CAT 2023 Question Paper | Quant Slot 3

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

Video Explanation

Explanatory Answer

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'