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

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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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New post 25 Apr 2017, 02:14
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

90% (01:11) correct 10% (01:25) wrong based on 61 sessions

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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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New post 25 Apr 2017, 02:50
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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New post 28 Apr 2017, 14:16
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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

Answer: D
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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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New post 21 May 2017, 21:19
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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New post 21 May 2017, 21:30
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 &nbs [#permalink] 21 May 2017, 21:30
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