Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

It is currently 24 May 2017, 20:37

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If 27^(4x + 2) 162^-2x 36^x 9^(6 2x) = 1, then what is

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

Hide Tags

2 KUDOS received
Manager
Manager
avatar
Joined: 02 Aug 2007
Posts: 230
Schools: Life
Followers: 3

Kudos [?]: 61 [2] , given: 0

If 27^(4x + 2) 162^-2x 36^x 9^(6 2x) = 1, then what is [#permalink]

Show Tags

New post 10 Jul 2008, 19:05
2
This post received
KUDOS
10
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

67% (03:23) correct 33% (02:30) wrong based on 720 sessions

HideShow timer Statistics

If 27^(4x + 2) × 162^-2x × 36^x × 9^(6 – 2x) = 1, then what is the value of x?

A. -9
B. -6
C. 3
D. 6
E. 9
[Reveal] Spoiler: OA
1 KUDOS received
Director
Director
avatar
Joined: 14 Aug 2007
Posts: 729
Followers: 10

Kudos [?]: 196 [1] , given: 0

Re: PS - Powers, what is the value of x? [#permalink]

Show Tags

New post 10 Jul 2008, 19:14
1
This post received
KUDOS
x-ALI-x wrote:
If 27^(4x + 2) × 162^-2x × 36^x × 9^(6 – 2x) = 1, then what is the value of x?


A) -9
B) -6
C) 3
D) 6
E) 9


(3^3)^(4x + 2) * (3^4 * 2)^-2x * (3^2 * 2^2) ^x * (3^2)^(6-2x) = 1

the 2 ^ -2x from second term and 2^2x from the third term gets canclled

giving us all all terms with base 3.

3^ (2x + 18) = 1

2x + 18 must be 0 in order to satisfy this

x= -9

A
Intern
Intern
avatar
Joined: 14 Nov 2012
Posts: 3
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: If 27^(4x + 2) 162^-2x 36^x 9^(6 2x) = 1, then what is [#permalink]

Show Tags

New post 14 Nov 2012, 13:03
This is the last part of the answer from the CAT explanation.

2^0 × 3^2x + 18 = 1
3^2x + 18 = 1
3^2x + 18 = 3^0
2x + 18 = 0
2x = -18
x = -9

where does the 3^0 comes from?
Current Student
avatar
Joined: 25 Jun 2012
Posts: 139
Location: United States
GMAT 1: 700 Q47 V40
GMAT 2: 740 Q48 V44
GPA: 3.48
Followers: 3

Kudos [?]: 20 [0], given: 18

Re: If 27^(4x + 2) 162^-2x 36^x 9^(6 2x) = 1, then what is [#permalink]

Show Tags

New post 14 Nov 2012, 13:06
3^0 is substituted for 1 to show both sides of the equation with the same base

Posted from my mobile device
Intern
Intern
avatar
Joined: 07 Nov 2012
Posts: 3
Followers: 0

Kudos [?]: 0 [0], given: 1

Re: If 27^(4x + 2) 162^-2x 36^x 9^(6 2x) = 1, then what is [#permalink]

Show Tags

New post 04 Jan 2013, 05:10
Can anyone explain how the 18 comes into play?

Also 2^0 in the second explanation.

Thanks.
Expert Post
8 KUDOS received
Math Expert
User avatar
P
Joined: 02 Sep 2009
Posts: 38858
Followers: 7728

Kudos [?]: 106059 [8] , given: 11607

Re: If 27^(4x + 2) 162^-2x 36^x 9^(6 2x) = 1, then what is [#permalink]

Show Tags

New post 04 Jan 2013, 06:08
8
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
xALIx wrote:
If 27^(4x + 2) × 162^-2x × 36^x × 9^(6 – 2x) = 1, then what is the value of x?

A. -9
B. -6
C. 3
D. 6
E. 9


\(27^{4x + 2} * 162^{-2x} * 36^x * 9^{6-2x} = 1\)

\(3^{3*(4x + 2)} * (2^{-2x}*81^{-2x}) * (4^{x}*9^x) * 3^{2(6-2x)} = 1\)

\(3^{3*(4x + 2)} * (2^{-2x}*3^{-8x}) * (2^{2x} *3^{2x})* 3^{2(6-2x)} = 1\) --> \(2^{-2x}*2^{2x}=1\). So, we have that:

\(3^{3*(4x + 2)-8x+2x+2(6-2x)} = 1\)

\(3^{2x+18}=1\) --> \(2x+18=0\) --> \(x=-9\).

Answer: A.
_________________

New to the Math Forum?
Please read this: 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?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
Joined: 16 May 2013
Posts: 6
Concentration: Nonprofit, Real Estate
GRE 1: 317 Q160 V157
GPA: 3.85
WE: Marketing (Education)
Followers: 1

Kudos [?]: 0 [0], given: 2

Re: If 27^(4x + 2) 162^-2x 36^x 9^(6 2x) = 1, then what is [#permalink]

Show Tags

New post 16 May 2013, 12:38
Quick question: How I am I supposed to know that 162 equals 2*3^4 ??? Is there a calculation to it or is 81= 3^4 common knowledge? thanks
Expert Post
Math Expert
User avatar
P
Joined: 02 Sep 2009
Posts: 38858
Followers: 7728

Kudos [?]: 106059 [0], given: 11607

Re: If 27^(4x + 2) 162^-2x 36^x 9^(6 2x) = 1, then what is [#permalink]

Show Tags

New post 16 May 2013, 23:58
NicolasFSS wrote:
Quick question: How I am I supposed to know that 162 equals 2*3^4 ??? Is there a calculation to it or is 81= 3^4 common knowledge? thanks


If you don't know that 81=3^4 you can do the following: 162=2*81=2*9*9=2*3^2*3^2=2*3^4.

I'd advice to know the powers of 2 till 2^10 and the powers of 3 till 3^5.
_________________

New to the Math Forum?
Please read this: 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?
Extra-hard Quant Tests with Brilliant Analytics

SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1857
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 51

Kudos [?]: 2168 [0], given: 193

Re: If 27^(4x + 2) 162^-2x 36^x 9^(6 2x) = 1, then what is [#permalink]

Show Tags

New post 27 Feb 2014, 01:03
Bunuel wrote:
xALIx wrote:
If 27^(4x + 2) × 162^-2x × 36^x × 9^(6 – 2x) = 1, then what is the value of x?

A. -9
B. -6
C. 3
D. 6
E. 9


\(27^{4x + 2} * 162^{-2x} * 36^x * 9^{6-2x} = 1\)

\(3^{3*(4x + 2)} * (2^{-2x}*81^{-2x}) * (4^{x}*9^x) * 3^{2(6-2x)} = 1\)

\(3^{3*(4x + 2)} * (2^{-2x}*3^{-8x}) * (2^{2x} *3^{2x})* 3^{2(6-2x)} = 1\) --> \(2^{-2x}*2^{2x}=1\). So, we have that:

\(3^{3*(4x + 2)-8x+2x+2(6-2x)} = 1\)

\(3^{2x+18}=1\) --> \(2x+18=0\) --> \(x=-9\).

Answer: A.



I did in the same way, however taking more time
Any shorter approach please?
_________________

Kindly press "+1 Kudos" to appreciate :)

Expert Post
Math Expert
User avatar
P
Joined: 02 Sep 2009
Posts: 38858
Followers: 7728

Kudos [?]: 106059 [0], given: 11607

Re: If 27^(4x + 2) 162^-2x 36^x 9^(6 2x) = 1, then what is [#permalink]

Show Tags

New post 27 Feb 2014, 05:30
PareshGmat wrote:
Bunuel wrote:
xALIx wrote:
If 27^(4x + 2) × 162^-2x × 36^x × 9^(6 – 2x) = 1, then what is the value of x?

A. -9
B. -6
C. 3
D. 6
E. 9


\(27^{4x + 2} * 162^{-2x} * 36^x * 9^{6-2x} = 1\)

\(3^{3*(4x + 2)} * (2^{-2x}*81^{-2x}) * (4^{x}*9^x) * 3^{2(6-2x)} = 1\)

\(3^{3*(4x + 2)} * (2^{-2x}*3^{-8x}) * (2^{2x} *3^{2x})* 3^{2(6-2x)} = 1\) --> \(2^{-2x}*2^{2x}=1\). So, we have that:

\(3^{3*(4x + 2)-8x+2x+2(6-2x)} = 1\)

\(3^{2x+18}=1\) --> \(2x+18=0\) --> \(x=-9\).

Answer: A.



I did in the same way, however taking more time
Any shorter approach please?


Not every question has a silver bullet approach.
_________________

New to the Math Forum?
Please read this: 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?
Extra-hard Quant Tests with Brilliant Analytics

Senior Manager
Senior Manager
avatar
Joined: 20 Dec 2013
Posts: 268
Location: India
Followers: 0

Kudos [?]: 89 [0], given: 29

Re: If 27^(4x + 2) 162^-2x 36^x 9^(6 2x) = 1, then what is [#permalink]

Show Tags

New post 08 Mar 2014, 20:38
Option A.
All terms are variants of power of 3.
We reduce each term to some power of 3 and after cancellation get 3^(2x+18)=1
2x+18=0
X=-9

Posted from my mobile device
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 15432
Followers: 649

Kudos [?]: 207 [0], given: 0

Premium Member
Re: If 27^(4x + 2) 162^-2x 36^x 9^(6 2x) = 1, then what is [#permalink]

Show Tags

New post 22 Jul 2015, 02:42
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 Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Current Student
User avatar
Joined: 12 Aug 2015
Posts: 306
Concentration: General Management, Operations
GMAT 1: 640 Q40 V37
GMAT 2: 650 Q43 V36
GMAT 3: 600 Q47 V27
GPA: 3.3
WE: Management Consulting (Consulting)
Followers: 4

Kudos [?]: 376 [0], given: 1474

Re: If 27^(4x + 2) 162^-2x 36^x 9^(6 2x) = 1, then what is [#permalink]

Show Tags

New post 23 Aug 2015, 02:37
Hi

any shorter route to solution? this is a classical manhattan cat question - simple concept, a lot of iterations. gmac would unlikely post something like this, wouldnt it?

looking forward to any shortcut
_________________

KUDO me plenty

Manager
Manager
User avatar
Joined: 10 Jun 2015
Posts: 128
Followers: 1

Kudos [?]: 26 [0], given: 0

Re: If 27^(4x + 2) 162^-2x 36^x 9^(6 2x) = 1, then what is [#permalink]

Show Tags

New post 23 Aug 2015, 05:49
xALIx wrote:
If 27^(4x + 2) × 162^-2x × 36^x × 9^(6 – 2x) = 1, then what is the value of x?

A. -9
B. -6
C. 3
D. 6
E. 9


You have only two prime factors, 2 and 3, involved in this question of exponents.
162=2*3^4
36 =2^2 * 3^2
Therefore, 2^-2x and 2^2x get cancelled.
Now, check only exponents of 3
3^12x * 3^6 * 3^-8x * 3^2x * 3^12 * 3^-4x=1
3^2x * 3^18 = 3^0
Implies 2x+18 = 0
x = -9
Intern
Intern
avatar
Joined: 20 Aug 2016
Posts: 11
Location: United Kingdom
Schools: Stanford '19 (S)
GMAT 1: 720 Q48 V40
GPA: 4
Followers: 0

Kudos [?]: 6 [0], given: 32

Premium Member
Technique: If 27^(4x + 2) 162^-2x 36^x 9^(6 2x) = 1, then what is [#permalink]

Show Tags

New post 08 Oct 2016, 05:27
Hi everyone - Thank you all for your posts.. I thought I would try do my bit

Powers and bases and rate questions have been my nemisis when it has come to pushing the upper ends of quant scores - mainly as I kept getting these wrong! .. I would lose track of the calculations in trying to keep the scientific notation. It was costing me 1-2 questions a test and really frustrating me but most importantly was costing time.

The below technique is one which has turned these problems on their head for me ... i hope its useful It is not perfect but its very helpful for these types of questions, especially if like me you fight the constant battle against the demon of attention to detail (and his sidekick - messy writing)

My method for base questions is analyse vertically in form Base - Power - Variable(s) - Exponent. Using this, this question came together in around 1m50 while I reckon it would have been a 3m+ expedition prior to this method.

Step 1 .... quick scan reveals that this is likely to be a base question. Sketch quick table and then do the factorisation one by one.

27 - 3^3
162 = 81 x 2 = 3^4 and 2^1
36 = 9 x 4 = 3^2 and 2^2
9 = 3^2

Image

Powers of 2 cancel
Base 3 / Exponent = 12x – 8x + 2x – 4x + 12 + 6 = 18 +2x
3^(18+2x) = 3^0
X= -9
CEO
CEO
User avatar
G
Joined: 17 Jul 2014
Posts: 2503
Location: United States (IL)
Concentration: Finance, Economics
Schools: Stanford '19 (D)
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Followers: 26

Kudos [?]: 342 [0], given: 168

GMAT ToolKit User Premium Member Reviews Badge
Re: If 27^(4x + 2) 162^-2x 36^x 9^(6 2x) = 1, then what is [#permalink]

Show Tags

New post 21 Oct 2016, 06:53
xALIx wrote:
If 27^(4x + 2) × 162^-2x × 36^x × 9^(6 – 2x) = 1, then what is the value of x?

A. -9
B. -6
C. 3
D. 6
E. 9



needs to be used math function on the forum...it gets difficult to understand what is what...

27 = 3^3
27^(4x + 2) = 3^(12x+6)

162 = 3^4 * 2
162^-2x = 3^(-8x) * 2^(-2x)

36^x = 3^2x * 2^2x

9^(6 – 2x) = 3^(12-4x)

now.

3^(12x+6) * 3^(-8x) * 2^(-2x) * 3^2x * 2^2x * 3^(12-4x)

powers of 2 cancel, and we have 2^0, which is equal to 1.
rest, we can rewrite as 3 to a long power:
12x+6-8x+2x+12-4x=2x+18.
since 3^(2x+18) = 1, it must be true that 2x+18=0. x=-9
Manager
Manager
avatar
B
Joined: 12 Nov 2016
Posts: 195
Followers: 0

Kudos [?]: 7 [0], given: 135

Re: If 27^(4x + 2) 162^-2x 36^x 9^(6 2x) = 1, then what is [#permalink]

Show Tags

New post 19 Apr 2017, 23:00
xALIx wrote:
If 27^(4x + 2) × 162^-2x × 36^x × 9^(6 – 2x) = 1, then what is the value of x?

A. -9
B. -6
C. 3
D. 6
E. 9


No shortcuts in this problem- best to just think fast and work hard to force out the answer

74x + 2 × 162-2x × 36x × 96 – 2x = 1
(33)4x + 2 × (2 × 34)-2x × (22 × 32)x × (32)6 – 2x = 1
312x + 6 × 2-2x × 3-8x × 22x × 32x × 312 – 4x = 1
2-2x + 2x × 312x + 6 – 8x + 2x + 12 – 4x = 1
20 × 3 2x + 18 = 1
3 2x + 18 = 1

Any number to the zero power equals 1 so set 3's algebraic expression exponent equal to 0

2x + 18 = 0

(-9)

The correct answer is A.
Re: If 27^(4x + 2) 162^-2x 36^x 9^(6 2x) = 1, then what is   [#permalink] 19 Apr 2017, 23:00
    Similar topics Author Replies Last post
Similar
Topics:
12 Experts publish their posts in the topic For all integers x>1. <x>=2x+(2x-1)+(2x-2)+......2+1. What SergeNew 7 29 May 2016, 00:43
3 Experts publish their posts in the topic If y^2 = 2, what is the value of 2^(x-y)(x+y)/2^(x-1)(x+1) enigma123 4 27 Feb 2017, 12:05
2 Experts publish their posts in the topic If 2^(x+2) - 3(2^(x-1))=5/8(2^(16-x))[/m], what is the value of x? tonebeeze 6 16 Apr 2011, 21:15
21 Experts publish their posts in the topic If xy = 1, what is the value of 2^(x + y)^2/2^(x-y)^2? tonebeeze 24 05 Dec 2016, 01:30
8 Experts publish their posts in the topic If xy=1, what is the value of 2(x+y)^2/2(x-y)^2? 5va 6 08 Jun 2016, 11:09
Display posts from previous: Sort by

If 27^(4x + 2) 162^-2x 36^x 9^(6 2x) = 1, then what is

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


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.