Exponents

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m_blooms: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Sat Apr 12, 2008 12:16 pm

by m_blooms » Tue May 06, 2008 5:56 am

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

What is the value of n?

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Source: Beat The GMAT — Problem Solving | Tue May 06, 2008 5:56 am

Sakhalin: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Sat May 03, 2008 9:27 am

by Sakhalin » Tue May 06, 2008 7:20 am

I think the answer for n=21

5^21*4^11=2*10^n
5^21*2^22=2*5^n*2^n
Threfore n must equal 21

I am not sure. Please let me know if you know the correct solution

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Sakhalin: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Sat May 03, 2008 9:27 am

by Sakhalin » Tue May 06, 2008 7:21 am

I think the answer for n=21

5^21*4^11=2*10^n
5^21*2^22=2*5^n*2^n
Threfore n must equal 21

I am not sure. Please let me know if you know the correct solution

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VP_RedSoxFan: GMAT Instructor; Posts: 85; Joined: Thu May 01, 2008 12:56 pm; Location: Salt Lake City, UT; Thanked: 24 times; GMAT Score:750+

by VP_RedSoxFan » Tue May 06, 2008 7:28 am

The only way to solve this one is to realize what the exponents really mean.

You can think of 5^21 as a list of 21 5's multiplied together.

4^11 = (2^2)^11 = 2^22 and you can think of this as a list of 22 2's multiplied together.

Instead of multiplying the all of the 5's and then all of the 2's, then multiplying their products together, you can match up a 5 and 2. Now instead of 21 5's and 22 2's, you have 21 10's and a 2 to multiply together. And, clearly, another way to write that would be 2 * 10^21

The answer is 21

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AleksandrM: Legendary Member; Posts: 566; Joined: Fri Jan 04, 2008 11:01 am; Location: Philadelphia; Thanked: 31 times; GMAT Score:640

by AleksandrM » Tue May 06, 2008 9:53 am

I got 21 as well. The key in this one is to see that when you split 10^n the result is not 2 * 5^n but is 2^n * 5^n. Another mistake that could be made is to ignore the 2 and forget that it is 2^1, leaving a 1 behind.

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