Is abs(x) = y - z? condition 1: x + y = z condition 2: x

Question

Is abs(x) = y - z?

condition 1: x + y = z

condition 2: x < 0

Fig · Answer

I get (C):

|x| = y-z => y >= z

1) x+y = z
<=> x = z-y
<=> -x = y-z
<=> |x| = |y-z|

As we don't know either y >=z : we cannot conclude
INSUFF

2) INSUFF

(1) & (2) :
x < 0
<=> -x > 0
<=> y - z > 0

Thus
|x| = |y-z| = y-z

ywilfred · Answer

St1:

x+y = z

If x = 3, y = 2, z = 5 --> |x| != y-z

If x = -5, y = 3, z = -2 ---> |x| = y-z

Insufficient.

St2: 

Insufficient as we do not have any information about y and z.

Using St1 and St2:

We're told x is negative. So |x| = y-z --> -x = y-z --> z = x+y. Sufficient.

Ans C

shahnandan · Answer

stmt 1,

if u plug in numbers 

x y z
5 3 8 YES
o 4 4 NO
so, insuff

stm2,
y and z can be anything

combining--it holds good
Hence C.

mrmikec · Answer

|x| = y - z?

so if:
if x>0, x = y - z
if x<0, -x = y - z gives me z = x + y

condition 1. x + y = z

I thought I could conclude that this means x<0 thus SUFFICIENT

condition 2. x<0 INSUFFICIENT

Why is my rationale for condition 1 incorrect?

Thanks

paddyboy · Answer

If X < 0, then -X > 0... big mistake

haas_mba07 · Answer

B. Stmt2 is sufficient.

Stmt1:
Take x= -7, y = 8 , z = 1
and 
x = 3, y = 2, z = 5

Then in one case answer is yes and the other no.

=> Not sufficient.

Stmt2:

x < 0, => -x +y =z i.e x= y-z => abs(x) = y-z
Sufficient.

likar · Answer

I'm getting  (C) 

 If x>0 
x=y-z

 If x<0 
-x=y-z

 From statement (1): 
x+y=z
from this we get:
-x=y-z
Conclusion: This is valid only when x<0, therefore INSUFF.

 From statement (2): 
x<0
Conclusion: We don't know any information about y and z, therefore INSUFF.

 Statements together: 
If x<0, the conclusion from (1) is valid, therefore SUFF.

Is abs(x) = y - z? condition 1: x + y = z condition 2: x

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