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CAT 1995 | Question: 65

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Let

  • $le(x, y) =$ least of x and y (i.e., $\min(x, y))$
  • $me(x, y) =$ maximum of x and y (i.e., $\max(x, y))$
  • $mo(x) = |x|$ (absolute value)

For real numbers $a, b,$ which of the following must be true?

  1. $mo(le(a, b)) ≥ me(mo(a), mo(b))$
  2. $mo(le(a, b)) > me(mo(a), mo(b))$
  3. $mo(le(a, b)) < le(mo(a), mo(b))$
  4. $mo(le(a, b)) ≥ le(mo(a), mo(b))$

1 Answer

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$$le(mo(a), mo(b)) ≤ mo(le(a, b)) ≤ me(mo(a), mo(b)).$$

Hence only option D is guaranteed true.

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