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5^21 * 4^11 = 2 * 10^n What is n? A- 11 B- 21 C- 22

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5^21 * 4^11 = 2 * 10^n What is n? A- 11 B- 21 C- 22  [#permalink] New post 13 Sep 2005, 10:25
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5^21 * 4^11 = 2 * 10^n

What is n?

A- 11
B- 21
C- 22
D- 23
E- 32


GMATPrep says the answer is B. But, of course, their software provides no explanation. Can anybody explain this one to me?

By the way, does this question seem like a ridiculously hard 1st question, or is it just me?
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Senior Manager
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Joined: 27 Aug 2005
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Location: Montreal, Canada
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 [#permalink] New post 13 Sep 2005, 10:42
Actually, the numbers don't work out that complicated, if you know your properties of exponents.

The first thing to notice is that 4^11 can be expressed as (2^2)^11, which, due to exponent properties, equals 2^22:

5^21 * 4^11 = 2 * 10^n
5^21 * 2^22 = 2 * 10^n

Then, you can divide both sides by 2. Remember when you divide 2^n by 2, you subtract 1 from n:

5^21 * 2^21 = 10^n

Now you have a product of two bases to the same exponent. So because a^n*b^n = (ab)^n:

(5*2)^21 = 10^n
10^21 = 10^n
21=n
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 [#permalink] New post 13 Sep 2005, 10:59
You can actually just pick the numbers out for each prime factor.

21 = n
  [#permalink] 13 Sep 2005, 10:59
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5^21 * 4^11 = 2 * 10^n What is n? A- 11 B- 21 C- 22

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