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daretodream: Senior | Next Rank: 100 Posts; Posts: 76; Joined: Tue Oct 28, 2008 6:08 am; Thanked: 2 times

by daretodream » Fri Feb 19, 2010 3:31 am

5^21 x 4^11 = 2 x 10^n
n=?

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Source: Beat The GMAT — Problem Solving | Fri Feb 19, 2010 3:31 am

harsh.champ: Legendary Member; Posts: 1132; Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members; Location: India; Thanked: 64 times; GMAT Score:760

by harsh.champ » Fri Feb 19, 2010 3:35 am

daretodream wrote:5^21 x 4^11 = 2 x 10^n
n=?

R.H.S.= (2) x (2)^n x (5)^n
=[(2)^(n+1)] x 5^n

L.H.S. = 5^21 X 2^22

So, comparing exponents we get n=21

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Fri Feb 19, 2010 12:36 pm

daretodream wrote:5^21 x 4^11 = 2 x 10^n
n=?

5^21*4^11 = 2*10^n

5^21* (2^2)^11 = 2*10^n

5^21* 2^22 = 2*10^n

2* (5^21* 2^21) = 2*10^n

2* (5*2)^21 =2*10^n

2* (10)^21 =2*10^n

n =21

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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Sat Feb 20, 2010 7:26 am

daretodream wrote:5^21 x 4^11 = 2 x 10^n
n=?

5^21 x 4^11 = 2 x 10^n
It is simple question of equation powers of similar base as discussed in some earlier post
--> 5^21 x 2^22 = 2 x (5x2)^n
--> 5^21 x 2^22 = 2^(n+1) x 5^n

[spoiler]so n = 21 ans[/spoiler]

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thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

by thephoenix » Sat Feb 20, 2010 7:57 am

daretodream wrote:5^21 x 4^11 = 2 x 10^n
n=?

LHS=5^21 * 2^22
RHS=2*(2*50)^n=2^(n+1) * 5^n

when LHS=RHS----> n=21

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