CAT 2022

Slot 3

QA

Question & Solution

$(\sqrt{\frac{7}{5}})^{3x-y}=\frac{875}{2401}$

$\left(\frac{7}{5}\right)^{\frac{\left(3x-y\right)}{2}}=\frac{125}{343}$

$\left(\frac{7}{5}\right)^{\frac{\left(3x-y\right)}{2}}=\left(\frac{7}{5}\right)^{-3}$

3x-y = -6

$(\frac{4a}{b})^{6x-y}=(\frac{2a}{b})^{y-6x}$

Therefor, y=6x as the bases are different so the power should be zero for the results to be equal.

3x-y=-6

or, 3x - 6x = -6

or x= 2

y= 6x = 12

x+y = 14