source: http://www.manhattangmat.com

Question

thearch · Answer

feel like A is the answer

1) can be only 2
2) can be 2 or -2

katrin · Answer

Looks like it's C.

A is not suff.: x can be =2 or -1

B illiminates x=-1

So it's C

thearch · Answer

formal solution for (1)

|x-x^2|=2
can be divided into 2 equations
x-x^2=2 roots 
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?):

katrin · Answer

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:

?

sparky · Answer

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

thearch · Answer

Nothing, I suppose!
Just wanted a formal solution in the sense that you build up the equations from which you get 2 and -2

AJB77 · Answer

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.

HongHu · Answer

(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.

source: http://www.manhattangmat.com

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