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

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New post 05 Mar 2019, 01:15
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A
B
C
D
E

Difficulty:

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Question Stats:

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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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New post 05 Mar 2019, 01:39
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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New post 05 Mar 2019, 04:36
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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Re: If x and y are positive integers and (x-y)^2+y^2=25, which of the foll  [#permalink]

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New post 07 Mar 2019, 01:15
=>

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.
Answer: B
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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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