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# If the expression x^2 – xy/5 + 25 can be expressed by (x – 5)^2, what

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Math Expert
Joined: 02 Sep 2009
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If the expression x^2 – xy/5 + 25 can be expressed by (x – 5)^2, what  [#permalink]

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25 Apr 2017, 03:14
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If the expression x^2 – 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) 5/x

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Intern
Joined: 17 May 2016
Posts: 17
Re: If the expression x^2 – xy/5 + 25 can be expressed by (x – 5)^2, what  [#permalink]

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25 Apr 2017, 03:50
xy/5 = 10x
y = 10 x 5 = 50

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Re: If the expression x^2 – xy/5 + 25 can be expressed by (x – 5)^2, what  [#permalink]

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28 Apr 2017, 15:16
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Bunuel wrote:
If the expression x^2 – 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) 5/x

We can FOIL the second expression (x – 5)^2 and equate the two expressions:

x^2 – xy/5 + 25 = x^2 -10x + 25

-xy/5 = -10x

-xy = -50x

y = 50

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Joined: 14 Apr 2017
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Re: If the expression x^2 – xy/5 + 25 can be expressed by (x – 5)^2, what  [#permalink]

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21 May 2017, 22:19
Here y can take any value if x equals 0 and the question does not state that x is not equal to 0. In that consideration, shouldn't the answer be "Cannot be determined"? I think the answer should be D (i.e.: y=50) only if the question explicitly mentions that x does not equal 0.
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Re: If the expression x^2 – xy/5 + 25 can be expressed by (x – 5)^2, what  [#permalink]

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21 May 2017, 22:30
mazhar7624 wrote:
Here y can take any value if x equals 0 and the question does not state that x is not equal to 0. In that consideration, shouldn't the answer be "Cannot be determined"? I think the answer should be D (i.e.: y=50) only if the question explicitly mentions that x does not equal 0.

But when it says x^2 - xy/5 + 25 = (x-5)^2

it means this expression is true for ALL values of x and y. So we have to generalise by the means of expanding (x-5)^2 and equating it with x^2 - xy/5 + 25
We cannot take a lone case of x=0.
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Re: If the expression x^2 – xy/5 + 25 can be expressed by (x – 5)^2, what  [#permalink]

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30 Nov 2019, 12:30
Hi All,

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

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Re: If the expression x^2 – xy/5 + 25 can be expressed by (x – 5)^2, what   [#permalink] 30 Nov 2019, 12:30
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