It is currently 20 Nov 2017, 14:52

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

Given: 4^(2t+1) - 4^(t+2) = 128, find t

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

Hide Tags

1 KUDOS received
Manager
Manager
avatar
Joined: 11 Jan 2011
Posts: 69

Kudos [?]: 28 [1], given: 3

GMAT 1: 680 Q44 V39
GMAT 2: 710 Q48 V40
GMAT ToolKit User
Given: 4^(2t+1) - 4^(t+2) = 128, find t [#permalink]

Show Tags

New post 15 Nov 2013, 01:52
1
This post received
KUDOS
11
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

40% (01:34) correct 60% (01:17) wrong based on 29 sessions

HideShow timer Statistics

Given: 4^(2t+1) - 4^(t+2) = 128
Find: t

[Reveal] Spoiler:
OA = 1.5

Last edited by Bunuel on 15 Nov 2013, 01:53, edited 1 time in total.
Edited the question.

Kudos [?]: 28 [1], given: 3

Expert Post
3 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42269

Kudos [?]: 132827 [3], given: 12378

Re: Given: 4^(2t+1) - 4^(t+2) = 128, find t [#permalink]

Show Tags

New post 15 Nov 2013, 02:00
3
This post received
KUDOS
Expert's post
4
This post was
BOOKMARKED
NvrEvrGvUp wrote:
Given: 4^(2t+1) - 4^(t+2) = 128
Find: t

[Reveal] Spoiler:
OA = 1.5


\(4^{2t+1} - 4^{t+2} = 128\);

\(4*4^{2t} - 4^2*4^{t} = 128\);

\(4*(4^t)^2 -16*4^t - 128=0\);

\((4^t)^2 -4*4^t - 32=0\);

Solve for 4^t: \(4^t=-4\) (discard, because 4^t cannot be negative) or \(4^t=8\).

\(4^t=8\) --> \(2^{2t}=2^3\) --> \(2t=3\) --> \(t=1.5\).

Hope it's clear.
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 132827 [3], given: 12378

Manager
Manager
avatar
Joined: 11 Jan 2011
Posts: 69

Kudos [?]: 28 [0], given: 3

GMAT 1: 680 Q44 V39
GMAT 2: 710 Q48 V40
GMAT ToolKit User
Re: Given: 4^(2t+1) - 4^(t+2) = 128, find t [#permalink]

Show Tags

New post 15 Nov 2013, 02:02
1
This post was
BOOKMARKED
Bunuel wrote:
NvrEvrGvUp wrote:
Given: 4^(2t+1) - 4^(t+2) = 128
Find: t

[Reveal] Spoiler:
OA = 1.5


\(4^{2t+1} - 4^{t+2} = 128\);

\(4*4^{2t} - 4^2*4^{t} = 128\);

\(4*(4^t)^2 -16*4^t - 128=0\);

\((4^t)^2 -4*4^t - 32=0\);

Solve for 4^t: \(4^t=-4\) (discard, because 4^t cannot be negative) or \(4^t=8\).

\(4^t=8\) --> \(2^{2t}=2^3\) --> \(2t=3\) --> \(t=1.5\).

Hope it's clear.


Hidden quadratic. Got it, thanks Bunuel.

Kudos [?]: 28 [0], given: 3

Intern
Intern
User avatar
Joined: 27 Sep 2013
Posts: 17

Kudos [?]: 8 [0], given: 0

Location: Netherlands
Re: Given: 4^(2t+1) - 4^(t+2) = 128, find t [#permalink]

Show Tags

New post 15 Nov 2013, 02:11
Why can't you solve it this way?

4^{2t+1} - 4^{t+2} = 128

(2^{2})^{2t+1} - (2^{2})^{t+2} = 2^{7}

2^{4t+2} - 2^{2t+4} = 2^{7}

4t+2 - (2t+4) = 7

4t+2 - 2t-4 = 7

2t - 2 = 7

2t = 9

t = 4.5

Is there something I'm missing here?

Kudos [?]: 8 [0], given: 0

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42269

Kudos [?]: 132827 [1], given: 12378

Re: Given: 4^(2t+1) - 4^(t+2) = 128, find t [#permalink]

Show Tags

New post 15 Nov 2013, 02:16
1
This post received
KUDOS
Expert's post
Daddydekker wrote:
Why can't you solve it this way?

4^{2t+1} - 4^{t+2} = 128

(2^{2})^{2t+1} - (2^{2})^{t+2} = 2^{7}

2^{4t+2} - 2^{2t+4} = 2^{7}

4t+2 - (2t+4) = 7

4t+2 - 2t-4 = 7

2t - 2 = 7

2t = 9

t = 4.5

Is there something I'm missing here?


\(2^x-2^y=2^z\) does not mean that \(x-y=z\).
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 132827 [1], given: 12378

Intern
Intern
User avatar
Joined: 27 Sep 2013
Posts: 17

Kudos [?]: 8 [0], given: 0

Location: Netherlands
Re: Given: 4^(2t+1) - 4^(t+2) = 128, find t [#permalink]

Show Tags

New post 15 Nov 2013, 02:18
Bunuel wrote:
Daddydekker wrote:
Why can't you solve it this way?

4^{2t+1} - 4^{t+2} = 128

(2^{2})^{2t+1} - (2^{2})^{t+2} = 2^{7}

2^{4t+2} - 2^{2t+4} = 2^{7}

4t+2 - (2t+4) = 7

4t+2 - 2t-4 = 7

2t - 2 = 7

2t = 9

t = 4.5

Is there something I'm missing here?


\(2^x-2^y=2^z\) does not mean that \(x-y=z\).


True, but bases are the same. So you can add right?

Kudos [?]: 8 [0], given: 0

Manager
Manager
avatar
Joined: 11 Jan 2011
Posts: 69

Kudos [?]: 28 [0], given: 3

GMAT 1: 680 Q44 V39
GMAT 2: 710 Q48 V40
GMAT ToolKit User
Re: Given: 4^(2t+1) - 4^(t+2) = 128, find t [#permalink]

Show Tags

New post 15 Nov 2013, 02:19
Daddydekker wrote:
Bunuel wrote:
Daddydekker wrote:
Why can't you solve it this way?

4^{2t+1} - 4^{t+2} = 128

(2^{2})^{2t+1} - (2^{2})^{t+2} = 2^{7}

2^{4t+2} - 2^{2t+4} = 2^{7}

4t+2 - (2t+4) = 7

4t+2 - 2t-4 = 7

2t - 2 = 7

2t = 9

t = 4.5

Is there something I'm missing here?


\(2^x-2^y=2^z\) does not mean that \(x-y=z\).


True, but bases are the same. So you can add right?


Nah, to get x - y = z the equation would have to be: \(\frac{2^x}{2^y}\)= 2^z

I initially solved it the same way you did as well and got 4.5.

Last edited by NvrEvrGvUp on 15 Nov 2013, 02:21, edited 1 time in total.

Kudos [?]: 28 [0], given: 3

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42269

Kudos [?]: 132827 [1], given: 12378

Re: Given: 4^(2t+1) - 4^(t+2) = 128, find t [#permalink]

Show Tags

New post 15 Nov 2013, 02:20
1
This post received
KUDOS
Expert's post
Daddydekker wrote:
Bunuel wrote:
Daddydekker wrote:
Why can't you solve it this way?

4^{2t+1} - 4^{t+2} = 128

(2^{2})^{2t+1} - (2^{2})^{t+2} = 2^{7}

2^{4t+2} - 2^{2t+4} = 2^{7}

4t+2 - (2t+4) = 7

4t+2 - 2t-4 = 7

2t - 2 = 7

2t = 9

t = 4.5

Is there something I'm missing here?


\(2^x-2^y=2^z\) does not mean that \(x-y=z\).


True, but bases are the same. So you can add right?


I don't understand what you mean. Please go through this topic for basics: math-number-theory-88376.html
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 132827 [1], given: 12378

Manager
Manager
avatar
Joined: 11 Jan 2011
Posts: 69

Kudos [?]: 28 [0], given: 3

GMAT 1: 680 Q44 V39
GMAT 2: 710 Q48 V40
GMAT ToolKit User
Re: Given: 4^(2t+1) - 4^(t+2) = 128, find t [#permalink]

Show Tags

New post 15 Nov 2013, 02:23
Bunuel wrote:
Daddydekker wrote:
Bunuel wrote:

\(2^x-2^y=2^z\) does not mean that \(x-y=z\).


True, but bases are the same. So you can add right?


I don't understand what you mean. Please go through this topic for basics: math-number-theory-88376.html


He's thinking about this: \(\frac{2^x}{2^y}\)= 2^z, which becomes 2^(x-y) = 2^z

In this case, we can say that x - y = z since there are only 2 exponents on two sides of the equal sign with the same base

Kudos [?]: 28 [0], given: 3

Senior Manager
Senior Manager
User avatar
Joined: 10 Mar 2013
Posts: 268

Kudos [?]: 125 [0], given: 2405

GMAT 1: 620 Q44 V31
GMAT 2: 690 Q47 V37
GMAT 3: 610 Q47 V28
GMAT 4: 700 Q50 V34
GMAT 5: 700 Q49 V36
GMAT 6: 690 Q48 V35
GMAT 7: 750 Q49 V42
GMAT 8: 730 Q50 V39
Re: Given: 4^(2t+1) - 4^(t+2) = 128, find t [#permalink]

Show Tags

New post 17 Nov 2013, 14:07
This is a crazy problem even after one discovers the hidden quadratic.

Kudos [?]: 125 [0], given: 2405

SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1851

Kudos [?]: 2715 [0], given: 193

Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: Given: 4^(2t+1) - 4^(t+2) = 128, find t [#permalink]

Show Tags

New post 26 Feb 2014, 02:25
4^(2t+1) - 4^(t+2) = 128

Dividing by 4 to the equation

4^(2t) - 4^t . 4 = 32

(4^t) ^ 2 - 4^t . 4 - 32 = 0

Let 4^t = a

a^2 - 4a - 32 = 0

Roots are a = 8 & -4 (neglect -4 as -ve)

So, a = 8

4^x = 8 = 4 ^ ( 1 + 1/2)

[ 8 can be written as 4 x 2 = 4^1 + 4^(1/2) ]

So, x = 3/2 = 1.5 = Answer
_________________

Kindly press "+1 Kudos" to appreciate :)

Kudos [?]: 2715 [0], given: 193

Manager
Manager
User avatar
Joined: 10 Jun 2015
Posts: 126

Kudos [?]: 30 [0], given: 0

Re: Given: 4^(2t+1) - 4^(t+2) = 128, find t [#permalink]

Show Tags

New post 14 Aug 2015, 06:53
NvrEvrGvUp wrote:
Given: 4^(2t+1) - 4^(t+2) = 128
Find: t

[Reveal] Spoiler:
OA = 1.5

128 = 2^7 = 2^7*(2-1) =2^8-2^7
4t +2=8
t = 1.5

Kudos [?]: 30 [0], given: 0

Director
Director
avatar
G
Joined: 07 Dec 2014
Posts: 836

Kudos [?]: 266 [0], given: 15

Given: 4^(2t+1) - 4^(t+2) = 128, find t [#permalink]

Show Tags

New post 20 Sep 2016, 14:22
Given: 4^(2t+1) - 4^(t+2) = 128
Find: t

if 2^8-2^7=256-128=128
then 4^4-4^3.5=128
t=1.5

Kudos [?]: 266 [0], given: 15

Manager
Manager
avatar
Joined: 29 Aug 2008
Posts: 111

Kudos [?]: 48 [0], given: 284

Re: Given: 4^(2t+1) - 4^(t+2) = 128, find t [#permalink]

Show Tags

New post 21 Sep 2016, 00:10
Bunuel wrote:
NvrEvrGvUp wrote:
Given: 4^(2t+1) - 4^(t+2) = 128
Find: t

[Reveal] Spoiler:
OA = 1.5


\(4^{2t+1} - 4^{t+2} = 128\);

\(4*4^{2t} - 4^2*4^{t} = 128\);

\(4*(4^t)^2 -16*4^t - 128=0\);

\((4^t)^2 -4*4^t - 32=0\);

Solve for 4^t: \(4^t=-4\) (discard, because 4^t cannot be negative) or \(4^t=8\).

\(4^t=8\) --> \(2^{2t}=2^3\) --> \(2t=3\) --> \(t=1.5\).

Hope it's clear.


I managed to get the same equation, but never noticed the quardratic in there. Thanks for the approach.

Kudos [?]: 48 [0], given: 284

Expert Post
Target Test Prep Representative
User avatar
S
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1684

Kudos [?]: 906 [0], given: 5

Re: Given: 4^(2t+1) - 4^(t+2) = 128, find t [#permalink]

Show Tags

New post 26 Oct 2017, 15:38
NvrEvrGvUp wrote:
Given: 4^(2t+1) - 4^(t+2) = 128
Find: t

[Reveal] Spoiler:
OA = 1.5


4^(2t+1) - 4^(t+2) = 128

4^2t x 4 - 4^t x 4^2 = 128

4(4^t)^2 - 16(4^t) - 128 = 0

If we let x = 4^t, we have:

4x^2 - 16x - 128 = 0

x^2 - 4x - 32 = 0

(x - 8)(x + 4) = 0

x = 8 or x = -4

Since x = 4^t, we have:

4^t = 8 or 4^t = -4

Notice that 4 is positive, so 4^t also will be positive for any values of t, and thus 4^t can’t be -4. We are left with 4^t = 8:

2^(2t) = 2^3

2t = 3

t = 3/2
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 906 [0], given: 5

Re: Given: 4^(2t+1) - 4^(t+2) = 128, find t   [#permalink] 26 Oct 2017, 15:38
Display posts from previous: Sort by

Given: 4^(2t+1) - 4^(t+2) = 128, find t

  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 | Emoji artwork provided by EmojiOne

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®.