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# What is the value of x?

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Manager
Joined: 15 Dec 2015
Posts: 116
GMAT 1: 660 Q46 V35
GPA: 4
WE: Information Technology (Computer Software)
What is the value of x?  [#permalink]

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30 Aug 2017, 17:09
2
1
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Difficulty:

75% (hard)

Question Stats:

45% (00:35) correct 55% (00:52) wrong based on 99 sessions

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What is the value of x?

(1) $$\sqrt{x} = x-2$$

(2) x is not equal to 1.
Math Expert
Joined: 02 Aug 2009
Posts: 6787
Re: What is the value of x?  [#permalink]

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30 Aug 2017, 20:12
1
1
DH99 wrote:
What is the value of x?

1. √ x = x-2

2. x is not equal to 1.

Hi..

1) √x=x-2
Square both sides
$$x=x^2-4x+4.....x^2-5x+4=0....x^2-4x-x+4=0.........(x-4)(x-1)=0$$
So x can be 4 or 1..
Substitute in equation and see if values are valid.
A) 2
√4=4-2=2.... Valid
B) 1
√1=1-2=-1..... Not valid
SQUARE Root has to be POSITIVE

Only possible value :- 4
Sufficient

2) X is not 1..
Nothing much.
But only to tempt you to click C....the C trap
Insufficient
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Joined: 06 Aug 2017
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GMAT 1: 570 Q50 V18
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What is the value of x?  [#permalink]

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24 Sep 2017, 17:41
chetan2u wrote:
DH99 wrote:
What is the value of x?

1. √ x = x-2

2. x is not equal to 1.

Hi..

1) √x=x-2
Square both sides
$$x=x^2-4x+4.....x^2-5x+4=0....x^2-4x-x+4=0.........(x-4)(x-1)=0$$
So x can be 4 or 1..
Substitute in equation and see if values are valid.
A) 2
√4=4-2=2.... Valid
B) 1
√1=1-2=-1..... Not valid
SQUARE Root has to be POSITIVE

Only possible value :- 4
Sufficient

2) X is not 1..
Nothing much.
But only to tempt you to click C....the C trap
Insufficient

Thanks Chetan

Answer to this question teach us a very good lesson. Whenever we are doing squire on both the sides of the equation to solve it, always check putting the solution back into the equation to see if the value really satisfy the original equation.

For example, in this case by solving (by squiring both the sides) equation given in option 1, we get solution as 1 and 4, however putting back the value in the original equation clearly shows value=1 do not satisfy the original equation.

The reason for this is that for the simplicity we are doing squire on both the sides, but mathematically it produced a fundamentally different equation as compared to the original equation.
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What is the value of x? &nbs [#permalink] 24 Sep 2017, 17:41
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# What is the value of x?

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