Find all School-related info fast with the new School-Specific MBA Forum

It is currently 21 Sep 2014, 12:18

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If 4^4x = 1600, what is the value of (4^x–1)^2?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Intern
Intern
avatar
Joined: 21 Sep 2013
Posts: 18
Location: United States
Concentration: Finance, General Management
GMAT Date: 10-25-2013
GPA: 3
WE: Operations (Mutual Funds and Brokerage)
Followers: 0

Kudos [?]: 8 [1] , given: 64

If 4^4x = 1600, what is the value of (4^x–1)^2? [#permalink] New post 18 Oct 2013, 09:52
1
This post received
KUDOS
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

69% (02:35) correct 31% (02:13) wrong based on 113 sessions
If 4^(4x) = 1600, what is the value of [4^(x–1)]^2?

A. 40
B. 20
C. 10
D. 5/2
E. 5/4
[Reveal] Spoiler: OA
Expert Post
3 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23504
Followers: 3510

Kudos [?]: 26605 [3] , given: 2714

Re: If 4^4x = 1600, what is the value of (4^x–1)^2? [#permalink] New post 18 Oct 2013, 09:59
3
This post received
KUDOS
Expert's post
Yash12345 wrote:
If 4^(4x) = 1600, what is the value of [4^(x–1)]^2?

A. 40
B. 20
C. 10
D. 5/2
E. 5/4


4^{4x} = 1600 --> 4^{2x} = 40 -

(4^{(x-1)})^2=4^{2(x-1)}=4^{2x-2}=\frac{4^{2x}}{4^2}=\frac{40}{16}=\frac{5}{2}.

Answer: D.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 10 Sep 2012
Posts: 3
GMAT Date: 08-27-2013
GPA: 3.5
WE: Investment Banking (Energy and Utilities)
Followers: 0

Kudos [?]: 5 [0], given: 26

Re: If 4^4x = 1600, what is the value of (4^x–1)^2? [#permalink] New post 20 Oct 2013, 05:00
Bunuel wrote:
Yash12345 wrote:
If 4^(4x) = 1600, what is the value of [4^(x–1)]^2?

A. 40
B. 20
C. 10
D. 5/2
E. 5/4


4^{4x} = 1600 --> 4^{2x} = 40 -

4^{(x-1)^2}=4^{2(x-1)}=4^{2x-2}=\frac{4^{2x}}{4^2}=\frac{40}{16}=\frac{5}{2}.

Answer: D.


I am getting the answer as 5/4.. I just can figure out what have i missed?

4^4 . 4^x = 4^3 . 5^2
4^2x = 25

now, 4^2x/4^2 = 25/16 =5/4.
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23504
Followers: 3510

Kudos [?]: 26605 [1] , given: 2714

Re: If 4^4x = 1600, what is the value of (4^x–1)^2? [#permalink] New post 20 Oct 2013, 05:06
1
This post received
KUDOS
Expert's post
chitrasekar2k5 wrote:
Bunuel wrote:
Yash12345 wrote:
If 4^(4x) = 1600, what is the value of [4^(x–1)]^2?

A. 40
B. 20
C. 10
D. 5/2
E. 5/4


4^{4x} = 1600 --> 4^{2x} = 40 -

4^{(x-1)^2}=4^{2(x-1)}=4^{2x-2}=\frac{4^{2x}}{4^2}=\frac{40}{16}=\frac{5}{2}.

Answer: D.


I am getting the answer as 5/4.. I just can figure out what have i missed?

4^4 . 4^x = 4^3 . 5^2
4^2x = 25

now, 4^2x/4^2 = 25/16 =5/4.


4^{4}*4^x=4^{4+x} not 4^{4x}: a^n*a^m=a^{n+m}

Check here for more: math-number-theory-88376.html
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Senior Manager
Senior Manager
avatar
Joined: 07 Apr 2012
Posts: 410
Followers: 1

Kudos [?]: 1 [0], given: 58

CAT Tests
Re: If 4^4x = 1600, what is the value of (4^x–1)^2? [#permalink] New post 02 Nov 2013, 02:35
Bunuel wrote:
Yash12345 wrote:
If 4^(4x) = 1600, what is the value of [4^(x–1)]^2?

A. 40
B. 20
C. 10
D. 5/2
E. 5/4


4^{4x} = 1600 --> 4^{2x} = 40 -

4^{(x-1)^2}=4^{2(x-1)}=4^{2x-2}=\frac{4^{2x}}{4^2}=\frac{40}{16}=\frac{5}{2}.

Answer: D.

Is there another aproach?What if I don't realize the 4^{4x} = 1600 --> 4^{2x} = 40 - ?
Expert Post
4 KUDOS received
Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Joined: 10 Oct 2012
Posts: 627
Followers: 41

Kudos [?]: 579 [4] , given: 135

Premium Member
Re: If 4^4x = 1600, what is the value of (4^x–1)^2? [#permalink] New post 02 Nov 2013, 22:29
4
This post received
KUDOS
Expert's post
ronr34 wrote:
Bunuel wrote:
Yash12345 wrote:
If 4^(4x) = 1600, what is the value of [4^(x–1)]^2?

A. 40
B. 20
C. 10
D. 5/2
E. 5/4


4^{4x} = 1600 --> 4^{2x} = 40 -

4^{(x-1)^2}=4^{2(x-1)}=4^{2x-2}=\frac{4^{2x}}{4^2}=\frac{40}{16}=\frac{5}{2}.

Answer: D.

Is there another aproach?What if I don't realize the 4^{4x} = 1600 --> 4^{2x} = 40 - ?



I think what Bunuel did is the easiest approach. However, if you are worried that this might not strike you, start with the unknown entity.

4^{(x-1)^2} = [\frac{4^x}{4^1}]^2 = [\frac{4^{2x}}{4^2}] and let t = [\frac{4^{2x}}{4^2}]

Now, given that 4^{4x} = 1600. Thus,t^2 = [\frac{4^{4x}}{4^4}] =[\frac{1600}{16*16}] = [\frac{100}{16}]and t = \frac{10}{4} =\frac{5}{2}
_________________

All that is equal and not-Deep Dive In-equality

Hit and Trial for Integral Solutions

Senior Manager
Senior Manager
avatar
Joined: 07 Apr 2012
Posts: 410
Followers: 1

Kudos [?]: 1 [0], given: 58

CAT Tests
Re: If 4^4x = 1600, what is the value of (4^x–1)^2? [#permalink] New post 03 Nov 2013, 00:30
Great!!!
Thanks a lot.
Intern
Intern
avatar
Joined: 16 Feb 2013
Posts: 8
Followers: 0

Kudos [?]: 0 [0], given: 9

Re: If 4^4x = 1600, what is the value of (4^x–1)^2? [#permalink] New post 20 Feb 2014, 15:43
Bunuel wrote:
Yash12345 wrote:
If 4^(4x) = 1600, what is the value of [4^(x–1)]^2?

A. 40
B. 20
C. 10
D. 5/2
E. 5/4


4^{4x} = 1600 --> 4^{2x} = 40 -

4^{(x-1)^2}=4^{2(x-1)}=4^{2x-2}=\frac{4^{2x}}{4^2}=\frac{40}{16}=\frac{5}{2}.

Answer: D.



Hi Bunuel, why isn't (x-1)^2 is not treated like (a-b)^2 formula?

Thanks
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23504
Followers: 3510

Kudos [?]: 26605 [1] , given: 2714

Re: If 4^4x = 1600, what is the value of (4^x–1)^2? [#permalink] New post 20 Feb 2014, 23:18
1
This post received
KUDOS
Expert's post
streamingline wrote:
Bunuel wrote:
Yash12345 wrote:
If 4^(4x) = 1600, what is the value of [4^(x–1)]^2?

A. 40
B. 20
C. 10
D. 5/2
E. 5/4


4^{4x} = 1600 --> 4^{2x} = 40 -

4^{(x-1)^2}=4^{2(x-1)}=4^{2x-2}=\frac{4^{2x}}{4^2}=\frac{40}{16}=\frac{5}{2}.

Answer: D.



Hi Bunuel, why isn't (x-1)^2 is not treated like (a-b)^2 formula?

Thanks


Actually parenthesis were missing there. Edited, it should read: (4^{(x-1)})^2=4^{2(x-1)}=4^{2x-2}=\frac{4^{2x}}{4^2}=\frac{40}{16}=\frac{5}{2}.

If exponentiation is indicated by stacked symbols, the rule is to work from the top down, thus:
a^m^n=a^{(m^n)} and not (a^m)^n, which on the other hand equals to a^{mn}.

So:
(a^m)^n=a^{mn};

a^m^n=a^{(m^n)} and not (a^m)^n.

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

1 KUDOS received
Director
Director
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 926
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 6

Kudos [?]: 239 [1] , given: 167

If 4^4x = 1600, what is the value of (4^x–1)^2? [#permalink] New post 24 Feb 2014, 00:28
1
This post received
KUDOS
One more approach:

Refer Step I to Step VI
Attachment:
power.jpg
power.jpg [ 47.28 KiB | Viewed 576 times ]

4^{4x} = 1600

Dividing both sides by 4^4
\frac{4^{4x}}{4^4} = \frac{1600}{4^4}

4^{4x-4} = \frac{100}{16}

4^{(x-1)^4} = \frac{10^2}{4^2}

Square root both sides

4^{(x-1)^2} = \frac{10}{4} = \frac{5}{2}

Answer = D
_________________

Kindly press "+1 Kudos" to appreciate :)


Last edited by PareshGmat on 02 Sep 2014, 20:01, edited 1 time in total.
Intern
Intern
avatar
Joined: 07 Jul 2013
Posts: 3
Followers: 0

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

Re: If 4^4x = 1600, what is the value of (4^x–1)^2? [#permalink] New post 27 Feb 2014, 08:32
Bunuel wrote:
Yash12345 wrote:
If 4^(4x) = 1600, what is the value of [4^(x–1)]^2?

A. 40
B. 20
C. 10
D. 5/2
E. 5/4


4^{4x} = 1600 --> 4^{2x} = 40 -

(4^{(x-1)})^2=4^{2(x-1)}=4^{2x-2}=\frac{4^{2x}}{4^2}=\frac{40}{16}=\frac{5}{2}.

Answer: D.


Hi Bruno,

thank you for posting all these answers. They are a great tool!!

Quick question though. I just want to confirm the steps of 4^{4x} = 1600 TO 4^{2x} = 40 -

Do you just squareroot the two sides? \sqrt{4^{4x}} = \sqrt{1600}
So the base, 4, doesn't change, only the ^4x gets rooted to ^2x. Is that right?

Thank you again!
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23504
Followers: 3510

Kudos [?]: 26605 [1] , given: 2714

Re: If 4^4x = 1600, what is the value of (4^x–1)^2? [#permalink] New post 27 Feb 2014, 10:08
1
This post received
KUDOS
Expert's post
hieracity wrote:
Bunuel wrote:
Yash12345 wrote:
If 4^(4x) = 1600, what is the value of [4^(x–1)]^2?

A. 40
B. 20
C. 10
D. 5/2
E. 5/4


4^{4x} = 1600 --> 4^{2x} = 40 -

(4^{(x-1)})^2=4^{2(x-1)}=4^{2x-2}=\frac{4^{2x}}{4^2}=\frac{40}{16}=\frac{5}{2}.

Answer: D.


Hi Bruno,

thank you for posting all these answers. They are a great tool!!

Quick question though. I just want to confirm the steps of 4^{4x} = 1600 TO 4^{2x} = 40 -

Do you just squareroot the two sides? \sqrt{4^{4x}} = \sqrt{1600}
So the base, 4, doesn't change, only the ^4x gets rooted to ^2x. Is that right?

Thank you again!


Yes:
4^{4x} = 1600;

(4^{2x})^2 = 40^2;

4^{2x} =40.

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Re: If 4^4x = 1600, what is the value of (4^x–1)^2?   [#permalink] 27 Feb 2014, 10:08
    Similar topics Author Replies Last post
Similar
Topics:
2 Experts publish their posts in the topic Given 2^(4x) = 1600, what is the value of [2^(x-1)]^4 fozzzy 1 17 Jun 2013, 05:07
9 Experts publish their posts in the topic If 4x-12 >= x + 9, which of the following must be true saxenagarima 19 26 Sep 2010, 09:48
X^3-3x^2-4x+12 GMATBLACKBELT 2 07 Jan 2009, 14:23
If 4^4x = 1600, what is the value of (4^(x 1))^2? 40 20 10 study 3 11 Dec 2008, 01:45
6 Experts publish their posts in the topic If 4^(4x) = 1600, what is the value of [4^(x–1)]^2? alimad 12 23 Nov 2007, 07:56
Display posts from previous: Sort by

If 4^4x = 1600, what is the value of (4^x–1)^2?

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| 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®.