Absolute Value

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ZY<XY<0 is |X-Z| + |x| = |Z|

(1) Z<X
(2) Y<0

The answer is D, could you pls explain with testing values?

[theCodeToGMAT]

To find: |X-Z| + |x| = |Z|

Statement 1:
Z<X ==> y is +ve ==> x & z both are negative
Both x & z are negative
Let x = -5 & z = -8
=> |-5 + 8 | + |5| = |8|
=> 3 + 5 = 8
=> 8 = 8
SUFFICIENT

Statement 2:
y < 0 ==> x & z are positive & z > x
Let z = 8 & x = 5
=> | 5 - 8 | + |5| = |8|
=> 3 + 5 = 8
= 8 = 8
SUFFICIENT

Answer[spoiler] {D}[/spoiler]

[sanju09]

ZY<XY<0 is |X-Z| + |x| = |Z|

(1) Z<X
(2) Y<0

The answer is D, could you pls explain with testing values?

If ZY < XY < 0, then either Y < 0 and Z, X > 0 or Y > 0 and Z, X < 0.

If Y < 0 and Z, X > 0, the condition ZY < XY < 0 will be true only if Z > X.

And if Y > 0 and Z, X < 0, the condition ZY < XY < 0 will be true only if Z < X.


(1) If Z < X, then the condition ZY < XY < 0 is true only if Z, X > 0 and Y < 0. Let's take X = 3 and Z = 2, so that |3 - 2| + |3| is NO ≠ |2|. Sufficient

(2) If Y < 0, then the condition ZY < XY < 0 is true only if Z, X > 0 and Z < X. Let's recycle X = 3 and Z = 2, so that |3 - 2| + |3| is NO ≠ |2|. [spoiler]Sufficient

Take D

In other words, each statement implies the other, hence D in case of sufficiency otherwise E in case of insufficiency.
[/spoiler]

[[email protected]]

Now my question is will we have a scenario where the two sttmnts contradict each other?

Statement one gives us y is positive whereas statement two says its negative!

Thnks

To find: |X-Z| + |x| = |Z|

Statement 1:
Z<X ==> y is +ve ==> x & z both are negative
Both x & z are negative
Let x = -5 & z = -8
=> |-5 + 8 | + |5| = |8|
=> 3 + 5 = 8
=> 8 = 8
SUFFICIENT

Statement 2:
y < 0 ==> x & z are positive & z > x
Let z = 8 & x = 5
=> | 5 - 8 | + |5| = |8|
=> 3 + 5 = 8
= 8 = 8
SUFFICIENT

Answer[spoiler] {D}[/spoiler]

[theCodeToGMAT]

Now my question is will we have a scenario where the two sttmnts contradict each other?

Statement one gives us y is positive whereas statement two says its negative!

Thnks

No, I don't think so..

Both statement will not contradict because

|X-Z| + |x| = |Z|

Here,

|X-Z| ==> is always the difference between x & z... and signs of x & z will always be same as ZY<XY<0

And, the magnitude of x & z will vary correspondingly based on signs

[GMATGuruNY]

ZY<XY<0 is |X-Z| + |x| = |Z|?

(1) Z<X
(2) Y<0

|x-z| = the distance between x and z.
|x| = the distance between x and 0.
|z| = the distance between z and 0.

Constraint in the question stem: zy < xy < 0.
Case 1: If y is POSITIVE, then x and z are NEGATIVE, with z "more negative" than x, so that zy < xy.
Case 2: If y is NEGATIVE, then x and z are POSITIVE, with z "more positive" than x, so that zy < xy.

Case 1:
z<---|x-z|--->x<---|x|--->0..........y
In the number line above, the red portion represents |z|: the distance between z and 0.
|x-z| + |x| is equal to the red portion.
Thus:
|x-z| + |x| = |z|.

Case 2:
y..........0<---|x|--->x<---|x-z|--->z
In the number line above, the red portion represents |z|: the distance between z and 0.
|x-z| + |x| is equal to the red portion.
Thus:
|x-z| + |x| = |z|.

The two statements are IRRELEVANT.
Given that zy < xy < 0, it will ALWAYS be true that |x-z| + |x| = |z|.
Thus:
in statement 1, the answer to the question stem is YES, since it will always be true that |x-z| + |x| = |z|.
In statement 2, the answer to the question stem is YES, since it will always be true that |x-z| + |x| = |z|.

The correct answer is D.

Since the two statements are irrelevant, this problem is flawed.