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Absolute Inequality

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by iwillsurvive101 » Fri May 18, 2012 1:19 pm
BTG Community, Please help me clarify the solution to this problem.

Is |x| = y-z?

(1) x + y = z
(2) x < 0

Solution:

I got so far:

Question Rephrase:

Is x = y -z OR Is x = z -y ? (Solving the absolute value - 2 Possibilitues)

Statement1:
x+y=z

=> Case1: Is x = y-z?
Using x+y=z to answer the above
I got y=z?

NO

=> Case2: Is x = z -y?
Using x+y=z
I got 0=0

YES

Yes & NO == Insufficient

Statement2: x < 0

If x < 0
Does not tell me much about y and z. Insufficient.

Statement1 & 2 Together

If x<0 and y=z 0 </ 0 NO. Sufficient. (I have a jambled logic here)


Please help with some details.
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Source: — Data Sufficiency |
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by aneesh.kg » Fri May 18, 2012 2:18 pm
iwillsurvive101 wrote:BTG Community, Please help me clarify the solution to this problem.

Is |x| = y-z?

(1) x + y = z
(2) x < 0

Solution:

I got so far:

Question Rephrase:

Is x = y -z OR Is x = z -y ? (Solving the absolute value - 2 Possibilitues)
Hi,

I just want to check if you know when is x = y - z and when is x = z - y?

Well, this comes from the definition of modulus of which says that:
|x| = x when x > 0,
|x| = - x when x < 0

So,
x = y - z when x > 0 and
x = z - y when x < 0.

Let me take over from you from the part where you tried combining the statements and got confused.

When you combine the two statements we know that x < 0 and x = z - y.
And, the question which was 'Is |x| = y - z?' before simplifies to 'Is x = z - y?' now because x < 0.

So, Is x = z - y?
YES, Statement(1) tells us exactly that.

SUFFICIENT

Please let me know if this makes sense.
Aneesh Bangia
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by Anurag@Gurome » Fri May 18, 2012 10:07 pm
Since |x| = y - z, so y - z ≥ 0
We have to find if y - z ≥ 0 and if y - z = |x|

(1) x + y = z
-x = y - z
If x > 0, then y - z = negative
If x ≤ 0, then y - z = positive
No definite answer; NOT sufficient.

(2) x < 0 is definitely NOT sufficient as we have to find if y - z is equal to |x| or not.

Combining (1) and (2), we get the answer to the question; SUFFICIENT.

The correct answer is C.
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