GMAT Prep ?? (Roots)

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dferm: Master | Next Rank: 500 Posts; Posts: 446; Joined: Thu Jul 26, 2007 1:07 pm; Thanked: 6 times

GMAT Prep ?? (Roots)

by dferm » Thu Aug 21, 2008 10:54 am

Please Help...

I know it is simple but these questions seem to be taking me a lot of time...

(1/5)^m (1/4)^18 = 1/2(10)^35, then m =

A. 17
B. 18
C. 34
D. 35
E. 36

Please explain a concise way of applying methods to these kinds of problems.

Thanks.

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Source: Beat The GMAT — Problem Solving | Thu Aug 21, 2008 10:54 am

pepeprepa: Legendary Member; Posts: 661; Joined: Tue Jul 08, 2008 12:58 pm; Location: France; Thanked: 48 times

by pepeprepa » Thu Aug 21, 2008 11:56 am

You are right you must not spend time on this type of question.

(1/5)^m (1/4)^18 = 1/(2*(10)^35)
(I hope this is how the question starts, I am not sure given how the parenthesis are placed)

Let's try to put the right part of the equation in the same organization as the left part, I mean with 1/5 and 1/4

1/(2*(10)^35)= 1/2 * 1/(10^35)
you know 10=5*2 so we can write
1/(2*(10)^35)= 1/2 * 1/(5^35 * 2^35)
1/(2*(10)^35)= 1/(2^36) * 1/5^35
2^36=2^(18*2)=(2^2)^18=4^18 so we can write:
1/(2*(10)^35)= 1/( 4^18 ) * 1/5^35

Now let's compare it to the left part:

(1/5)^m * (1/4)^18= 1/( 4^18 ) * 1/5^35

You have your answer.
For this kind of question you must now common rules on powers, and you have to try to compare both sides so to put them with the same factors.

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leugene: Junior | Next Rank: 30 Posts; Posts: 29; Joined: Thu Jul 24, 2008 4:38 pm; Thanked: 1 times

by leugene » Thu Aug 21, 2008 1:53 pm

What a brilliant explanation. Thanks.

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4meonly: Legendary Member; Posts: 891; Joined: Sat Aug 16, 2008 4:21 am; Thanked: 27 times; Followed by:1 members; GMAT Score:660(