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

It is currently 15 Feb 2019, 23:27

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 in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
  • Free GMAT Strategy Webinar

     February 16, 2019

     February 16, 2019

     07:00 AM PST

     09:00 AM PST

    Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
  • $450 Tuition Credit & Official CAT Packs FREE

     February 15, 2019

     February 15, 2019

     10:00 PM EST

     11:00 PM PST

    EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299)

Given 2^(4x) = 1600, what is the value of [2^(x-1)]^4

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

Hide Tags

 
Director
Director
avatar
Joined: 29 Nov 2012
Posts: 749
Given 2^(4x) = 1600, what is the value of [2^(x-1)]^4  [#permalink]

Show Tags

New post Updated on: 17 Jun 2013, 05:18
2
9
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

72% (02:27) correct 28% (02:49) wrong based on 152 sessions

HideShow timer Statistics

Given \(2^{4x} = 1600\), what is the value of \(\frac{[2^{(x-1)}]^4}{[2^x]^2}\)

A. 2
B. 5/2
C. 5
D. 25/4
E. 24

Originally posted by fozzzy on 17 Jun 2013, 05:07.
Last edited by Bunuel on 17 Jun 2013, 05:18, edited 1 time in total.
Edited the question.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 52905
Re: Given 2^4x = 1600, what is the value of [2^(x-1)]^4 / [2^x]^  [#permalink]

Show Tags

New post 17 Jun 2013, 05:17
3
4
Given \(2^{4x} = 1600\), what is the value of \(\frac{[2^{(x-1)}]^4}{[2^x]^2}\)

A. 2
B. 5/2
C. 5
D. 25/4
E. 24

\(\frac{[2^{(x-1)}]^4}{[2^x]^2}=\frac{2^{4(x-1)}}{2^{2x}}=2^{4x-4-2x}=2^{2x-4}=\frac{2^{2x}}{16}\).

Since \(2^{4x} = 1600\), then \(2^{2x}=\sqrt{1600}=40\).

Therefore, \(\frac{2^{2x}}{16}=\frac{40}{16}=\frac{5}{2}\).

Answer: B.
_________________

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

General Discussion
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2827
Re: Given 2^(4x) = 1600, what is the value of [2^(x-1)]^4  [#permalink]

Show Tags

New post 21 Mar 2017, 05:17
fozzzy wrote:
Given \(2^{4x} = 1600\), what is the value of \(\frac{[2^{(x-1)}]^4}{[2^x]^2}\)

A. 2
B. 5/2
C. 5
D. 25/4
E. 24


We can simplify the question:

2^(4x - 4)/2^(2x)

2^(4x - 4 - 2x)

2^(2x - 4)

2^(2x)/2^4

We know that 2^4 = 16, and notice that 2^(2x) = √2^(4x). Thus

√2^(4x) = √1600

2^(2x) = 40

Thus, 2^(2x)/2^4 = 40/16 = 5/2.

Answer: B
_________________

Jeffery Miller
Head of GMAT Instruction

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

Director
Director
avatar
G
Joined: 09 Mar 2018
Posts: 919
Location: India
Given 2^(4x) = 1600, what is the value of [2^(x-1)]^4  [#permalink]

Show Tags

New post 04 Feb 2019, 23:20
fozzzy wrote:
Given \(2^{4x} = 1600\), what is the value of \(\frac{[2^{(x-1)}]^4}{[2^x]^2}\)

A. 2
B. 5/2
C. 5
D. 25/4
E. 24


\(\frac{[2^{(x-1)}]^4}{[2^x]^2}\)

which can be written as

2^{4x - 4 -2x}

2^2x-4

2^2x/16 ---------(a)

\(2^{4x} = 1600\)

2^4x = 40^2

2^{4x*1/2} = 40 ^2*1/2

2^2x = 40

Lets put the value in (a)

40/16 = 5/2

B
_________________

If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.

Manager
Manager
avatar
B
Joined: 22 Sep 2018
Posts: 239
CAT Tests
Given 2^(4x) = 1600, what is the value of [2^(x-1)]^4  [#permalink]

Show Tags

New post 05 Feb 2019, 14:44
fozzzy wrote:
Given \(2^{4x} = 1600\), what is the value of \(\frac{[2^{(x-1)}]^4}{[2^x]^2}\)

A. 2
B. 5/2
C. 5
D. 25/4
E. 24


I need to improve my speed on these questions... Took me 5 minutes because I made careless mistakes and had to re-do the question 3 times.

My reasoning:

We can simply both equations to get the values we need.

\(\frac{[2^{(x-1)}]^4}{[2^x]^2} = \frac{[2^{(4x-4)}]}{[2^x]^2} = \frac{[2^{4x}] +[2^{-4}]}{[2^2x]}\)

From \(2^{4x} = 1600\) we can square both sides by \(\frac{1}{2}\) to get \(2^{2x} = 40\)

Plugging everything back into the question we get

\(\frac{1600}{40*16}\) = \(\frac{5}{2}\)
GMAT Club Bot
Given 2^(4x) = 1600, what is the value of [2^(x-1)]^4   [#permalink] 05 Feb 2019, 14:44
Display posts from previous: Sort by

Given 2^(4x) = 1600, what is the value of [2^(x-1)]^4

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.