GMAT Prep fraction problem

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tdot_gmat-er: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Sun Mar 30, 2008 5:39 pm

by tdot_gmat-er » Tue Apr 01, 2008 4:21 pm

Hey guys, so here's the first question I saw on the GMAT Prep test. Needless to say, I am stumped. Any ideas?

If (1/5)^m * (1/4)^18 = 1 / (2 * (10)^35), what's the value of m?

Also, what's the best way to approach number theory problems? I've been through OG, Kaplan, and PR but they really don't provide much strategy for these. Do you guys have any strategies or resources?

Thx!

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Source: Beat The GMAT — Problem Solving | Tue Apr 01, 2008 4:21 pm

Kaunteya1: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Thu Mar 06, 2008 11:04 am; Thanked: 1 times

by Kaunteya1 » Tue Apr 01, 2008 5:04 pm

If (1/5)^m * (1/4)^18 = 1 / (2 * (10)^35), what's the value of m?

(1/5)^m = 1/5^m

1 to the power of anything equals 1

(1/4)^18 = 1/4^18 (4=2^2) so 1/4^18 = 1/2^36

now we have the following:

1/5^m x 1/2^36 = 1/(2x10^35)

Because every denominator is under 1 we can set the denominators to equal each other:

5^m x 2^36 = 2 x 10^35

10^35 = 2^35 x 5^35 so now we get the following

5^m x 2^36 = 2 x 2^35 x 5^35 note the 2 x 2^35 = 2^1 x 2^35 = 2^36

5^m x 2^36 = 2^36 x 5^35
we can cancel out the 2^36 on both sides.
5^m = 5^35

m=35

Hope that helps.

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