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

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itchyallover: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Tue Jul 15, 2008 6:45 am

by itchyallover » Wed Jul 23, 2008 5:06 pm

Hi All, would someone please help explain this question? It's from GMAP Prep 1. Many thanks.

5^21 * 4^11 = 2 * 10^N
N=?

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Source: Beat The GMAT — Problem Solving | Wed Jul 23, 2008 5:06 pm

ildude02: Master | Next Rank: 500 Posts; Posts: 320; Joined: Sun Jan 13, 2008 10:00 pm; Thanked: 10 times

by ildude02 » Wed Jul 23, 2008 6:53 pm

you can reduce the equation futhur,

5 ^ 21 x 2 ^22 = 2 .(5x2)^n
=> 5 ^21 .x 2 ^ 22 = 2 ^n+1 x 5^n; equating the similar powers, n = 21.

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pepeprepa: Legendary Member; Posts: 661; Joined: Tue Jul 08, 2008 12:58 pm; Location: France; Thanked: 48 times

by pepeprepa » Wed Jul 23, 2008 9:47 pm

21 as well
My way:
5^10 x 20^11 = 20 x 10^(N-1)
(5x20)^10=10^(N-1)
10^20=10^(N-1)
N=21

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gmatutor: Senior | Next Rank: 100 Posts; Posts: 30; Joined: Sun Dec 17, 2006 1:53 pm; Location: London; Thanked: 7 times

by gmatutor » Thu Jul 24, 2008 1:17 am

Prime factor
5^21 * 4^11 = 2 * 10^N =>

5^21 * (2^2)^11 = 2* (2*5)^N

There must be the same number of each prime on both sides of the equation. Since there are 21 fives on one side there must be 21 fives on the other.

N=21

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mdwolman: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Mon Oct 11, 2010 6:04 am

by mdwolman » Fri Jan 14, 2011 4:24 am

Hi,

How do you get from 2 x (5x2)^n to ----> 2^n+1 x 5^n?

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arora007: Community Manager; Posts: 1048; Joined: Mon Aug 17, 2009 3:26 amFollowed by: 27 members; Location: India; Thanked: 51 times; GMAT Score:670

by arora007 » Fri Jan 14, 2011 4:35 am

mdwolman, you have to balance out the 5^21 on rhs,right?

now the 10 = (2*5) , now whatever be the power of 2 , you need the power of 5 to be balanced...

so feel confident while choosing N=21

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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Fri Jan 14, 2011 5:38 am

mdwolman wrote:How do you get from 2 x (5x2)^n to ----> 2^n+1 x 5^n?

We can write (5*2)^n = (2^n)*(5^n)

Thus 2*(5*2)^n = 2*(2^n)*(5^n) = (2*(2^n))*(5^n) = (2^(n + 1))*(5^n)

It is an application of a property of exponents,

(x^a)*(x^b) = x^(a + b)

Here, x = 2, a = 1 and b = n.

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Rahula g: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Thu Jan 13, 2011 4:35 am

by Rahula g » Fri Jan 14, 2011 8:21 am

itchyallover wrote:
5^21 * 4^11 = 2 * 10^N
N=?

5^21 * 2^11 * 2^11 = 2 * 5^N * 2^N

5^21 * 2^22 = 5^N * 2^N+1

N= 21

rahul@gurome wrote:

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