what is the value of N?

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deepoe: Master | Next Rank: 500 Posts; Posts: 151; Joined: Wed Feb 11, 2009 2:45 am; Thanked: 3 times

by deepoe » Thu Feb 26, 2009 3:53 am

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

OA = 21

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Source: Beat The GMAT — Problem Solving | Thu Feb 26, 2009 3:53 am

DanaJ: Site Admin; Posts: 2567; Joined: Thu Jan 01, 2009 10:05 amFollowed by: 550 members; Thanked: 712 times; GMAT Score:770

by DanaJ » Thu Feb 26, 2009 4:04 am

I have a feeling that this question has been answered many times before, but here goes:
10 = 2*5 and this is your starting point.
You have that 4^11 over there that might confuse you. You get that 4^11 = (2^2)^11 = 2^(2*11) = 2^22. Now, you must multiply this with 5^21 and you get that 5^21 * 2^22 = 2 * (5^21 * 2^21) = 2 * (5*2)^21 = 2*10^21.
This will make n = 21.

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kaf: Senior | Next Rank: 100 Posts; Posts: 53; Joined: Mon Feb 09, 2009 12:18 am; Thanked: 1 times

by kaf » Wed Mar 11, 2009 4:34 am

DanaJ

Can you please explain how

5^21 * 2^22 = 2 * (5^21 * 2^21)

thanks

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DanaJ: Site Admin; Posts: 2567; Joined: Thu Jan 01, 2009 10:05 amFollowed by: 550 members; Thanked: 712 times; GMAT Score:770

by DanaJ » Wed Mar 11, 2009 5:08 am

kaf: Sure.
Just look at 2^22: it's 2^(21+1) or 2^21 * 2^1 = 2^21 * 2.
This means that 5^21 * 2^22 = 5^21 * 2^21 * 2 and then you just put the two in a parenthesis, giving you 2*(5^21 + 2^21).

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