Oct 14 08:00 PM PDT  11:00 PM PDT Join a 4day FREE online boot camp to kick off your GMAT preparation and get you into your dream bschool in R2.**Limited for the first 99 registrants. Register today! Oct 15 12:00 PM PDT  01:00 PM PDT Join this live GMAT class with GMAT Ninja to learn to conquer your fears of long, kooky GMAT questions. Oct 16 08:00 PM PDT  09:00 PM PDT EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299) Oct 19 07:00 AM PDT  09:00 AM PDT Does GMAT RC seem like an uphill battle? eGMAT is conducting a free webinar to help you learn reading strategies that can enable you to solve 700+ level RC questions with at least 90% accuracy in less than 10 days. Sat., Oct 19th at 7 am PDT Oct 20 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58335

If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value
[#permalink]
Show Tags
30 Jul 2018, 21:56
Question Stats:
75% (02:11) correct 25% (02:49) wrong based on 1032 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)
Official Answer and Stats are available only to registered users. Register/ Login.
_________________




Math Expert
Joined: 02 Aug 2009
Posts: 7953

Re: If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value
[#permalink]
Show Tags
30 Jul 2018, 23:12
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 = \(\frac{a(1r^n)}{1r}=1*(1\frac{1}{4}^4)/(1\frac{1}{4})=\frac{255}{256}/\frac{3}{4}=\frac{255*4}{256*3}=\frac{85}{64}\)... \(b = 1 + \frac{a}{4}=1+\frac{85}{64*4}=\frac{341}{256}\).... \(ab=\frac{85}{64}\frac{341}{256}=\frac{340341}{256}=\frac{1}{256}\) B
_________________




Retired Moderator
Joined: 30 Jan 2015
Posts: 798
Location: India
Concentration: Operations, Marketing
GPA: 3.5

Re: If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value
[#permalink]
Show Tags
31 Jul 2018, 02:47
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
Joined: 11 Jul 2018
Posts: 19

Re: If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value
[#permalink]
Show Tags
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
Joined: 02 Sep 2009
Posts: 58335

Re: If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value
[#permalink]
Show Tags
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 = \(\frac{a(1r^n)}{1r}=1*(1\frac{1}{4}^4)/(1\frac{1}{4})=\frac{255}{256}/\frac{3}{4}=\frac{255*4}{256*3}=\frac{85}{64}\)... \(b = 1 + \frac{a}{4}=1+\frac{85}{64*4}=\frac{341}{256}\).... \(ab=\frac{85}{64}\frac{341}{256}=\frac{340341}{256}=\frac{1}{256}\) B _______________ Edited. Thank you.
_________________



Intern
Joined: 07 Feb 2017
Posts: 25

Re: If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value
[#permalink]
Show Tags
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, \(ba = \frac{1}{256}\)



Intern
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
31 Jul 2018, 10:06
can this be done in 2 minutes?



Senior RC Moderator
Joined: 02 Nov 2016
Posts: 4062
GPA: 3.39

Re: If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value
[#permalink]
Show Tags
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) BunuelI think this question is already appeared in OG Quantitative review 2018. Kindly verify
_________________



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8040
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
10 Aug 2018, 19:06
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
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



Manager
Joined: 16 Mar 2017
Posts: 61
Location: France
Concentration: Marketing, Strategy
GMAT 1: 640 Q38 V40 GMAT 2: 710 Q47 V41
WE: Marketing (Retail)

Re: If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value
[#permalink]
Show Tags
13 Aug 2018, 04:52
whatfielddoido wrote: can this be done in 2 minutes? Apparently yes "73% (01:44) correct"
_________________



Manager
Joined: 28 Mar 2017
Posts: 67
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
14 Aug 2018, 01:32
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.
_________________
* * * Wish my good luck for 700 before Christmas! If you think my post provided any help, please give +1 kudos, it helps a lot! <3



Manager
Joined: 19 Aug 2016
Posts: 75

Re: If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value
[#permalink]
Show Tags
26 Aug 2018, 20:16
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) Hi Bunuel, I took the LCM of b=1+1/4a Then b became 5/4a I got the answer as 85/256 Why can't we take the LCM and do it this way? And if we can then either way, we must get the same answer.. Please help...thanks



VP
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1019
WE: Supply Chain Management (Energy and Utilities)

Re: If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value
[#permalink]
Show Tags
26 Aug 2018, 21:11
Hi Bunuel, I took the LCM of b=1+1/4a Then b became 5/4aI got the answer as 85/256 Why can't we take the LCM and do it this way? And if we can then either way, we must get the same answer.. Please help...thanks[/quote] Hi zanaik89, Refer the highlighted portion, It should be : \(b=1+\frac{1}{4}a\)(2) =\(\frac{4+a}{4}\) (Though we don't require this step) a=1+\(\frac{1}{4} + \frac{1}{16} + \frac{1}{64}\)=\(\frac{64+16+4+1}{64}\)=\(\frac{85}{64}\)(1) Hence \(ab=\frac{85}{64}(1+\frac{1}{4}*\frac{85}{64})=\frac{85}{64}1\frac{85}{4*64}=\frac{(4*85)(4*64)85}{4*64}\)=\(\frac{1}{256}\) Another Method:\(a=1+\frac{1}{4}+\frac{1}{16}+\frac{1}{64}\) So, \(\frac{1}{4}a=\frac{1}{4}+\frac{1}{16}+\frac{1}{64}+\frac{1}{256}\) (Dividing both sides by 4) So, \(b=1+\frac{1}{4}a=1+\frac{1}{4}+\frac{1}{16}+\frac{1}{64}+\frac{1}{256}\) Hence, \(ab=(1+\frac{1}{4}+\frac{1}{16}+\frac{1}{64})(1+\frac{1}{4}+\frac{1}{16}+\frac{1}{64}+\frac{1}{256})\) Or, \(a−b=−\frac{1}{256}\)
_________________
Regards,
PKN
Rise above the storm, you will find the sunshine



Intern
Joined: 18 Jun 2017
Posts: 8

Re: If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value
[#permalink]
Show Tags
09 Dec 2018, 12:11
Hello to everyone! Is there any way to solve this task in 1 minute, please? Any tricks or magic?
The task is not complicated, but the problem takes more than 1.5 to be solved out.
Thanks.



Intern
Joined: 01 May 2017
Posts: 35

Re: If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value
[#permalink]
Show Tags
09 Jan 2019, 11:10
get value of A and B then substitute, you will easily get the answer.



Intern
Joined: 11 Oct 2018
Posts: 21
Location: Germany

Re: If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value
[#permalink]
Show Tags
12 Jan 2019, 07:24
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) Hi, this is my first post. Hope I did it correctly. \(a=1+\frac{1}{4}+\frac{1}{16}+\frac{1}{64}\) \(b=1+\frac{1}{4}+\frac{1}{16}+\frac{1}{64}+\frac{1}{256}\) \(ab=1+\frac{1}{4}+\frac{1}{16}+\frac{1}{64}1\frac{1}{4}\frac{1}{16}\frac{1}{64}\frac{1}{256}\) or \(ab=11+\frac{1}{4}\frac{1}{4}+\frac{1}{16}\frac{1}{16}+\frac{1}{64}\frac{1}{64}\frac{1}{256}\) Just simplify: \(=\frac{1}{256}\)



Intern
Joined: 24 Apr 2018
Posts: 1

If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value
[#permalink]
Show Tags
26 Apr 2019, 21:56
a=1+1/4+1/4^2 +1/4^3
B=1+1/4a , substitue vaule a in to b
b= 1+1/4(1+1/4+1/4^2 +1/4^3 ) = 1+1/4+1/4^2 +1/4^3 +1/4^4
ab= 1+1/4+1/4^2 +1/4^3  (1+1/4+1/4^2 +1/4^3 +1/4^4 )
=1/4^4 =1/256



Intern
Joined: 26 May 2019
Posts: 16
WE: Accounting (Accounting)

Re: If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value
[#permalink]
Show Tags
04 Aug 2019, 19:19
Tried both geometric progression method and substitution, and substitution was faster for me. Geometric progression just had too much calculation with all the fractions; substitution reduced the calculations. Given: \(a = 1 + \frac{1}{4} + \frac{1}{16} + \frac{1}{64} = \frac{85}{64}\) \(b = 1 + (\frac{1}{4})*a\) Substitution Method: a  b \(= \frac{85}{64}  (1 + (\frac{1}{4})*(\frac{85}{64}))\) \(= \frac{85}{64}  \frac{64}{64}  (\frac{1}{4})*(\frac{85}{64})\) \(= \frac{21}{64}  (\frac{1}{4})*(\frac{85}{64})\) \(= \frac{84}{256}  \frac{85}{256}\) \(= \frac{1}{256}\) Answer is B \(\frac{1}{256}\) 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)



Intern
Joined: 22 Sep 2018
Posts: 1

Re: If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value
[#permalink]
Show Tags
17 Aug 2019, 01:43
Simpler method > no LCM, No GP
ab = (1 + 1/4 + 1/16 + 1/64)  (1 + (1/4) * a)
ab = 1/4 + 1/16 + 1/64  (1/4)*a
ab = 1/4 (1 + 1/4 + 1/16  a)
From the value of 'a' given in the question, we can derive > 1 + 1/4 + 1/16 = a  1/64
So, ab = 1/4 (a  1/64  a)
ab = 1/4 * 1/64 = 1/256



SVP
Joined: 03 Jun 2019
Posts: 1682
Location: India

If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value
[#permalink]
Show Tags
17 Aug 2019, 01:58
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) Given: \(a = 1 + \frac{1}{4} + \frac{1}{16} + \frac{1}{64}\) and \(b = 1 + \frac{1}{4}a\) Asked: What is the value of a – b ? \(a  b = a  (1 + \frac{1}{4}a) = \frac{3}{4} a 1\) \(a = 1 + \frac{1}{4} + \frac{1}{16} + \frac{1}{64}\) \(a = \frac{64+16+4+1}{64}\) \(a = \frac{64+16+4+1}{64}\) \(a = \frac{85}{64}\) \(a  b = a  (1 + \frac{1}{4}a) = \frac{3}{4} a 1\) \(a  b = \frac{3}{4} *\frac{85}{64} 1\) \(a  b = \frac{255}{256} 1\) \(a  b = \frac{1}{256}\) IMO B Another method: \(a = 1 + \frac{1}{4} + \frac{1}{16} + \frac{1}{64}\) \(\frac{a}{4} = \frac{1}{4} + \frac{1}{16} + \frac{1}{64}+ \frac{1}{256}\) \(b = 1 + \frac{1}{4} + \frac{1}{16} + \frac{1}{64}+ \frac{1}{256}\) \(a  b = (1 + \frac{1}{4} + \frac{1}{16} + \frac{1}{64})  (1 + \frac{1}{4} + \frac{1}{16} + \frac{1}{64}+ \frac{1}{256})\) \(a  b = \frac{1}{256}\) IMO B
_________________
"Success is not final; failure is not fatal: It is the courage to continue that counts." Please provide kudos if you like my post. Kudos encourage active discussions. My GMAT Resources:  Efficient LearningAll you need to know about GMAT quantTele: +911140396815 Mobile : +919910661622 Email : kinshook.chaturvedi@gmail.com




If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value
[#permalink]
17 Aug 2019, 01:58



Go to page
1 2
Next
[ 23 posts ]



