CAT 2022 Slot 3 QA Q15 Inequalities & Modulus

Question 15 of the Quantitative Ability (QA) section, CAT 2022 Slot 3, with CAT's official answer and a worked solution.

If \(c=\frac{16 x}{y}+\frac{49 y}{x}\) for some non-zero real numbers \(x\) and \(y\), then \(c\) cannot take the value
  1. A
    -70
  2. B
    60
  3. C
    -50
  4. D
    -60

Answer: (C) -50 Inequalities & Modulus MCQ

Solution

  1. Let \(t=\frac xy\neq0\); then \(c=\frac{16}t+49t\).
  2. For \(t\gt0\), AM-GM gives \(c\ge2\sqrt{16\cdot49}=56\); for \(t\lt0\), \(c\le-56\).
  3. So \(|c|\ge56\): \(-70, 60, -60\) are possible but \(-50\) is not.

Same concept in other years

See every question on AM–GM bound on a sum of reciprocal-type terms.

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