CAT 2023 Slot 3 QA Q22 Functions & Graphs

Question 22 of the Quantitative Ability (QA) section, CAT 2023 Slot 3, with CAT's official answer and a worked solution.

Suppose \(f(x, y)\) is a real-valued function such that \(f(3 x+2 y, 2 x-5 y)=19 x\), for all real numbers \(x\) and \(y\). The value of \(x\) for which \(f(x, 2 x)=27\), is

TITA: type in the answer. There are no options and no negative marking.

Answer: 3 Functions & Graphs TITA

Solution

  1. Let \(u=3x+2y,\ v=2x-5y\). Then \(5u+2v = 19x\), so \(f(u,v)=5u+2v\).
  2. \(f(x,2x) = 5x+4x = 9x = 27 \Rightarrow x=3\).

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