GMATPrep Problem

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jaydeer44: Senior | Next Rank: 100 Posts; Posts: 44; Joined: Mon Feb 25, 2008 10:36 pm

by jaydeer44 » Tue Mar 25, 2008 9:06 pm

Can someone help with the following problem? The answer is B.

Thanks!

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Source: Beat The GMAT — Problem Solving | Tue Mar 25, 2008 9:06 pm

ikant: Senior | Next Rank: 100 Posts; Posts: 62; Joined: Wed Mar 05, 2008 8:57 am; Location: mumbai, India; Thanked: 5 times

by ikant » Tue Mar 25, 2008 9:14 pm

Hello,

Just divide the LHS by 2 and the equation becomes :

5^21 * 2^21 = 10 ^ n

=> 10^21 = 10^n

n = 21.

"To do is to be"

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jaydeer44: Senior | Next Rank: 100 Posts; Posts: 44; Joined: Mon Feb 25, 2008 10:36 pm

by jaydeer44 » Tue Mar 25, 2008 9:18 pm

thanks!

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Jeffers: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Thu Jun 14, 2007 8:05 am

by Jeffers » Mon Mar 31, 2008 7:50 am

Can someone explain this to me? I thought when you multiply powers you add them together?

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Jeffers: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Thu Jun 14, 2007 8:05 am

by Jeffers » Mon Mar 31, 2008 7:50 am

Can someone explain this to me? I thought when you multiply powers you add them together?

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Mon Mar 31, 2008 9:31 am

Jeffers wrote:Can someone explain this to me? I thought when you multiply powers you add them together?

When we multiply two powers with the same base, we add the exponents.

However, when we multiply two bases with the same power, we multiply the bases and the power stays the same.

So:

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

To help understand this, we can visualize 2^21 as a string of 21 2s, multiplied together. Similarly, we can visualize 5^21 as a string of 21 5s, multiplied together.

So, 2^21 * 5^21 is really just 21 2s and then 21 5s, all multiplied together.

Instead of writing all the 2s in a row and all the 5s in a row, we could have alternated them (since for multiplication, the order of terms is irrelevant).

So, we can visualize a string of 2*5*2*5*2*5... that contains 21 2s and 21 5s in total.

Now, let's put brackets around each pair of terms to get:

(2*5)*(2*5)*(2*5)... and we'll have 21 bracketed pairs.

Since 2*5 = 10 we can rewrite this as:

(10)*(10)*(10).... with 21 10s in a row, which of course we can rewrite as:

10^21.

Hope that helps!

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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Jeffers: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Thu Jun 14, 2007 8:05 am

by Jeffers » Mon Mar 31, 2008 11:39 am

It does thank you!

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