What is the source of the problem ?

imho OA should be C too. Here's my explanation :

Given,

Is |x| = y-z ?

Rephrase the Question :

x = y-z or -x = y-z ( => x = z-y ),

so the question could be re-phrased as : x = y-z or z-y . Is this True ?

Statement 1 :

x+y = z or

x = z-y => This statement says that x is only equal to z-y but not y-z , Hence insufficient

Statement 2 :

x < 0 => |x| = -x ( as per definition of absolute value ). It does not give info about y or z . Hence insufficient.

Taken Together :

From statement 1 , x = z - y

From statement 2, x < 0 => |x| = -x. But from above we have -x = - (z-y) = (y-z). Hence x can be both z-y or y-z. Sufficient

Hence Ans is C !

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