GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 07 Dec 2019, 00:07

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Manager
Manager
avatar
Joined: 17 Mar 2010
Posts: 128
If 3^(6x) = 8,100, what is the value of [3^(x-1)]^3?  [#permalink]

Show Tags

New post Updated on: 12 Jan 2018, 11:42
2
21
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

67% (02:18) correct 33% (02:43) wrong based on 447 sessions

HideShow timer Statistics

If \(3^{6x}=8,100\), what is the value of \((3^{x-1})^3\)?

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

Originally posted by amitjash on 08 Aug 2010, 03:51.
Last edited by Bunuel on 12 Jan 2018, 11:42, edited 2 times in total.
Renamed the topic and edited the question.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59587
If 3^(6x) = 8,100, what is the value of [3^(x-1)]^3?  [#permalink]

Show Tags

New post 08 Aug 2010, 04:10
9
7
Most Helpful Community Reply
Intern
Intern
avatar
Joined: 30 Jun 2012
Posts: 7
If 3^(6x) = 8,100, what is the value of [3^(x-1)]^3?  [#permalink]

Show Tags

New post 01 Jul 2012, 16:44
5
If \(3^{6x}=8,100\), what is the value of \((3^{x-1})^3\)?

A. 90
B. 30
C. 10
D. 10/3
E. 10/9
General Discussion
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59587
If 3^(6x) = 8,100, what is the value of [3^(x-1)]^3?  [#permalink]

Show Tags

New post 01 Jul 2012, 16:50
2
1

8. Exponents and Roots of Numbers



Check below for more:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread

Hope it helps.
_________________
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59587
Re: If 3^(6x) = 8,100, what is the value of [3^(x-1)]^3?  [#permalink]

Show Tags

New post 08 Aug 2010, 08:41
1
mainhoon wrote:
Excellent. No a side note, Bunuel, I started approaching this using the "power of prime in a number" - I had seen the link somewhere which had the formula N/p + N/p^2+N/p^3... until N>p^x and thought of equating that to 6x and solve thus. I know yours is much simpler. However would that approach have worked? Is that formula exactly saying what is the highest power of the prime in the number?


No need to complicate simple questions.

The formula is correct (everything-about-factorials-on-the-gmat-85592.html) but it has nothing to do with this problem, (highest power of 3 in 81,000 won't be equal to 6x, because 3^(6x)=81,000=2^m*3^n*5^k, so as 81,000 has other factors than 3 in it then 6x won't be an integer at all).
_________________
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 9850
Location: Pune, India
Re: If 3^(6x) = 8,100, what is the value of [3^(x-1)]^3?  [#permalink]

Show Tags

New post 05 Dec 2010, 19:56
1
1
ajit257 wrote:
Q11:
If 3^6x = 8,100, what is the value of 3^((x – 1)3) ?
3
A. 90
B. 30
C. 10
D. 10/3
E. 10/9


In a question such as this where you have \(3^{6x} = 8100\) where 8100 is not a perfect sixth power but the options do not have irrational numbers, you should immediately go and analyze what is asked. You will not need to solve for x. You will end up using either \(3^{6x} = 8100\) or \(3^{3x} = 90\)
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Director
Director
avatar
Status: Apply - Last Chance
Affiliations: IIT, Purdue, PhD, TauBetaPi
Joined: 18 Jul 2010
Posts: 574
Schools: Wharton, Sloan, Chicago, Haas
WE 1: 8 years in Oil&Gas
Re: If 3^(6x) = 8,100, what is the value of [3^(x-1)]^3?  [#permalink]

Show Tags

New post 08 Aug 2010, 08:18
Excellent. No a side note, Bunuel, I started approaching this using the "power of prime in a number" - I had seen the link somewhere which had the formula N/p + N/p^2+N/p^3... until N>p^x and thought of equating that to 6x and solve thus. I know yours is much simpler. However would that approach have worked? Is that formula exactly saying what is the highest power of the prime in the number?
Director
Director
avatar
Status: Apply - Last Chance
Affiliations: IIT, Purdue, PhD, TauBetaPi
Joined: 18 Jul 2010
Posts: 574
Schools: Wharton, Sloan, Chicago, Haas
WE 1: 8 years in Oil&Gas
Re: If 3^(6x) = 8,100, what is the value of [3^(x-1)]^3?  [#permalink]

Show Tags

New post 08 Aug 2010, 08:56
When I think some more, I don't think we can use that formula. Isn't that formula for factorials - (a) N! not N and (b) as you rightly pointed out it would result in a fraction for 6x, not integer.

For 3^(3x) = 90, if I wanted to solve it, it is clear than x is fractional. So is the answer basically taking logarithms? Any other way?
Manager
Manager
avatar
Joined: 14 Nov 2011
Posts: 114
Location: United States
Concentration: General Management, Entrepreneurship
GPA: 3.61
WE: Consulting (Manufacturing)
GMAT ToolKit User
Re: If 3^(6x) = 8,100, what is the value of [3^(x-1)]^3?  [#permalink]

Show Tags

New post 01 Jun 2013, 20:09
Bunuel wrote:
amitjash wrote:
If 3^6x = 8,100, what is the value of (3^x – 1)^3 ?

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


Please when posting such questions make sure that it's not ambiguous.

Correct question is: If 3^(6x) = 8,100, what is the value of [3^(x-1)]^3?
Or it can be written using the formating as: If \(3^{6x}=8,100\), what is the value of \((3^{x-1})^3\)? (It's not hard at all).

\(3^{6x}=(3^{3x})^2=90^2=8,100\) --> \(3^{3x}=90\).

\((3^{x-1})^3= 3^{3x-3}=\frac{3^{3x}}{3^3}=\frac{90}{27}=\frac{10}{3}\).

Answer: D.

Check Number Theory chapter of Math Book for exponents (link in my signature).



Hi Bunnel,

Please point out the mistake in this approach. Why am I not getting correct answer by this method.

3^6x=8100=3^4*2^2*5^2
=> 6x=4, as all nos are primes
=> x= 2/3

Now, 3^(3*(x-1)) = 3^(3*(-1/3)) = 3^(-1) = 1/3.

Still based on denominator I chose D.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59587
If 3^(6x) = 8,100, what is the value of [3^(x-1)]^3?  [#permalink]

Show Tags

New post 02 Jun 2013, 04:13
cumulonimbus wrote:
Bunuel wrote:
amitjash wrote:
If 3^6x = 8,100, what is the value of (3^x – 1)^3 ?

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


Please when posting such questions make sure that it's not ambiguous.

Correct question is: If 3^(6x) = 8,100, what is the value of [3^(x-1)]^3?
Or it can be written using the formating as: If \(3^{6x}=8,100\), what is the value of \((3^{x-1})^3\)? (It's not hard at all).

\(3^{6x}=(3^{3x})^2=90^2=8,100\) --> \(3^{3x}=90\).

\((3^{x-1})^3= 3^{3x-3}=\frac{3^{3x}}{3^3}=\frac{90}{27}=\frac{10}{3}\).

Answer: D.

Check Number Theory chapter of Math Book for exponents (link in my signature).



Hi Bunnel,

Please point out the mistake in this approach. Why am I not getting correct answer by this method.

3^6x=8100=3^4*2^2*5^2
=> 6x=4, as all nos are primes
=> x= 2/3

Now, 3^(3*(x-1)) = 3^(3*(-1/3)) = 3^(-1) = 1/3.

Still based on denominator I chose D.


From \(3^{6x}=8100=3^4*2^2*5^2\) we cannot say that 6x = 4 --> 3^4 = 8100 = 3^4*2^2*5^2 --> 1=2^2*5^2 which is not correct.
_________________
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1727
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If 3^(6x) = 8,100, what is the value of [3^(x-1)]^3?  [#permalink]

Show Tags

New post 26 Aug 2014, 01:25
\(3^{6x} = 8100\)

Square root both sides

\(3^{3x} = 90\)

Divide both sides by 27

\(\frac{3^{3x}}{27} = \frac{90}{27}\)

\(3^{3x-3} = \frac{10}{3}\)

\([3^{(x-1)}]^3 = \frac{10}{3}\)

Answer = D
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13724
Re: If 3^(6x) = 8,100, what is the value of [3^(x-1)]^3?  [#permalink]

Show Tags

New post 12 Dec 2018, 07:42
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Bot
Re: If 3^(6x) = 8,100, what is the value of [3^(x-1)]^3?   [#permalink] 12 Dec 2018, 07:42
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne