CAT 2019 Slot 1 QA Question & Solution
AlgebraMedium
Question
If $(5.55)^x = (0.555)^y = 1000$, then the value of $\frac{1}{x} - \frac{1}{y}$ is
Options
$\frac{1}{3}$
3
1
$\frac{2}{3}$
Solution
We have, $(5.55)^x = (0.555)^y = 1000$
Taking log in base 10 on both sides,
x($\log_{10}555$-2) = y($\log_{10}555$-3) = 3
Then, x($\log_{10}555$-2) = 3.....(1)
y($\log_{10}555$-3) = 3 .....(2)
From (1) and (2)
=> $\log_{10}555$=$\ \frac{\ 3}{x}$+2=$\ \frac{\ 3}{y}+3$
=> $\frac{1}{x} - \frac{1}{y}$ = $\frac{1}{3}$