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

It is currently 20 Aug 2018, 03:52

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

If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 48044
If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value  [#permalink]

Show Tags

New post 30 Jul 2018, 21:56
1
4
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

76% (01:43) correct 24% (02:09) wrong based on 164 sessions

HideShow timer Statistics

If \(a = 1 + \frac{1}{4} + \frac{1}{16} + \frac{1}{64}\) and \(b = 1 + \frac{1}{4}a\), then what is the value of a – b ?


A. -85/256

B. -1/256

C. -1/4

D. 125/256

E. 169/256


NEW question from GMAT® Quantitative Review 2019


(PS14293)

_________________

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

Intern
Intern
avatar
Joined: 11 Jul 2018
Posts: 20
Re: If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value  [#permalink]

Show Tags

New post 30 Jul 2018, 22:49
Value of a = 1 + 1/4 = 1.25 (ignoring other bit which will make it slightly bigger than 1.25)
Value of b = 1 + 1/(4*1.25) = 1 + 1/5 = 1.20

Roughly a - b = 1.25 - 1.20 = .05 => Actual value of a will be slightly more than 1.25 and therefore, value of b will be slightly less than what is present. This will mean this difference will slightly bigger but not drastically big.

I will go with smaller option of D.

This is not a proper way to solve this query as it can be solve using equations or GP series etc in a proper manner but that will be too time consuming in exam.
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6556
Re: If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value  [#permalink]

Show Tags

New post 30 Jul 2018, 23:12
1
Bunuel wrote:
If \(a = 1 + \frac{1}{4} + \frac{1}{16} + \frac{1}{64}\) and \(b = 1 + \frac{1}{4a}\), then what is the value of a – b ?


A. -85/256

B. -1/256

C. -1/4

D. 125/256

E. 169/256


NEW question from GMAT® Quantitative Review 2019


(PS14293)


Bunuel, pl relook ..\(b = 1 + \frac{1}{4a}\) should be \(b = 1 + \frac{1}{4}*a\)
otherwise you will not get the denominator as a multiple of 4

\(a = 1 + \frac{1}{4} + \frac{1}{16} + \frac{1}{64}=1+\frac{1}{2^2}+\frac{1}{2^4}+\frac{1}{2^6}\)...
it is a geometric progression
sum = \(\frac{a(1-r^n)}{1-r}=1*(1-\frac{1}{4}^4)/(1-\frac{1}{4})=\frac{255}{256}/\frac{3}{4}=\frac{255*4}{256*3}=\frac{85}{64}\)...

\(b = 1 + \frac{a}{4}=1+\frac{85}{64*4}=\frac{341}{256}\)....

\(a-b=\frac{85}{64}-\frac{341}{256}=\frac{340-341}{256}=\frac{-1}{256}\)

B
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 48044
Re: If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value  [#permalink]

Show Tags

New post 30 Jul 2018, 23:15
chetan2u wrote:
Bunuel wrote:
If \(a = 1 + \frac{1}{4} + \frac{1}{16} + \frac{1}{64}\) and \(b = 1 + \frac{1}{4a}\), then what is the value of a – b ?


A. -85/256

B. -1/256

C. -1/4

D. 125/256

E. 169/256


NEW question from GMAT® Quantitative Review 2019


(PS14293)


Bunuel, pl relook ..\(b = 1 + \frac{1}{4a}\) should be \(b = 1 + \frac{1}{4}*a\)
otherwise you will not get the denominator as a multiple of 4

\(a = 1 + \frac{1}{4} + \frac{1}{16} + \frac{1}{64}=1+\frac{1}{2^2}+\frac{1}{2^4}+\frac{1}{2^6}\)...
it is a geometric progression
sum = \(\frac{a(1-r^n)}{1-r}=1*(1-\frac{1}{4}^4)/(1-\frac{1}{4})=\frac{255}{256}/\frac{3}{4}=\frac{255*4}{256*3}=\frac{85}{64}\)...

\(b = 1 + \frac{a}{4}=1+\frac{85}{64*4}=\frac{341}{256}\)....

\(a-b=\frac{85}{64}-\frac{341}{256}=\frac{340-341}{256}=\frac{-1}{256}\)

B

_______________
Edited. Thank you.
_________________

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

Director
Director
User avatar
G
Joined: 30 Jan 2015
Posts: 525
Location: India
Concentration: Operations, Marketing
GPA: 3.5
CAT Tests
Re: If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value  [#permalink]

Show Tags

New post 31 Jul 2018, 02:47
1
Bunuel wrote:
If \(a = 1 + \frac{1}{4} + \frac{1}{16} + \frac{1}{64}\) and \(b = 1 + \frac{1}{4}a\), then what is the value of a – b ?


a = 1 + 1/4 + 1/16 + 1/64
a = ( 64 + 16 + 4 + 1 ) / 64
a = 85 / 64

Now,
b = 1 + 1/4 * 85/64
b = 1 + 85/256
b = 341/256

Therefore,
a - b = 85/64 - 341/256
a - b = ( 85*4 - 341 ) / 256
a - b = (340 - 341)/256
a - b = - 1 / 256

Hence, B.
_________________

The few, the fearless !

Thanks :-)

Intern
Intern
avatar
B
Joined: 07 Feb 2017
Posts: 13
Re: If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value  [#permalink]

Show Tags

New post 31 Jul 2018, 09:49
Bunuel wrote:
If \(a = 1 + \frac{1}{4} + \frac{1}{16} + \frac{1}{64}\) and \(b = 1 + \frac{1}{4}a\), then what is the value of a – b ?


A. -85/256

B. -1/256

C. -1/4

D. 125/256

E. 169/256


NEW question from GMAT® Quantitative Review 2019


(PS14293)


Easier way to do rather than using Geo series formula is using substitution method.

\(b=1+\frac{1}{4} a\)
\(b=a+\frac{1}{256}\)
so, \(b-a = -\frac{1}{256}\)
Intern
Intern
avatar
B
Status: GMAT PREP
Joined: 22 Jul 2018
Posts: 3
Concentration: Technology, Entrepreneurship
Re: If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value  [#permalink]

Show Tags

New post 31 Jul 2018, 10:06
can this be done in 2 minutes?
SVP
SVP
User avatar
V
Status: Preparing for the GMAT
Joined: 02 Nov 2016
Posts: 1630
Location: Pakistan
GPA: 3.39
Premium Member CAT Tests
Re: If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value  [#permalink]

Show Tags

New post 06 Aug 2018, 02:42
Bunuel wrote:
If \(a = 1 + \frac{1}{4} + \frac{1}{16} + \frac{1}{64}\) and \(b = 1 + \frac{1}{4}a\), then what is the value of a – b ?


A. -85/256

B. -1/256

C. -1/4

D. 125/256

E. 169/256


NEW question from GMAT® Quantitative Review 2019


(PS14293)


Bunuel

I think this question is already appeared in OG Quantitative review 2018. Kindly verify
_________________

Official PS Practice Questions
Press +1 Kudos if this post is helpful

Target Test Prep Representative
User avatar
G
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3182
Location: United States (CA)
Re: If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value  [#permalink]

Show Tags

New post 10 Aug 2018, 19:06
1
Bunuel wrote:
If \(a = 1 + \frac{1}{4} + \frac{1}{16} + \frac{1}{64}\) and \(b = 1 + \frac{1}{4}a\), then what is the value of a – b ?


A. -85/256

B. -1/256

C. -1/4

D. 125/256

E. 169/256


a - b

a - (1 + ¼a)

¾a - 1

¾(1 + ¼ + 1/16 + 1/64) - 1

¾(64/64 + 16/64 + 4/64 + 1/64) - 1

¾(85/64) - 1

255/256 - 256/256

-1/256

Answer: B
_________________

Scott Woodbury-Stewart
Founder and CEO

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

Intern
Intern
User avatar
B
Joined: 16 Mar 2017
Posts: 13
GMAT 1: 640 Q38 V40
Re: If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value  [#permalink]

Show Tags

New post 13 Aug 2018, 04:52
whatfielddoido wrote:
can this be done in 2 minutes?


Apparently yes ;) "73% (01:44) correct"
Intern
Intern
avatar
B
Joined: 28 Mar 2017
Posts: 8
Location: Sweden
Concentration: Finance, Statistics
Re: If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value  [#permalink]

Show Tags

New post 14 Aug 2018, 01:32
1
How I solved it in 30s.

a= 1+0.25+(small numbers)=almost 1.3
b= 1+0,25*1.3=1+ slightly more than 0.3.
a - b= (less than) 1.3 - (more than) 1.3 = negative, but close to 0.

Answer options allow for B as best answer choice. B is correct.
Re: If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value &nbs [#permalink] 14 Aug 2018, 01:32
Display posts from previous: Sort by

If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value

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

Events & Promotions

PREV
NEXT


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®.