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Difficult Quant - Exponent Question

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GMATpaduan: Newbie | Next Rank: 10 Posts; Posts: 9; Joined: Sun May 27, 2007 11:06 am

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!!

GOOD LUCK ALL!

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Source: Beat The GMAT — Problem Solving | Sun May 27, 2007 11:13 am

jayhawk2001: Community Manager; Posts: 789; Joined: Sun Jan 28, 2007 3:51 pmFollowed by: 1 member; Location: Silicon valley, California; Thanked: 30 times

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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GMATpaduan: Newbie | Next Rank: 10 Posts; Posts: 9; Joined: Sun May 27, 2007 11:06 am

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

GOOD LUCK ALL!

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Sadowski: Senior | Next Rank: 100 Posts; Posts: 91; Joined: Fri Apr 27, 2007 7:08 am; Location: Durham, NC; Thanked: 1 times

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.

Thanks!

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drhomler: Master | Next Rank: 500 Posts; Posts: 141; Joined: Thu May 03, 2007 1:15 pm

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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