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Senior Manager
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source: http://www.manhattangmat.com [#permalink] New post 13 Jun 2005, 10:10
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
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Senior Manager
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 [#permalink] New post 13 Jun 2005, 10:12
feel like A is the answer

1) can be only 2
2) can be 2 or -2
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 [#permalink] New post 13 Jun 2005, 10:23
Looks like it's C.

A is not suff.: x can be =2 or -1

B illiminates x=-1

So it's C
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 [#permalink] New post 13 Jun 2005, 12:21
formal solution for (1)

|x-x^2|=2
can be divided into 2 equations
x-x^2=2 roots[2;-1]
x-x^2=-2 no real roots

What is a formal solution for (2)??

You should come up with the following results( Can Mathcad be wrong?):
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 [#permalink] New post 13 Jun 2005, 13:23
OK:

Solution for #1 is -1 or 2

So A isn't enough

Solution for # 2 is -2 or 2

So B isn't enough either

Combine A and B: the only way to satisfy both equations is to use 2.

What is wrong in my line of reasoning :roll: ?
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 [#permalink] New post 13 Jun 2005, 15:33
C. The easiest way is to graph it (without 2).

This problem is too hard for GMAT. Both functions have negative solutions that aren't too obvious, and probably not integer
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 [#permalink] New post 13 Jun 2005, 22:45
katrin wrote:
OK:

Solution for #1 is -1 or 2

So A isn't enough

Solution for # 2 is -2 or 2

So B isn't enough either

Combine A and B: the only way to satisfy both equations is to use 2.

What is wrong in my line of reasoning :roll: ?

Nothing, I suppose!
Just wanted a formal solution in the sense that you build up the equations from which you get 2 and -2
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 [#permalink] New post 16 Jun 2005, 04:35
In (1), we know |x^2| = x^2, so it reduces to solving

x-x^2=2 or x-x^2=-2

First one has no real solutions, second one has 2 and -1

So (1) gives 2 and -1 as possible values of x. Not suff

(2) alone does not tell us anything either

But together, they give x=2

C is the answer

If I saw this in my GMAT, I'd likely have solved (1) and assumed that (2) would not give us a unique solution and chosen C.
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 [#permalink] New post 16 Jun 2005, 11:50
(1)|x-|x^2||=2
Since x^2>=0 it redueces to |x-x^2|=2
(x-x^2) is always less than zero if x is an integer (very easy to prove)
So it reduces to
x^2-x-2=0
x=2 or x=-1
Insufficient

(2)|x^2-|x||=2
If x>0
|x^2-x|=2
x=2 (solve as (1))

If x<0
x=-2 (by symmetry. You can solve it too like before)
Insufficient

Combined:
x=2
sufficient

I disagree this is too hard for GMAT. I say it is a perfect GMAT question.
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Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.

  [#permalink] 16 Jun 2005, 11:50
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