Problem Solving

I think get it now. **lightbulb**

We are looking for a rephrasing that FORCES z>1.
if x+y is 2, then z can be zero
if x+y is 1, then z can be zero
if x+y is 0, then z can be 1
if x+y is -1, then z must be greater than 1. In order for x+y+z>0.

BUT one thing I still don't get.... shouldn't it be rephrased as .... if x+y <= -1 , then z>1.

I think its should be x+y<=-1

However here rephrasing the question necessary.we can solve the question from 2 statements itself.

Guys, you are wrong. x+y should be <-1 and not <=-1

It is given that x+y+z>0 and we have to find if z>0 ie.. the minimum value of z = 1.

Now if z = 1, x+y cannot be -1. It has to be less than -1 (only then x+y+z will be greater than 0)

Therefore, z>0 can be rephrased as x+y <-1

selango wrote:I think its should be x+y<=-1

However here rephrasing the question necessary.we can solve the question from 2 statements itself.

Nithi,

The original question is "is z>1?".

missrochelle wrote:If x+y+z>0, is z>1 ?

MGMAT rephrased this to be: Is x+y <-1.

Can someone explain? I don't see how we make this deduction.

(I fixed the question to "is z > 1".)

Since the question asks us about z, let's isolate z in the original inequality:

x+y+z>0

z > -x - y

z > -(x + y)

Now we ask ourselves, WHEN will z be greater than 1?

Well, since z > -(x + y), z will definitely be greater than 1 if "-(x+y)" is greater than or equal to 1.

So, we can rephrase the question:

Is -(x+y) >= 1?

Multiplying both sides by -1 (which flips the inequality):

is x + y <= -1?