Exponent Problem

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Thonk02: Junior | Next Rank: 30 Posts; Posts: 18; Joined: Fri Jan 30, 2009 1:30 pm

by Thonk02 » Mon Jul 06, 2009 10:02 am

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

N = ?

A. 20
B. 21
C. 22
D. 23
E. 32

I have no idea where to even start with this one. Any help would be appreciative.

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Source: Beat The GMAT — Problem Solving | Mon Jul 06, 2009 10:02 am

jakesing: Junior | Next Rank: 30 Posts; Posts: 21; Joined: Fri Jun 12, 2009 2:10 pm; Thanked: 1 times

by jakesing » Mon Jul 06, 2009 10:06 am

4^11=(2^2)^11=2^22

So you have 5^21x2^22=2x10^n

Divide both sides by 2, you'll get:

5^21x2^21=10^n.

Use the property that says (x^n)x(y^n)=(xy^n), you get:

10^21=10^n.

n=21.

Hope that helps!

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learnitboy: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Mon Jun 29, 2009 8:15 pm

by learnitboy » Mon Jul 06, 2009 10:11 am

4^11=2^22=2*2^21

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

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ghacker: Master | Next Rank: 500 Posts; Posts: 148; Joined: Wed Jun 03, 2009 8:04 pmFollowed by: 1 member; Thanked: 18 times

by ghacker » Tue Jul 07, 2009 9:09 am

n = 21

n depends on the powers of 5 ( since the powers of 2 > powers of 5)

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