Data Sufficiency

Is mod x + mod x -1 = 1?
(1) x >= 0
(2) x <=1
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Answer:

Question : Is |x| + |x-1| = 1 ?

Stmt1: x > 0.
Suppose x is 1/2. Then |x| = 1/2 and |x-1| = |1/2 - 1| = 1/2
1/2 + 1/2 = 1.
If x = 3. Then |3| = 3 and |3 - 1| = 2.
3 + 2 <> 1. Hence this is insufficient.

Stmt2: x<=1.
Suppose x = 1. Then |1| + |1-1| = 1 + 0 = 1.
If x = -3. Then |-3| + |-3 - 1| = 3 + 4 = 7.
Hence this is also insufficient.

Combining Stmt1 and Stmt2, 0 < x <=1.
Put x to be any fraction greater than zero and less than 1 (we have already proved the equation for x = 1).
|x| will give you the value of the fraction and |x-1| will give you the fraction you need to add to x to make it 1.

Hence both combined are sufficient to answer whether the given equation will be equal to 1 or not.

C is the answer.