GMAT prep

[sahaldar]

Q) If M= 4^1/2 +4^1/3 + 4^1/4 then M=

a) M<3
b) M=3
c) 3<M<4
d) M=4
e) M>4

ans) e

what's the shortest way to solve this problem

[blah45]

M= 4^1/2 +4^1/3 + 4^1/4
convert all to power of 2
M = 2 + 2^(2/3) + 2^(1/2)

2^(1/2) ~= 1.4
2^(1/2) < 2^(2/3) < 2. I just took => 2^(2/3) = 1.5

so, M = 2 + 1.5 + 1.4 = 2 + 2.9 = 4.9

[givemeanid]

M = 4^1/2 +4^1/3 + 4^1/4

You know 4^1/2 = 2.
Now, the smallest value of m^n where m > 1 and n > 0 is 1.
So M = 2 + x + y where x >=1 and y>=1
M > 4.