Algebra Inequalities

cramya wrote:Question:

If x+y+z>1 is z > 1

(or)

Is x+y < -1 then we know z > 1

Stmt I

z > x+y+1

z-1 > x+y

Therefore z-1+z > 0 (replace x+y in x+y+z>0 by z-1)

2z>1

z>1/2

INSUFF

Stmt II

x+y < -1

Exactly what we need

SUFF

Choose B

lunarpower wrote:the most routine, and possibly most straightforward, way to answer this question is with the following standard fact about inequalities (note that the "alligator" is the "<" or ">" sign):

you can ADD inequalities if the alligators face the same way.

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in statement (1), you know that
x + y + z > 0
and
z > x + y + 1

you can just add these together, giving x + y + 2z > x + y + 1. then cancel (i.e., subtract) the x and the y, giving 2z > 1, or z > 1/2. this is insufficient to answer the question of whether z is greater than 1.

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in statement (2), you know that
x + y + z > 0
and
0 > x + y + 1 (i.e., the second statement, just written the other way so that the alligator is the same as the first one)

you can just add these together, giving x + y + z > x + y + 1. then cancel (i.e., subtract) the x and the y, giving z > 1.
sufficient.

ans (b)