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GMAT Prep Sample Test Question 1

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GMAT Prep Sample Test Question 1

by mdown » Wed May 26, 2010 6:43 pm
I'm reviewing my score on the free GMAT practice test #1 and can't figure out the first question:

[(1/5)^m] * [(1/4)^18] = 1/[2(10)^35] solve for m

Answer is 35 but unfortunately the test doesn't explain this at all, anybody know the trick to this one?
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by Rahul@gurome » Wed May 26, 2010 6:52 pm
[(1/5)^m] * [(1/2)^36] = 1/[2(2)^35 * (5)^35]
[1/(5^m)] * [1/(2^36)] = 1/[(2)^36 * (5)^35]
Comparing the exponent of 5 on the right hand side as well left hand side, we get
m = 35
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by indiantiger » Wed May 26, 2010 7:06 pm
[(1/5)^m] * [(1/4)^18] = 1/[2(10)^35]

Lets convert this to

=>2*(10)^35 = 5^m*4^18 (by cross multiply)
=> 2* 2^35 (5*^35) = 5^m * 2^36 ( 10 can be expressed as = 5*2 and 4 = 2*2)
=> 2^36 * 5^35 = 5^m * 2^36

to make LHS = RHS we need to have the same powers on the both the sides as the bases are the same

which leads to m = 35.
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by mdown » Thu May 27, 2010 5:16 am
Thanks guys, I figured out how to break down the right side but didn't think to change the left side to (1/2)^36. Just for my own info, what level of difficulty do you think this problem is compared to other GMAT problems? Would this be considered a medium difficulty?
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by Patrick_GMATFix » Thu May 27, 2010 5:56 am
This is a low-intermediate level; GMATPrep question 1132. You can find and practice similar questions with the Solutions Engine if you find that you struggle with exponents.

Best of luck,
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