CAT 2016 Quantitative Ability

Question : 11 of 34

Marks: +1, -0

\text"log"_c a= 1/2, \text" log"_db =1/3

where a, b, c and d are distinct natural numbers and a < b < c < d, what is the minimum possible value of a + b + c + d?

Solution:

\log_{ {c}}a=\;\;{1}/{2}\;\text"or"\; {c}= {a}^{2} .....(i)

\log_{d}b=\;\;{1}/{3}\;\text"or"\;d=b^{3} ....(ii)

Clearly, ‘a’ and ‘b’ cannot be equal to 1.
∴

a_{mm}=2\;\text"and"\;b_{mn}=3

The minimum possible value of a + b + c + d
= 2 + 3 + 4 +27 = 36

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