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# What is the value of x?

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Math Expert
Joined: 02 Sep 2009
Posts: 47037
What is the value of x? [#permalink]

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17 Sep 2017, 02:58
00:00

Difficulty:

35% (medium)

Question Stats:

69% (00:55) correct 31% (01:20) wrong based on 35 sessions

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What is the value of x?

(1) 4/x + 4 + x = 0
(2) 6/x + 1 = x

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Senior Manager
Joined: 09 Mar 2017
Posts: 444
Location: India
Concentration: Marketing, Organizational Behavior
WE: Information Technology (Computer Software)
Re: What is the value of x? [#permalink]

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17 Sep 2017, 03:23
Bunuel wrote:
What is the value of x?

(1) 4/x + 4 + x = 0
(2) 6/x + 1 = x

St.1:: 4/x + 4 + x = 0
or x^2 + 4*x + 4 = 0
or (x+2)^2 = 0
so, we have two cases (x+2) = 0 and -(x+2) = 0. Since this is not inequality, we have x= -2 in both cases. hence Sufficient.

St.2 :: 6/x + 1 = x
or 6 + x = x^2
or x^2 -x -6 = 0
To express it in terms of factors i.e (a-b)^2 , the middle term must equal 2ab. a = x => 2*x*b = x => b = (1/2) or 0.5
So, we have (x^2 -x -6) = (x-0.5)^2 - (25/4)
or (x-0.5)^2 - (5/2)^2=0
this is of form a^2 - b^2 = (a+b)(a-b)
solving , we get (x+2)(x-3) = 0
x= -2 or 3 --------> two values. Not sufficient.

So, "A" is the answer in my opinion.
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Re: What is the value of x?   [#permalink] 17 Sep 2017, 03:23
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