|x| + |y| > |x + z|

Q1:x

Q2:z

greg, Any shortcut???

|x| + |y| > |x + z|

Q1:x

Q2:z

greg, Any shortcut???

Let |y| = 0. Then take x =-5 and z = 6, and x = 5 and z = -1.

Since |x| + |y| > |x + z|, x or z must be a negative number and the other is a positive. However, there is no information about which one is negative or positive, it could be -x,z or z,-x, therefore D.

How did you arrive at this conclusion?

First, I know that |x + z| could be any of these 4

(1) |x + z|

(2) |(-x) + (-z)|

(3) |(-x) + z|

(4) |x + (-z)|

The question tells us that:

|x| + |y| > |x + z|

Which means that scenario (1) and (2) is out since they will be equal.

So we know that |x + z| must actually be |x + (-z)| or |(-x) + z| which tells us that one of them must be negative. But we can’t deduce which one, therefore, answer D.

Y can be a larger positive than Z so z can or cannot be negative

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Well, for example, x= 2 y = 3 z = 4

|x| + |y| = 2 + 3 = 5

|x + z| = |2 + 4| = 6

You can also have:

x,y,z = -1, 2, -4

|x| + |y| = 1 + 2 = 3

|x + z| = |-1 -4| = |-5| = 5

So, no you can have scenario (1) and (2)

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Hey thank you, I made a reading mistake and thought it’s |x| + |z| compare to |x + z|.

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