Absolute values

[beater]

If x, y, and z are nonzero numbers, is (x)(y + z) > 0?

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

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

[logitech]

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

[ronniecoleman]

IMO C

[logitech]

IMO C

Roonie..seems like you could not quit your IMO habit yet ?

[ronniecoleman]

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

[cramya]

Good solution Logitech!