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(3x+2y,2x−5y)=19x, for all real numbers x and y. The value of x for which f(x,2x)=27, is
let a=3x+2y;b=2x−5y
Let's try to write x in terms of a and b
5a+2b=15x+10y+4x−10y=19x
19x=5a+2b
f(3x+2y,2x−5y)=19x
∴f(a,b)=5a+2b
f(x,2x)=5x+4x=9x=27
⇒x=3
The question is " Suppose f(x,y) is a real-valued function such that f(3x+2y,2x−5y)=19x, for all real numbers x and y. The value of x for which f(x,2x)=27, is "
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