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jfranco23: Senior | Next Rank: 100 Posts; Posts: 75; Joined: Fri Jan 16, 2009 2:00 pm; Thanked: 1 times; GMAT Score:550

by jfranco23 » Fri Mar 06, 2009 4:55 pm

If 3^(6x) = 8100, what is the value of ((3^(x-1))^3

A. 90
B. 30
C. 10
D. 10/3
E. 10/9

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Source: Beat The GMAT — Problem Solving | Fri Mar 06, 2009 4:55 pm

truplayer256: Master | Next Rank: 500 Posts; Posts: 392; Joined: Thu Jan 15, 2009 12:52 pm; Location: New Jersey; Thanked: 76 times

by truplayer256 » Fri Mar 06, 2009 5:10 pm

If 3^(6x) = 8100, what is the value of ((3^(x-1))^3

A. 90
B. 30
C. 10
D. 10/3
E. 10/9

((3^(x-1))^3 is the same thing as ([3^x]/[3])^(3) and this simplifies to (3^3x)/(27). Now all we have to do is find 3^3x. Well, we're given that 3^6x=8100 and if we take the square root of both sides we get 3^3x=90. Our answer is therefore 90/27 or 10/3 D.

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