Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 16 Mar 2010
Posts: 171

If 3^(6x) = 8,100, what is the value of [3^(x1)]^3? [#permalink]
Show Tags
08 Aug 2010, 02:51
2
This post received KUDOS
11
This post was BOOKMARKED
Question Stats:
70% (01:49) correct 30% (03:18) wrong based on 323 sessions
HideShow timer Statistics
If \(3^{6x}=8,100\), what is the value of \((3^{x1})^3\)? A. 90 B. 30 C. 10 D. 10/3 E. 10/9
Official Answer and Stats are available only to registered users. Register/ Login.
Last edited by Bunuel on 12 Jan 2018, 10:42, edited 2 times in total.
Renamed the topic and edited the question.



Math Expert
Joined: 02 Sep 2009
Posts: 43810

If 3^(6x) = 8,100, what is the value of [3^(x1)]^3? [#permalink]
Show Tags
08 Aug 2010, 03:10
7
This post received KUDOS
Expert's post
8
This post was BOOKMARKED



Director
Status: Apply  Last Chance
Affiliations: IIT, Purdue, PhD, TauBetaPi
Joined: 17 Jul 2010
Posts: 674
Schools: Wharton, Sloan, Chicago, Haas
WE 1: 8 years in Oil&Gas

Re: If 3^(6x) = 8,100, what is the value of [3^(x1)]^3? [#permalink]
Show Tags
08 Aug 2010, 07:18
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?
_________________
Consider kudos, they are good for health



Math Expert
Joined: 02 Sep 2009
Posts: 43810

Re: If 3^(6x) = 8,100, what is the value of [3^(x1)]^3? [#permalink]
Show Tags
08 Aug 2010, 07:41
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 ( everythingaboutfactorialsonthegmat85592.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).
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Director
Status: Apply  Last Chance
Affiliations: IIT, Purdue, PhD, TauBetaPi
Joined: 17 Jul 2010
Posts: 674
Schools: Wharton, Sloan, Chicago, Haas
WE 1: 8 years in Oil&Gas

Re: If 3^(6x) = 8,100, what is the value of [3^(x1)]^3? [#permalink]
Show Tags
08 Aug 2010, 07:56
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?
_________________
Consider kudos, they are good for health



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7938
Location: Pune, India

Re: If 3^(6x) = 8,100, what is the value of [3^(x1)]^3? [#permalink]
Show Tags
05 Dec 2010, 18:56
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 My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Intern
Joined: 30 Jun 2012
Posts: 9

If 3^(6x) = 8,100, what is the value of [3^(x1)]^3? [#permalink]
Show Tags
01 Jul 2012, 15:44
5
This post was BOOKMARKED
If \(3^{6x}=8,100\), what is the value of \((3^{x1})^3\)?
A. 90 B. 30 C. 10 D. 10/3 E. 10/9



Math Expert
Joined: 02 Sep 2009
Posts: 43810

If 3^(6x) = 8,100, what is the value of [3^(x1)]^3? [#permalink]
Show Tags
01 Jul 2012, 15:50



Manager
Joined: 14 Nov 2011
Posts: 139
Location: United States
Concentration: General Management, Entrepreneurship
GPA: 3.61
WE: Consulting (Manufacturing)

Re: If 3^(6x) = 8,100, what is the value of [3^(x1)]^3? [#permalink]
Show Tags
01 Jun 2013, 19:09
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^(x1)]^3? Or it can be written using the formating as: If \(3^{6x}=8,100\), what is the value of \((3^{x1})^3\)? (It's not hard at all). \(3^{6x}=(3^{3x})^2=90^2=8,100\) > \(3^{3x}=90\). \((3^{x1})^3= 3^{3x3}=\frac{3^{3x}}{3^3}=\frac{90}{27}=\frac{10}{3}\). 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*(x1)) = 3^(3*(1/3)) = 3^(1) = 1/3. Still based on denominator I chose D.



Math Expert
Joined: 02 Sep 2009
Posts: 43810

If 3^(6x) = 8,100, what is the value of [3^(x1)]^3? [#permalink]
Show Tags
02 Jun 2013, 03:13
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^(x1)]^3? Or it can be written using the formating as: If \(3^{6x}=8,100\), what is the value of \((3^{x1})^3\)? (It's not hard at all). \(3^{6x}=(3^{3x})^2=90^2=8,100\) > \(3^{3x}=90\). \((3^{x1})^3= 3^{3x3}=\frac{3^{3x}}{3^3}=\frac{90}{27}=\frac{10}{3}\). 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*(x1)) = 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.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1839
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: If 3^(6x) = 8,100, what is the value of [3^(x1)]^3? [#permalink]
Show Tags
26 Aug 2014, 00:25
\(3^{6x} = 8100\) Square root both sides \(3^{3x} = 90\) Divide both sides by 27 \(\frac{3^{3x}}{27} = \frac{90}{27}\) \(3^{3x3} = \frac{10}{3}\) \([3^{(x1)}]^3 = \frac{10}{3}\) Answer = D
_________________
Kindly press "+1 Kudos" to appreciate



NonHuman User
Joined: 09 Sep 2013
Posts: 13827

Re: If 3^(6x) = 8,100, what is the value of [3^(x1)]^3? [#permalink]
Show Tags
29 Nov 2017, 01:29
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 Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: If 3^(6x) = 8,100, what is the value of [3^(x1)]^3?
[#permalink]
29 Nov 2017, 01:29






