josh80 wrote:If x, y, and z are nonzero numbers, is (x)(y + z) > 0?
(1) |x + y| = |x| + |y|
(2) |z + y| = |y| + |z|
Test the following combinations for (x,y) and (y,z):
Case 1: 1, 1
Case 2: 1, -1
Case 3: -1, 1
Case 4: -1, -1
Statement 1: |x+y| = |x| + |y|
Case 1: |1+1| = |1| + |1|
Case 2: |1 + (-1)| = |1| + |1|
Case 3: |(-1) + 1| = |-1| + |1|
Case 4: |(-1) + (-1)| = |-1| + |-1|
Only Cases 1 and 4 work.
Implication:
x and y have the SAME SIGN.
If x=1, y=1, and z=1, then (x)(y+z) > 0.
If x=1, y=1, and z=-1, then (x)(y+z) = 0.
INSUFFICIENT.
Statement 2: |z+y| = |y| + |z|
Implication:
y and z have the SAME SIGN (just as x and y have the same sign in statement 1).
If x=1, y=1, and z=1, then (x)(y+z) > 0.
If x=1, y=-1 and z=-1, then (x)(y+z) < 0.
INSUFFICIENT.
Statements combined:
Since x and y have the same sign, and y and z have the same sign, ALL 3 VARIABLES -- x, y, and z -- have the SAME SIGN.
If x>0, y>0 and z>0, then (x)(y+z) = (positive)(positive) = positive.
If x<0, y<0, and z<0, then (x)(y+z) = (negative)(negative) = positive.
Thus, (x)(y+z) > 0.
SUFFICIENT.
The correct answer is
C.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
