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MBA.Aspirant: Master | Next Rank: 500 Posts; Posts: 401; Joined: Tue May 24, 2011 1:14 am; Thanked: 37 times; Followed by:5 members

by MBA.Aspirant » Fri Jun 03, 2011 11:23 am

If (1/2)^24 (1/81)^k = 1/18^24 , then k =

8
12
16
24
36

Source: Beat The GMAT — Problem Solving | Fri Jun 03, 2011 11:23 am

cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 am; Location: India; Thanked: 310 times; Followed by:123 members; GMAT Score:750

by cans » Fri Jun 03, 2011 11:39 am

(1/2)^24 (1/81)^k = 1/18^24 => 2^24 * 81^k = 18^24
2^24 * 3^(4k) = 2^24 * 3^(2*24)
-> 4k=48
k=12
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pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pm; Thanked: 158 times; Followed by:21 members

by pemdas » Fri Jun 03, 2011 11:54 am

(1/81)^k = 1/18^24 : (1/2)^24 or (1/81)^k = (1/9)^24

(1/9)^2k = (1/9)^24, 2k=24 and k=12

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sunilramu: Junior | Next Rank: 30 Posts; Posts: 22; Joined: Thu Feb 24, 2011 4:47 am; Thanked: 1 times

by sunilramu » Fri Jun 03, 2011 12:22 pm

(1/2)^24 (1/81)^k = 1/18^24
=> (1/2)^24 (1/3^4)^k = 1/(2.3^2)^24
=> (1/2)^24 .(1/3^4k) = 1/(2^24). 1/3^48
=> 4k = 48
=> k=12

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