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If x and y are positive integers and (x-y)^2+y^2=25, which o

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If x and y are positive integers and (x-y)^2+y^2=25, which o

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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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Max@Math Revolution 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.

The correct answer is B.

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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.
Answer: B

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Max@Math Revolution 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
We need the sum of two perfect squares to equal 25. So the two numbers could be 9 and 16, since 3^2 + 4^2 = 5^2, or 9 + 16 = 25. Thus, if y = 3, then x = 7, so that (7 - 3)^2 + 3^2 = 25. Or, if y = 4, then x = 7, so that (7 - 4)^2 + 4^2 = 25. In either case, we see that x is 7.

(Note: We see that 0^2 + 5^2 = 25. That is, if y = 0, then x = 5, so that (5 - 0)^2 + 0^2 = 25; however this is not possible because y is given to be a positive integer. On the other hand if y = 5, then x = 5, so that (5 - 5)^2 + 5^2 = 5. We see that x could be 5 also; however, 5 is not one of the answer choices.)

Answer: B

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