What is the value of z?

Thanks MacFauz and Bunuel. I understand your explanation and yes, OA is C.

However, can you tell me where I am wrong :
- Statement 1 is clearly not sufficient because z could be 5 or -5.
- Statement 2 is z = -|z|, you can rewrite the expression such as -z = IzI (wright?) if we multiply both side by -1. In that case the only possible value for z is 0 because the only possible solution is - 0 = I0I. So it is sufficient, no??

help me please.
Thanks

Yes, z = -|z| is the same as |z|=-z. But in this case z could be 0 or any negative number. For example, z=-2 --> |z|=|-2|=2 and -z=-(-2)=2 --> |z|=-z.

Absolute value properties:
When \(x\leq{0}\) then \(|x|=-x\), or more generally when \(some \ expression\leq{0}\) then \(|some \ expression|\leq{-(some \ expression)}\). For example: \(|-5|=5=-(-5)\);

When \(x\geq{0}\) then \(|x|=x\), or more generally when \(some \ expression\geq{0}\) then \(|some \ expression|\leq{some \ expression}\). For example: \(|5|=5\).

For more check Absolute Value chapter of Math Book: math-absolute-value-modulus-86462.html

DS questions on absolute value to practice: search.php?search_id=tag&tag_id=37
PS questions on absolute value to practice: search.php?search_id=tag&tag_id=58

Tough absolute value and inequity questions with detailed solutions: inequality-and-absolute-value-questions-from-my-collection-86939.html

Hope it helps.

Thank you so much Bunuel. Your help is precious!

Statement 1 : Insufficient
Gives z=5 or -5

Statement 2 : Insufficient
Gives z in non positive

Combining both, z= -5
Hence, OA is (C).