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

 It is currently 13 Oct 2019, 23:00 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

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.  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 V
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

2
34 00:00

Difficulty:   35% (medium)

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)

_________________
Math Expert V
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

3
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
_________________
Retired Moderator D
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

6
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 General Discussion
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

2
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 V
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

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.
_________________
Intern  B
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

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

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  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

can this be done in 2 minutes?
Senior RC Moderator V
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

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

NEW question from GMAT® Quantitative Review 2019

(PS14293)

Bunuel

I think this question is already appeared in OG Quantitative review 2018. Kindly verify
_________________
Target Test Prep Representative D
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

3
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

_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

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  S
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

whatfielddoido wrote:
can this be done in 2 minutes?

Apparently yes "73% (01:44) correct"
_________________
Manager  S
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

2
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  B
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

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..

VP  D
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

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..

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

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, $$a-b=(1+\frac{1}{4}+\frac{1}{16}+\frac{1}{64})-(1+\frac{1}{4}+\frac{1}{16}+\frac{1}{64}+\frac{1}{256})$$
Or, $$a−b=−\frac{1}{256}$$
_________________
Regards,

PKN

Rise above the storm, you will find the sunshine
Intern  B
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

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  B
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

get value of A and B then substitute, you will easily get the answer.
Intern  B
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

3
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.

$$a=1+\frac{1}{4}+\frac{1}{16}+\frac{1}{64}$$
$$b=1+\frac{1}{4}+\frac{1}{16}+\frac{1}{64}+\frac{1}{256}$$

$$a-b=1+\frac{1}{4}+\frac{1}{16}+\frac{1}{64}-1-\frac{1}{4}-\frac{1}{16}-\frac{1}{64}-\frac{1}{256}$$
or
$$a-b=1-1+\frac{1}{4}-\frac{1}{4}+\frac{1}{16}-\frac{1}{16}+\frac{1}{64}-\frac{1}{64}-\frac{1}{256}$$

Just simplify:

$$=-\frac{1}{256}$$
Intern  B
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

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

a-b= 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  B
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

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  B
Joined: 22 Sep 2018
Posts: 1
GMAT 2: 660 Q44 V37 Re: If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value  [#permalink]

Show Tags

Simpler method -> no LCM, No GP

a-b = (1 + 1/4 + 1/16 + 1/64) - (1 + (1/4) * a)

a-b = 1/4 + 1/16 + 1/64 - (1/4)*a

a-b = 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, a-b = 1/4 (a - 1/64 - a)

a-b = 1/4 * -1/64 = -1/256
SVP  P
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

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 Learning
All you need to know about GMAT quant

Tele: +91-11-40396815
Mobile : +91-9910661622
E-mail : 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 ]

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

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  