Exponential Problem

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rintoo22: Senior | Next Rank: 100 Posts; Posts: 73; Joined: Sun May 06, 2012 2:19 am; Location: Cape Town; Thanked: 6 times

by rintoo22 » Wed Mar 20, 2013 2:37 am

Q. If ((36 to the power x) = 8,100), what is the value of ((3x - 1)to the power of 3) ?

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

Please post the solution

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Source: Beat The GMAT — Problem Solving | Wed Mar 20, 2013 2:37 am

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Anju@Gurome: GMAT Instructor; Posts: 511; Joined: Wed Aug 11, 2010 9:47 amFollowed by: 86 members; Location: Delhi, India; Thanked: 344 times

by Anju@Gurome » Wed Mar 20, 2013 2:48 am

rintoo22 wrote:Q. If ((36 to the power x) = 8,100), what is the value of ((3x - 1)to the power of 3)?

Are you sure that you have posted the question properly?
The solution for the question you have posted is beyond the scope of GMAT.

As far as I know, the actual question is as follows...

If 3^(6x) = 8100, what is the value of (3^(x - 1))^3?

3^(6x) = (3^(3x))^2 and 8100 = 90^2
So, 3^(3x) = 90 = 9*10 = (3^2)*10 = (3^3)*(10/3)
--> 3^(3x - 3) = 10/3
--> (3^(x - 1))^3 = 10/3

The correct answer is D.

Anju Agarwal
Quant Expert, Gurome

Backup Methods : General guide on plugging, estimation etc.
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rintoo22: Senior | Next Rank: 100 Posts; Posts: 73; Joined: Sun May 06, 2012 2:19 am; Location: Cape Town; Thanked: 6 times

by rintoo22 » Wed Mar 20, 2013 3:12 am

Thanks Anju. You hit the nail on head. It was a typo. Thank for the Response. Much Appreciated

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Mar 20, 2013 3:35 am

The correct problem appears above.

3^6x = 8100
(3^3x)Â² = 8100
3^3x = 90.

(3^(x-1))^3
= 3^(3x-3)
= (3^3x)/3Â³
= 90/27 (substituting 3^3x = 90)
= 10/3.

The correct answer is D.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Mar 20, 2013 4:27 am

If 3^(6x) = 8100, what is the value of (3^(x - 1))^3?
A. 90
B. 30
C. 10
D. 10/3
E. 10/9

Here's another approach

We're trying to find the value of 3^(x - 1))^3
Let's first simplify it by applying the Power of a Power law to get: 3^(3x - 3)
Then recognize that 3^(3x - 3) = (3^3x)/(3^3) [applying the Quotient Law in reverse]

We're told that 3^(6x) = 8100
Raise both sides by the power of 1/2 to get: 3^(6x)^(1/2) = 8100^(1/2)
Simplify to get: 3^(3x) = 90

Aside: raising a number to the power of 1/2 is the same as finding the square root of that number.

So, 3^(x - 1))^3 = 3^(3x - 3)
= (3^3x)/(3^3)
= 90/27
= [spoiler]3/10 = D[/spoiler]

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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