seema19 wrote:If X + Y + Z > 0, is Z > 1?
a) Z > X + Y + 1
b) X + Y + 1 < 0
Answer: B
My reasoning was - since Z > 1 + (X + Y), Z is definitely greater than 1. So, A is suff.
Since in option B, the inequality doesn't have Z, it is not enough to answer. So, B is insuff.
Can someone please tell, where I went going wrong in analyzing the first option?
The question stem gives an inequality.
Each statement gives an inequality.
One strategy is to ADD THE INEQUALITIES.
To add inequalities, the <> must face the same direction in each.
Statement 1: Z > X + Y + 1
Adding together X+Y+Z>0 and Z>X+Y+1, we get:
(X+Y+Z) + Z > 0 + (X+Y+1)
2Z > 1.
Z > 1/2.
INSUFFICIENT.
Statement 2: X + Y + 1 < 0
Adding together X+Y+Z>0 and 0>X+Y+1, we get:
(X+Y+Z) + 0 > 0 + (X+Y+1)
Z > 1.
SUFFICIENT.
The correct answer is
B.
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