CAT 2018

Slot 2

QA

Question & Solution

Given that, p$^{3}$ = q$^{4}$ = r$^{5}$ = s$^{6}$

p$^{3}$=s$^{6}$

p = s$^{\frac{6}{3}}$ = s$^{2}$   ................................(1)

Similarly, q = s$^{\frac{6}{4}}$ = s$^{\frac{3}{2}}$   .........(2)

Similarly, r = s$^{\frac{6}{5}}$   ......................(3)

$\Rightarrow$ $log_{s}{(pqr)}$ 

By substituting value of p, q, and r from equation (1), (2) and (3) 

$\Rightarrow$ $log_{s}{(s^{2}*s^{\frac{3}{2}}*s^{\frac{6}{5}})}$ 

$\Rightarrow$ $log_{s}(s^{\frac{47}{10}})$

$\Rightarrow$ $\dfrac{47}{10}$ 

Hence, option A is the correct answer.