Exponent Question--GMAT Prep

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mindruna: Junior | Next Rank: 30 Posts; Posts: 27; Joined: Mon Mar 19, 2007 6:23 pm; Location: Cambridge, MA

by mindruna » Sat Jul 28, 2007 9:44 am

Is there a simple way to solve this problem from GMAT Prep?

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

a) 11
b)21
c)22
d) 23
e) 32

The official answer is 21.

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Source: Beat The GMAT — Problem Solving | Sat Jul 28, 2007 9:44 am

RM: Senior | Next Rank: 100 Posts; Posts: 47; Joined: Sat Jun 16, 2007 10:58 pm

by RM » Sat Jul 28, 2007 10:09 am

You can factorize the equation to its prime factors.

5^21 x 4^11=2 x 10^n
5^21 x 2^22 = 2 x 2^n x 5^n
5^21 x 2^22 = 2^(n+1) x 5^n

We can equate powers of either prime factor 2 or 5.

i.e. 5^21 = 5^n, gives n = 21
Or, 2^22 = 2^(n+1), gives n = 21

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mindruna: Junior | Next Rank: 30 Posts; Posts: 27; Joined: Mon Mar 19, 2007 6:23 pm; Location: Cambridge, MA

thanks.

by mindruna » Sat Jul 28, 2007 10:31 am

That's so clear. Thank you so much.

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marvelxx35: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Tue Jul 03, 2007 7:41 am

by marvelxx35 » Mon Jul 30, 2007 6:20 am

when given 5^21 * 4^11 = 2 * 10^n,

simplify 4^11 to 2^22 to get, 5^21 * 2^22 = 2 * 10^n.

then, simplify again to get, 10^21 * 2 = 2 * 10^n.

you can clearly see that n = 21.

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