the answer is C since:

(1) x+y=z --> -x=y-z thus |x|=y-z is true only if x<=0.
for example, if x=1 then according to (1): -1=y-z which contradicts: 1=y-z
insufficient.

(2) x<0 insufficient as you said.

(1+2) sufficient. x<0, therefore in statement (1): -x=y-z, x is positive, which leads us to conclude that |x|=y-z is true.

is it C?

rtfact wrote:the answer is C since:

(1) x+y=z --> -x=y-z thus |x|=y-z is true only if x<=0.
for example, if x=1 then according to (1): -1=y-z which contradicts: 1=y-z
insufficient.

(2) x<0 insufficient as you said.

(1+2) sufficient. x<0, therefore in statement (1): -x=y-z, x is positive, which leads us to conclude that |x|=y-z is true.

Thanks......

i have same ques.
If in any ques it is asked mod x = mod y
and nothing about -ve and +ve.
Do we need to prove , x=y AND -x =-y........
I am putting essence on AND...it will be AND (both condition)or OR...means any1 of condition

vivek.kapoor83,

there can be different cases for |x| =|y|

x + -

y + -

check how many combos you can have.

Is |x|=y-z


statement 1:

x+y=z
x=z-y( if x>0)
x=y-z( if x<0)

Insufficient

statement 2

x<0

Insufficient

Combining both the statements we have x=y-z for x<0


So the ans should be C..Let me know if you still have any doubts