4), (-3,4), (4,3)$$ and $$(-4,3)$$.
So, $$(x,y) = (5,5), (7,4), (1,4), (7,3)$$ or $$(-1,3)$$.
Thus, $$x$$ could be $$5, 7$$ or $$1$$.

Therefore, B is the answer.
_________________ Re: If x and y are positive integers and (x-y)^2+y^2=25, which of the foll   [#permalink] 07 Mar 2019, 01:15
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If x and y are positive integers and (x-y)^2+y^2=25, which of the foll

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