CAT 2012 | Question: 4

Question

Which of the terms $2^{\frac{1}{3}},3^{\frac{1}{4}},4^{\frac{1}{6}},6^{\frac{1}{8}}$ and $10^{\frac{1}{12}}$ is the largest?

• A. $2^{\frac{1}{3}} \\$
• B. $3^{\frac{1}{4}} \\$
• C. $4^{\frac{1}{6}} \\$
• D. $10^{\frac{1}{12}}$

Answer 1

Given that $:2^{\frac{1}{3}},3^{\frac{1}{4}},4^{\frac{1}{6}},6^{\frac{1}{8}},10^{\frac{1}{12}}$

 LCM of $3,4,6,8,12 = 24$

Now, $2^{\frac{1}{3}\times 24},3^{\frac{1}{4}\times24},4^{\frac{1}{6}\times24},6^{\frac{1}{8}\times24},10^{\frac{1}{12}\times24}$

$\implies2^{8},3^{6},4^{4},6^{3},10^{2}$

$\implies 256,729,256,216,100$

$\therefore$ The largest number is $ = 729$

So, the correct answer is $(B).$