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yes, D it is. root of a square is equal to the abs value of the term squared. So if you have: Sqrt[(a-b)^2], this is equivalent to la-bl _________________
You know that |x| is positive.
Only thing left to make sure the equation is > 0
is to know that x<0. This way (-x) turns positive.
And finally, if x<0 it is surely <5.
D. let me be very clear about something. This is a terrible problem, but very doable. It comes from the OG, and it's actually one I use in my lessons.
The reason is this. You need to know the GMAT VERY well to do this one right, and quickly. And there's exactly one great gmat trick imbedded here which is a red flag: x-5 and 5-x are in the same problem.
Whenever you see the same numbers twice in a problem, reversed around the minus sign, don't freak out. Just remember, this is only a positive/negative question.
Why? Take a look at this example: 10-7 = 3, 7-10=-3. Do you see it? The answer of these two subtraction problems is the same, but one is negative. That will always be true. So it can be said that |10-7|=|7-10|
That's huge. Knowing this means we can forget any algebra crap we are now freaking out about and approach the problem conceptually.
How can the sqaure root of a number squared be equal to its negative? Well, only if the number itself is negative to begin with. Look at -5. If we square it, it's 25, and then if we square root that, we're down to 5! Bingo. If we started with 5, and then squared it, we'd get 25, and then square root, we're back to the same positive 5. So it must be that the number under the radical is negative and the number on the other side of the equal is positive!
Now we're ready to make the final call. If all that is true, then x-5 must be negative, or, more specifically, x must be less than 5.
THAT'S ALL WE NEED TO FIGURE OUT!
Now, to the statements.
1)-x|x|>0
How can this be true? If the product here is positive, then they ultimately must both be positive. The |x| is definately positive, so the -x must also be. That means x must be negative. If negative, then less than 0, so less than 5. ie, enough info.
2)5-x>0
Could it get any better? If 5-x is positive, then x-5 is negative, and this whole thing works out! ie, enough info.
D
ps - i've talked about this in more detail in some of my other posts, if you're interested...