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Difficult Quant - Exponent Question

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Difficult Quant - Exponent Question

by GMATpaduan » Sun May 27, 2007 11:13 am
Any idea on how to get the solution to the following problem?

(1/5)^m * (1/4)^18 = 1/2(10)^35 - what is m?


**The answer is 35 if that helps, but i have no idea how to arrive at the solution, because this was a problem from mba.com practice test, that provided no answer explanation)

Thank you!!
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Re: Difficult Quant - Exponent Question

by jayhawk2001 » Sun May 27, 2007 12:27 pm
GMATpaduan wrote:Any idea on how to get the solution to the following problem?

(1/5)^m * (1/4)^18 = 1/2(10)^35 - what is m?
(1/5)^m * (1/4)^18
= (1/5)^m * (1/2)^36
= (1/5)^m*(1/2)^m*(1/2)^36-m
= (1/10)^m*(1/2)^36-m

We can either use 36-m = 1, which gives us m =35 (co-efficients of 2)
or use co-efficients of 1/10 which gives us 35 directly
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Thank you

by GMATpaduan » Sun May 27, 2007 3:43 pm
Thank you. That is helpful.

Your way led me to a very similar way to work it out, without using the algebra: Is this method also valid?

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

(1/5)^m * (1/2)^36 = (1/2^35) * 1/10^35)

(1/5)^m * (1/2)^1 * (1/2)^35 = (1/2^35) * 1/10^35)

(1/10)^m * (1/2)^35 = (1/2^35) * 1/10^35)

m = 35
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WTF?

by Sadowski » Thu May 31, 2007 7:13 am
(1/5)^m * (1/4)^18 = 1/2(10)^35

Is this truly the correct formula? Or is the right side of the equation supposed to be 1/2*(1/10)^35?

In your math steps, as shown below, you go from 1/2*(10)^35 to (1/2)^35*(1/10)^35, but those are simply not equivalent.

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

(1/5)^m * (1/2)^36 = (1/2^35) * 1/10^35)

If the problem statement is exactly as you've written it, then you should come to this:

(1/5)^m*(1/2)^36=(1/2)*10^35
(1/5)^m*(1/2)*(1/2)^35=(1/2)*5^35*2^35
(1/5)^m*(1/2)^35=(5)^35*(2)^35

Hence, the equation doesn't make sense unless the right side is (1/10)^35.

Can someone verify? This seems obvious to me, but maybe I'm missing something.

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by drhomler » Thu May 31, 2007 10:24 am
I was wondering that very same thing. These questions in general usually pose a challenge for me so maybe Im missing something too.
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