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by gmatmachoman » Mon Dec 06, 2010 11:15 pm
Which among 2 ^1/2, 3 ^1/3, 4^ 1/4 , 6 ^1/6 and 12 ^1/12 is the largest ?

(1) 2^1/2
(2) 3^1/3
(3) 4^1/4
(4) 6^1/6
(5) 12^1/12
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by Rahul@gurome » Mon Dec 06, 2010 11:26 pm
gmatmachoman wrote:Which among 2 ^1/2, 3 ^1/3, 4^ 1/4 , 6 ^1/6 and 12 ^1/12 is the largest ?

(1) 2^1/2
(2) 3^1/3
(3) 4^1/4
(4) 6^1/6
(5) 12^1/12
a = 2^(1/2) => a^12 = (2^(1/2))^12 = 2^6 = 64
b = 3^(1/3) => b^12 = (3^(1/3))^12 = 3^4 = 81
c = 4^(1/4) => c^12 = (4^(1/4))^12 = 4^3 = 64
d = 6^(1/6) => d^12 = (6^(1/6))^12 = 6^2 = 36
e = 12^(1/12) => e^12 = (12^(1/12))^12 = 12

b^12 is largest => b is largest

The correct option is B.
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