GMAT Math : Minima for absolutes

Let’s illustrate the concept with an example :

What is the minimum value of m + |xy – 3x²|

  1. y = 2
  2. m = |y|

Recognize right away that the minimum value of |xy – 3x²| is 0 as it is an absolute value term.

Hence, we essentially need the value of m to determine the minimum value of the overall expression

Statement (1) does not help us in determining the value of m, but statement (2) tells us that m is also an absolute value term and hence its minimum value is also 0. Hence statement (2) alone is sufficient and we go with option (B)

Speed Tip: The minimum value of absolute value terms can be right away taken as 0

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