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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Correct Answer: 4

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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CAT 2018 Quant Questions
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