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If 5^21 x 4^11 = 2 x 10^n what is the value of n?

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joe
 Post subject: If 5^21 x 4^11 = 2 x 10^n what is the value of n?
 Post Posted: Sat May 16, 2009 8:22 pm 
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Posts: 2
If 5^21 x 4^11 = 2 x 10^n what is the value of n?

A - 11
B - 21
C - 22
D - 23
E - 24

Hi Stacey, this first question on the Prep CAT really threw me for a loop. Maybe it's obvious and I'm just not seeing it yet, but how is the answer (B) 21? Much thanks,

Joe
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RonPurewal
 Post subject: Re: If 5^21 x 4^11 = 2 x 10^n what is the value of n?
 Post Posted: Sun May 17, 2009 3:34 am 
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ManhattanGMAT Staff


Posts: 7146
tricky-exponents-t1187.html
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tm03
 Post subject: Re: If 5^21 x 4^11 = 2 x 10^n what is the value of n?
 Post Posted: Sun May 17, 2009 9:12 pm 
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Here is how I solved it:

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

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

I hope you find it helpful
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RonPurewal
 Post subject: Re: If 5^21 x 4^11 = 2 x 10^n what is the value of n?
 Post Posted: Mon May 18, 2009 9:14 pm 
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ManhattanGMAT Staff


Posts: 7146
the solution above is good. it's also pretty much identical to the solution in the post linked above it.

here's the essential takeaway here:
if you see POWERS OF SPECIFIC WHOLE NUMBERS, then you should BREAK THE WHOLE NUMBERS DOWN INTO PRIMES.

i don't think i've ever seen a gmat problem featuring powers of whole numbers for which this doesn't work.
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