Hi VJesus12,

We're told that X^2 - (X)(Y)/5 + 25 can be expressed as (X - 5)^2. We're asked for the value of Y. In simple terms, this question asks what value of Y will make the first expression be equal to the second expression.

(X - 5)^2 = X^2 - 10X + 25

Both the "X^2" and the "+25" are accounted for in the first expression, so we need -(X)(Y)/5 to equal - 10X....
thus Y/5 = 10
Y = 50

Final Answer: [spoiler=]D[/spoiler]

GMAT assassins aren't born, they're made,
Rich

VJesus12 wrote:If the expression \(x^2 - \dfrac{xy}5 + 25\) can be expressed by \((x - 5)^2\), what is the value of \(y?\)

(A) \(0\)
(B) \(5\)
(C) \(25\)
(D) \(50\)
(E) \(\dfrac5x\)

[spoiler]OA=D[/spoiler]

Source: Veritas Prep

GIVEN: (x - 5)² = x² - xy/5 + 25
Expand and simplify left side to get: x² - 10x + 25 = x² - xy/5 + 25
Subtract x² from both sides to get: -10x + 25 = -xy/5 + 25
Subtract 25 from both sides to get: -10x = -xy/5
Multiply both sides by 5 to get: -50x = -xy
Divide both sides by x to get: -50 = -y
Solve: y = 50

Answer: D

Cheers,
Brent

VJesus12 wrote:If the expression \(x^2 - \dfrac{xy}5 + 25\) can be expressed by \((x - 5)^2\), what is the value of \(y?\)

(A) \(0\)
(B) \(5\)
(C) \(25\)
(D) \(50\)
(E) \(\dfrac5x\)

[spoiler]OA=D[/spoiler]

Source: Veritas Prep

(x - 5)^2 = x^2 - 10x + 25

We equate the second terms of each expression, so we have

-10x = -xy/5

-50x = -xy

50 = y

Answer: D