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GMAT Prep fraction problem

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GMAT Prep fraction problem

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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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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