Bunuel wrote:

Is |a - b| + |c - b|= |c -a| ?

(1) a < b < c

(2) ab < 0

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question.

|a-b| +|c-b| = |c-a|

⇔ |a-b|+|b-c| = | (a-b) + (b-c) |

⇔ (a-b)(b-c) ≥ 0

Condition 1)

Since a - b < 0 and b - c < 0, we have (a-b)(b-c) > 0.

The condition 1) is sufficient.

Condition 2)

Since we don't have any information about c, the condition 2) only is not sufficient.

Therefore, the answer is A.

Note. We should keep in mind the following properties.

|x+y| ≤ |x| + |y| holds always.

|x+y| = |x| + |y| ⇔ xy ≥ 0

|x+y| < |x| + |y| ⇔ xy < 0

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