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

 It is currently 13 Oct 2019, 21:28

### 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

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

# If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58335
If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?  [#permalink]

### Show Tags

27 Nov 2017, 23:18
3
4
00:00

Difficulty:

25% (medium)

Question Stats:

79% (02:08) correct 21% (02:20) wrong based on 147 sessions

### HideShow timer Statistics

If $$3^{(6x)} = 810,000$$, what is the value of $$(3^{(x−1)})^3$$?

A. 10/3

B. 100/3

C. 200/3

D. 150

E. 300

_________________
Senior Manager
Joined: 09 Aug 2017
Posts: 479
Re: If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?  [#permalink]

### Show Tags

28 Nov 2017, 00:51
3^4*10^4= 3^6x
Take root of both side
900=3^3x...equ1

Now we have to solve for (3^(x-1))^3= (3^3x)/3^3 ....equ2
From equation 1 and 2, answer is 100/3.
"B"
Current Student
Joined: 15 Oct 2017
Posts: 17
Location: India
Concentration: Marketing, Finance
GMAT 1: 710 Q49 V38
GPA: 3.09
WE: Engineering (Aerospace and Defense)
Re: If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?  [#permalink]

### Show Tags

28 Nov 2017, 02:41
3^6x = 810,000;
3^3x = (810,000)^1/2 = 900

3^(3x-3)= (900/3^3) = 100/3
Intern
Joined: 26 Sep 2017
Posts: 4
Re: If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?  [#permalink]

### Show Tags

28 Nov 2017, 04:44
Given $$3^(6x) = 810,000$$
which is simplified as

$$(3^(3x))^2=9^2 * 10^4$$

$$3^(3x) = 9 * 10^2$$=$$3^2*10^2$$

hence, $$(3^(x-1))^3=((3^x)/3)^3=3^(3x)/3^3$$
=$$(3^2 * 10^2)/(3^3)$$
=100/3

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9696
Location: Pune, India
Re: If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?  [#permalink]

### Show Tags

28 Nov 2017, 06:04
1
3
Bunuel wrote:
If $$3^{(6x)} = 810,000$$, what is the value of $$(3^{(x−1)})^3$$?

A. 10/3

B. 100/3

C. 200/3

D. 150

E. 300

$$(3^{x−1})^3 = 3^{3x}/27$$

We know
$$3^{6x} = 810,000$$
So $$3^{3x} = 900$$ (taking square root on both sides)

We get $$3^{3x}/27 = 900/27 = 100/3$$

_________________
Karishma
Veritas Prep GMAT Instructor

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8040
Location: United States (CA)
Re: If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?  [#permalink]

### Show Tags

29 Nov 2017, 18:13
1
Bunuel wrote:
If $$3^{(6x)} = 810,000$$, what is the value of $$(3^{(x−1)})^3$$?

A. 10/3

B. 100/3

C. 200/3

D. 150

E. 300

Let’s first re-express (3^(x - 1))^3, noting that when we have an exponent raised to an exponent, we multiply the two exponents. Thus, (3^(x - 1))^3 = 3^(3x - 3) = (3^3x)(3^-3) = (3^3x)/(3^3), so really we need to determine the value of 3^3x/27.

Simplifying the given equation, we have:

3^6x = 810,000

Taking the square root of both sides, we have:

3^3x = 900

Thus, (3^3x)/(27) = 900/27 = 100/3.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Intern
Joined: 24 Oct 2016
Posts: 17
Re: If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?  [#permalink]

### Show Tags

12 Jan 2018, 09:04
Hi bunnel,

I understood how this problem is solved, but I’m confused with the question given . How can anything to the power of 3 will result in multiples of 10?
I mean how can 3^6x = 810000

Bunuel wrote:
If $$3^{(6x)} = 810,000$$, what is the value of $$(3^{(x−1)})^3$$?

A. 10/3

B. 100/3

C. 200/3

D. 150

E. 300
Math Expert
Joined: 02 Sep 2009
Posts: 58335
Re: If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?  [#permalink]

### Show Tags

12 Jan 2018, 09:18
1
gvrk_77 wrote:
Hi bunnel,

I understood how this problem is solved, but I’m confused with the question given . How can anything to the power of 3 will result in multiples of 10?
I mean how can 3^6x = 810000

Bunuel wrote:
If $$3^{(6x)} = 810,000$$, what is the value of $$(3^{(x−1)})^3$$?

A. 10/3

B. 100/3

C. 200/3

D. 150

E. 300

You are forgetting that x might not be an integer. So, $$3^{(6x)} = 810,000$$ for some irrational x, which is approximately 2.0639...
_________________
Intern
Joined: 24 Oct 2016
Posts: 17
Re: If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?  [#permalink]

### Show Tags

12 Jan 2018, 11:25
Thanks Bunnel.

Then I think in question they should have mention as approximate value, because it won’t be terminating
Why I was so skeptical is that I have written 810000 = 3^4 * 10^4,, and from here I was trying to equate with 3^6x and I’m going nowhere

Bunuel wrote:
gvrk_77 wrote:
Hi bunnel,

I understood how this problem is solved, but I’m confused with the question given . How can anything to the power of 3 will result in multiples of 10?
I mean how can 3^6x = 810000

Bunuel wrote:
If $$3^{(6x)} = 810,000$$, what is the value of $$(3^{(x−1)})^3$$?

A. 10/3

B. 100/3

C. 200/3

D. 150

E. 300

You are forgetting that x might not be an integer. So, $$3^{(6x)} = 810,000$$ for some irrational x, which is approximately 2.0639...
Math Expert
Joined: 02 Sep 2009
Posts: 58335
Re: If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?  [#permalink]

### Show Tags

12 Jan 2018, 11:31
1
gvrk_77 wrote:
Thanks Bunnel.

Then I think in question they should have mention as approximate value, because it won’t be terminating
Why I was so skeptical is that I have written 810000 = 3^4 * 10^4,, and from here I was trying to equate with 3^6x and I’m going nowhere

No, you are wrong again. For the value of x, for which $$3^{(6x)} = 810,000$$, is true, $$(3^{(x−1)})^3$$ turns out to be EXACTLY 100/3. You should study the solutions above to understand that we can get the value of $$(3^{(x−1)})^3$$, without getting the value of x.
_________________
Intern
Joined: 24 Oct 2016
Posts: 17
Re: If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?  [#permalink]

### Show Tags

12 Jan 2018, 11:55
I have no problem with the answer, my only problem is with the IF condition. I’m solving for what EXACT value of x wil be 3^6x= 81000.00

Bunuel wrote:
gvrk_77 wrote:
Thanks Bunnel.

Then I think in question they should have mention as approximate value, because it won’t be terminating
Why I was so skeptical is that I have written 810000 = 3^4 * 10^4,, and from here I was trying to equate with 3^6x and I’m going nowhere

No, you are wrong again. For the value of x, for which $$3^{(6x)} = 810,000$$, is true, $$(3^{(x−1)})^3$$ turns out to be EXACTLY 100/3. You should study the solutions above to understand that we can get the value of $$(3^{(x−1)})^3$$, without getting the value of x.
Math Expert
Joined: 02 Sep 2009
Posts: 58335
If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?  [#permalink]

### Show Tags

12 Jan 2018, 12:01
gvrk_77 wrote:
I have no problem with the answer, my only problem is with the IF condition. I’m solving for what EXACT value of x wil be 3^6x= 81000.00

Bunuel wrote:
gvrk_77 wrote:
Thanks Bunnel.

Then I think in question they should have mention as approximate value, because it won’t be terminating
Why I was so skeptical is that I have written 810000 = 3^4 * 10^4,, and from here I was trying to equate with 3^6x and I’m going nowhere

No, you are wrong again. For the value of x, for which $$3^{(6x)} = 810,000$$, is true, $$(3^{(x−1)})^3$$ turns out to be EXACTLY 100/3. You should study the solutions above to understand that we can get the value of $$(3^{(x−1)})^3$$, without getting the value of x.

Not following you. Again, there exist some irrational x, for which $$3^{(6x)}$$ is EXACTLY 810,000. For that x, $$(3^{(x−1)})^3$$ is EXACTLY 100/3.

Similar questions to practice:
https://gmatclub.com/forum/if-3-6x-8-10 ... 98777.html
https://gmatclub.com/forum/if-2-8x-6400 ... 34587.html

8. Exponents and Roots of Numbers

Check below for more:
ALL YOU NEED FOR QUANT ! ! !

Hope it helps.
_________________
If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?   [#permalink] 12 Jan 2018, 12:01
Display posts from previous: Sort by