# CAT 2023 Question Paper | Quant Slot 3

###### CAT Previous Year Paper | CAT Quant Questions | Question 22

CAT 2023 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 22 : 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

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let $a = 3 x + 2 y ; b = 2 x - 5 y$
Let's try to write x in terms of a and b
$5 a + 2 b = 15 x + 10 y + 4 x - 10 y = 19 x$
$19 x = 5 a + 2 b$
$f ( 3 x + 2 y , 2 x - 5 y ) = 19 x$
$$therefore f$ a , b ) = 5 a + 2 b$
$f ( x , 2 x ) = 5 x + 4 x = 9 x = 27$
$$Rightarrow x = 3$ The question is " 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 "

##### Hence, the answer is '3'

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