# CAT 2018 Quant Questions

Question:
If p3 = q4 = r5 = s6, then the value of logs(pqr) is equal to

 16/5 1 24/5 47/10
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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)

$\Rightarrow$ $lo{g_s}(pqr)$

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

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

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

$\Rightarrow$ $\frac{{47}}{{10}}$

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