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sahaldar: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Mon Jun 18, 2007 10:51 pm

by sahaldar » Mon Jul 16, 2007 2:35 am

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

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Source: Beat The GMAT — Problem Solving | Mon Jul 16, 2007 2:35 am

blah45: Junior | Next Rank: 30 Posts; Posts: 28; Joined: Wed Jun 13, 2007 3:10 pm; Location: NJ, USA

by blah45 » Mon Jul 16, 2007 5:11 am

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

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givemeanid: Master | Next Rank: 500 Posts; Posts: 277; Joined: Sun Jun 17, 2007 2:51 pmFollowed by: 1 member; Location: New York, NY; Thanked: 6 times

by givemeanid » Mon Jul 16, 2007 5:17 am

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.

So It Goes

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