Discussion

Question:

For two real numbers a and b, let x = |a| + |b|, y = |a| − |b|, and z = |a − b|. Which of the following is true?

Explanation:

|a| and |b| are two non-negative numbers, hence we can be sure that |a| + |b| ≥ |a| - |b|, i.e., x ≥ y.

z = |a - b|, hence z will always lie between x and y.

⇒ x ≥ z ≥ y

Hence, option (c).

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