Exponent Question..

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rahul26: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Sun Jul 13, 2008 9:16 am

by rahul26 » Sun Apr 05, 2009 10:00 am

If 3^6x = 8,100, what is the value of (3x – 1)^3 ?

A. 90
B. 30
C. 10
D. 10 / 3
E. 10 / 9

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Source: Beat The GMAT — Problem Solving | Sun Apr 05, 2009 10:00 am

Feep: Senior | Next Rank: 100 Posts; Posts: 69; Joined: Wed Mar 04, 2009 4:15 pm; Thanked: 17 times; GMAT Score:780

by Feep » Sun Apr 05, 2009 11:49 pm

The answer should be B. 30.

There might be some wonderfully elegant algebraic solution to this problem, but I highly doubt it. This question tests your ability to do quick math and ballpark your answers.

Some quick multiplying-by-3 shows that we need a little more than 8 in the exponent to reach 8,100. (1, 3, 9, 27, 81, 243, 729, 2200ish, 6600ish). So, let's say 8.2ish. So, x equals 8.2/6.

Substituting into the second equation, we get (8.2/2 - 1)^3 = 3.1^3. You can multiply out, or you can see it'll be a bit more than 3^3, which is 27. So, 30.

Sometimes, you just gotta put your head down and power through. = P

Edit: The actual question is written differently, (3^(x-1))^3. The answer is D, in this case, and has a much more elegant solution. Please see the link below.

Last edited by Feep on Mon Apr 06, 2009 9:53 am, edited 1 time in total.

I tutor GMAT/GRE level mathematics privately in the Los Angeles region, as well as via Skype for a discounted rate. Send me a message if you're interested.

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Musiq: Senior | Next Rank: 100 Posts; Posts: 93; Joined: Thu Apr 10, 2008 1:42 pm; Location: Chicago; Thanked: 20 times

by Musiq » Mon Apr 06, 2009 9:04 am

To the OP (Rahul?),

This is not a good representation of a GMAT question. As Feep admirably shows you how to get to the answer using approximation, similarly the testmaker MUST let us know that they need an approximate value.

Did you miss that out of your question? Or is the question correct as is?

Also, is the left hand side of the equation (3^6 ) ( X) or (3) ^ (6X)?

Please let us know since this considerably chnages the approach to the problem.

Thanks in advance!

For love, not money.

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moutar: Senior | Next Rank: 100 Posts; Posts: 92; Joined: Wed Mar 25, 2009 12:13 pm; Thanked: 10 times

by moutar » Mon Apr 06, 2009 9:36 am

I think this is the actual question.

https://www.beatthegmat.com/ps-t33962.html

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Musiq: Senior | Next Rank: 100 Posts; Posts: 93; Joined: Thu Apr 10, 2008 1:42 pm; Location: Chicago; Thanked: 20 times

by Musiq » Mon Apr 06, 2009 9:59 am

moutar wrote:I think this is the actual question.

https://www.beatthegmat.com/ps-t33962.html

Elegant solution!

Thanks for responding.

To Rahul, please follow link that Moutar has posted...and go straight to his solution.

For love, not money.

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moutar: Senior | Next Rank: 100 Posts; Posts: 92; Joined: Wed Mar 25, 2009 12:13 pm; Thanked: 10 times

by moutar » Mon Apr 06, 2009 12:19 pm

Elegance is the way forward.

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logitech: Legendary Member; Posts: 2134; Joined: Mon Oct 20, 2008 11:26 pmFollowed by: 25 members; Thanked: 237 times; GMAT Score:730

Re: Exponent Question..

by logitech » Mon Apr 06, 2009 3:09 pm

3^6x = 8,100

9,16,25,35,..81,100 should always ring the perfect square ring.

3^3X=90

The question asks: 3^x/3^3 = 90/27=10/3

LGTCH
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"DON'T LET ANYONE STEAL YOUR DREAM!"

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