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

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

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

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Question Stats:

74% (02:12) correct 26% (02:51) wrong based on 647 sessions

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Re: If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value  [#permalink]

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New post 30 Jul 2018, 22:49
1
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.
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Re: If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value  [#permalink]

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New post 30 Jul 2018, 23:12
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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
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Re: If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value  [#permalink]

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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

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Re: If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value  [#permalink]

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New post 31 Jul 2018, 02:47
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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.
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Re: If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value  [#permalink]

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

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New post 31 Jul 2018, 10:06
can this be done in 2 minutes?
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Re: If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value  [#permalink]

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New post 06 Aug 2018, 02:42
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
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Re: If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value  [#permalink]

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New post 10 Aug 2018, 19:06
2
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
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Re: If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value  [#permalink]

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Re: If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value  [#permalink]

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New post 14 Aug 2018, 01:32
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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.
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Re: If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value  [#permalink]

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New post 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
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Re: If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value  [#permalink]

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New post 26 Aug 2018, 21:11
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[/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 \(a-b=\frac{85}{64}-(1+\frac{1}{4}*\frac{85}{64})=\frac{85}{64}-1-\frac{85}{4*64}=\frac{(4*85)-(4*64)-85}{4*64}\)=-\(\frac{1}{256}\)

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

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New post 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.
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Re: If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value  [#permalink]

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

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New post 12 Jan 2019, 07:24
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)


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:

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

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New post 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

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
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If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4a, then what is the value   [#permalink] 26 Apr 2019, 21:56
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