Is N=W ?

Here's the solution:

We are asked whether N = W i.e. whether N & W have equal value.
Let's look at the given statements.

Statement 1 says that N = |W|
Let's take a few quick examples to check this.
If N = 0 and W = 0, then N = |W| = 0. Here, N = W
But, if N = 2 and W = -2, then |W| = 2 which is not equal to N = -2. Hence N not equal to W
This statement is not sufficient.

Lets look at the next statement. Statement 2 says that W = |N|
Let's take a few quick examples to check this.
If N = 0 and W = 0, then W = |N| = 0. Here, N = W
But, if N = -2 and W = 2, then |N| = 2 which equal to W but N is not equal to W
This statement is not sufficient.

Lets tak Statements 1 and 2 together:
E.g. N = W = 0 or any other number - positive or negative
N = |W| and W = |N| will not be satisified by any other combination of numbers.
Hence these statements together are sufficient.

The correct answer option is C

Hope this helps!