Absolute value question

lightbulb wrote:Guys, this is from the GmatPrep:

If zy < xy < 0, is |x - z| + |x| = |z|

(1) z < x

(2) y > 0

Answer: D

Could someone please explain the answer?

Thank you.

zy < xy < 0

means that zy and xy have both two numbers with different signs. ( +-) or (-+)

and you will see that they both have "y" in common

SO:

A ) If Y>0 (X and Z) < 0 and X > Z so that we can have zy < xy < 0

B ) if Y<0 (X and Z) > 0 and X < Z so that we can have zy < xy < 0

Lets go back to statements:

1 ) z < x

This means that x - z > 0 so it can get out the absolute value sign as it is

and we also know that if x > Z they have to be both NEGATIVE NUMBERS ( look at A )

so:


IS |x - z| + |x| = |z| ?

X-Z + ( -X ) = -Z

which is |z|, since Z is negative it needs to be -Z

Sufficient

(2) y > 0

We already discussed this

A ) If Y>0 (X and Z) < 0 and X > Z so that we can have zy < xy < 0

Sufficient

Hence, it is D

Thanks. I used your response to solve the problem as follows:

Given:

If zy < xy < 0, is |x - z| + |x| = |z|

We can have two possibilities:

(I) y > 0. This implies
- z and x are both negative
- z is more negative than x (z < x)

(II) y < 0. This implies
- z and x are both positive
- z > x

So here we go:

(A) z < x
Now, either y > 0 or y < 0.
If y < 0, then both z and x are +ve, but, then z cannot be less than x because zy < xy < 0.

This implies: y > 0. Which further impiles z and x are both negative.

Plug z = -3, x = -2
|-2 - (-3)| + (-2) = (-3)
1 - 2 = -3
-1 = -3
The above statement is not true.
Therefore, under the given conditions, the algebraic expression is false - for sure.
So (A) is sufficient.

(B) y > 0
This impiles z and x are both negative and the problem reduces to (A).
So, (B) is also sufficient.

is |x - z| + |x| = |z|
distance between x and z + distance between 0 and x = distance between z and 0

This means, on a number line : 0................x..........z
we are also given zy < xy < 0

Statement 1 : z < x

If x>z, then automatically the answer to this Question is No.
we arrive at a conclusion using this statement that is |x - z| + |x| = |z| is not correct

Statement 2 : y > 0
this is same as statement (1)
ie : z < x

Thus is |x - z| + |x| = |z| is incorrect

With both the statements we are able to arrive at the same conclusion that is |x - z| + |x| = |z| is incorrect

So answer has to be D

Please correct me if I am wrong

Regards