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# source: http://www.manhattangmat.com

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Senior Manager
Joined: 19 Feb 2005
Posts: 486
Location: Milan Italy
Followers: 1

Kudos [?]: 11 [0], given: 0

source: http://www.manhattangmat.com [#permalink]  13 Jun 2005, 10:10
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
source: http://www.manhattangmat.com
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Senior Manager
Joined: 19 Feb 2005
Posts: 486
Location: Milan Italy
Followers: 1

Kudos [?]: 11 [0], given: 0

feel like A is the answer

1) can be only 2
2) can be 2 or -2
Intern
Joined: 13 Jan 2005
Posts: 4
Followers: 0

Kudos [?]: 0 [0], given: 0

Looks like it's C.

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

B illiminates x=-1

So it's C
Senior Manager
Joined: 19 Feb 2005
Posts: 486
Location: Milan Italy
Followers: 1

Kudos [?]: 11 [0], given: 0

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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Intern
Joined: 13 Jan 2005
Posts: 4
Followers: 0

Kudos [?]: 0 [0], given: 0

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 ?
Director
Joined: 18 Apr 2005
Posts: 548
Location: Canuckland
Followers: 1

Kudos [?]: 8 [0], given: 0

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
Senior Manager
Joined: 19 Feb 2005
Posts: 486
Location: Milan Italy
Followers: 1

Kudos [?]: 11 [0], given: 0

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 ?

Nothing, I suppose!
Just wanted a formal solution in the sense that you build up the equations from which you get 2 and -2
Senior Manager
Joined: 30 May 2005
Posts: 373
Followers: 1

Kudos [?]: 7 [0], given: 0

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

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.
SVP
Joined: 03 Jan 2005
Posts: 2246
Followers: 13

Kudos [?]: 226 [0], given: 0

(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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