Let us revisit the definition of mode. It goes like ...

mode (p) = p , if p > = zero
= - p , if p < zero.

Now let us take the question here,

Is mode (x) = y - z?

(A) says, x = z - y, thus by definition
mode (x) = z - y, if x = z - y > = zero
= y - z, if X = z - y < zero

Thus (A) is not enough to surely answer the question.

Let us look at (B), it says x > zero, (B) alone clearly does not suffice for the answer of the question.

Let's combine both (A) and (B) ; -- it clearly says that as X > zero;
mode (x) = y - z.

Thus [C] is the correct answer.

I hope it clears the doubt.

Hi amit,

I think I got it.... I was trying to figoure out the result of lXl = y- z (for example, if y=3, z=1, the result is x=2. With the same numbers for x = z - y, the result will be x=-2 ) So, whether the answer is 2 or -2, X is absolute value, so it dose not matter..

But I just realize the question is NOT asking the value of lXl but simply asking whether lXl is y-z (and not z=y).

Thanks again for your help.
Rina

Let x = 5, y = -8
Condition 1) z = x + y . Hence z = -3
(y-z) = -5. clearly |x| = 5 is not equal to (y-z)

As per condition (2) x < 0.
Let x = -3, y = -8. Hence according to condition (1) z = -11.
|x| = 3.
(y-z) = 3

Hence both conditions are required.