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Absolute values

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Absolute values

by beater » Thu Dec 18, 2008 6:05 pm
If x, y, and z are nonzero numbers, is (x)(y + z) > 0?

(1) |x + y| = |x| + |y|

(2) |z + y| = |y| + |z|

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Re: Absolute values

by logitech » Thu Dec 18, 2008 6:13 pm
beater wrote:If x, y, and z are nonzero numbers, is (x)(y + z) > 0?

(1) |x + y| = |x| + |y|

(2) |z + y| = |y| + |z|
St1) Tells us that X and Y have same signs

X,Y > 0 or X,Y<0 because if they have different signs |x + y| = |x| + |y| won't be correct.

(x)(y + z) > 0? we dont know anything about Z - INSUF

ST2) Z and Y same signs, no info for X INSUF

ST1+2)

now we know X,Y and Z have same signs!

Either they are both NEGATIVE or POSITIVE

(x)(y + z) will be greater than 0

-4 (-5+(-2) ) = 28

4 (5+2) = 28

So choose C
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by ronniecoleman » Fri Dec 19, 2008 1:18 am
IMO C
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by logitech » Fri Dec 19, 2008 1:25 am
ronniecoleman wrote:IMO C
Roonie..seems like you could not quit your IMO habit yet ? :)
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by ronniecoleman » Fri Dec 19, 2008 3:25 am
logitech wrote:
ronniecoleman wrote:IMO C
Roonie..seems like you could not quit your IMO habit yet ? :)
I am trying to.....


(1) |x + y| = |x| + |y| --- x and y have to be of same sign

(2) |z + y| = |y| + |z| z and y have to be of same sign

so x , y , z are of same sign

hence together (x)(y + z) > 0
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by cramya » Fri Dec 19, 2008 4:09 am
Good solution Logitech!