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If x − 1/2^6 − 1/2^7 − 1/2^8 = 2/2^9, then x =

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If x − 1/2^6 − 1/2^7 − 1/2^8 = 2/2^9, then x =  [#permalink]

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New post 04 Dec 2014, 07:34
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A
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D
E

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77% (01:53) correct 23% (02:39) wrong based on 128 sessions

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Re: If x − 1/2^6 − 1/2^7 − 1/2^8 = 2/2^9, then x =  [#permalink]

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New post 04 Dec 2014, 19:39
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\(x - \frac{1}{2^6} - \frac{1}{2^7} - \frac{1}{2^8} = \frac{2}{2^9}\)

\(x = \frac{1}{2^6} + \frac{1}{2^7} + \frac{1}{2^8} + \frac{2}{2^9}\)

\(x = \frac{1*2*2*2}{2^9} + \frac{1*2*2}{2^9} + \frac{1*2}{2^9} + \frac{2}{2^9}\)

\(x = \frac{8+4+2+2}{2^9} = \frac{16}{2^9} = \frac{1}{2^5}\)

Answer = D
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Re: If x − 1/2^6 − 1/2^7 − 1/2^8 = 2/2^9, then x =  [#permalink]

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New post 04 Dec 2014, 07:44
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1
x= 2/2^9+1/2^6+1/2^7+1/2^8
Take LCM i.e. 2^9

x=(2+2^3+2^2+2)/2^9
x=(2+8+4+2)/2^9
x=16/2^9
x=2^4/2^9
x=1/2^5

Ans - D
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Re: If x − 1/2^6 − 1/2^7 − 1/2^8 = 2/2^9, then x =  [#permalink]

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Re: If x − 1/2^6 − 1/2^7 − 1/2^8 = 2/2^9, then x =  [#permalink]

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New post 05 Dec 2014, 11:40
Choice D

When we start, notice that the RHS equals 2/2^9 = 1/2^8. Then add the factor of 1/2^8 to both sides yielding 2/2^8 on the RHS.
Keep doing this until you reach x-1/2^6 = 1/2^6, yielding x = 1/2^5.

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Re: If x − 1/2^6 − 1/2^7 − 1/2^8 = 2/2^9, then x =  [#permalink]

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New post 08 Mar 2015, 13:14
From this
\(x = \frac{1}{2^6} + \frac{1}{2^7} + \frac{1}{2^8} + \frac{2}{2^9}\)


To this
\(x = \frac{1*2*2*2}{2^9} + \frac{1*2*2}{2^9} + \frac{1*2}{2^9} + \frac{2}{2^9}\)

\(x = \frac{8+4+2+2}{2^9} = \frac{16}{2^9} = \frac{1}{2^5}\)



How?
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Re: If x − 1/2^6 − 1/2^7 − 1/2^8 = 2/2^9, then x =  [#permalink]

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New post 08 Mar 2015, 13:39
erikvm wrote:
From this
\(x = \frac{1}{2^6} + \frac{1}{2^7} + \frac{1}{2^8} + \frac{2}{2^9}\)


To this
\(x = \frac{1*2*2*2}{2^9} + \frac{1*2*2}{2^9} + \frac{1*2}{2^9} + \frac{2}{2^9}\)

\(x = \frac{8+4+2+2}{2^9} = \frac{16}{2^9} = \frac{1}{2^5}\)



How?


This is also basic (finding the common denominator):

\(x = \frac{1}{2^6} + \frac{1}{2^7} + \frac{1}{2^8} + \frac{2}{2^9}=\frac{2^3}{2^9} + \frac{2^2}{2^9} + \frac{2}{2^9} + \frac{2}{2^9}=\frac{2^3+2^2+2+2}{2^9}\).
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Re: If x − 1/2^6 − 1/2^7 − 1/2^8 = 2/2^9, then x =  [#permalink]

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New post 08 Feb 2017, 19:49
Bunuel wrote:

Tough and Tricky questions: Exponents.



If \(x - \frac{1}{2^6} - \frac{1}{2^7} - \frac{1}{2^8} = \frac{2}{2^9}\), then x =

A) 1/2
B) 1/2^3
C) 1/2^4
D) 1/2^5
E) 1/2^9


We can multiply the given equation by 2^9 and we have:

x(2^9) - 2^3 - 2^2 - 2^1 = 2

x(2^9) = 2 + 2^1 + 2^2 + 2^3

x(2^9) = 16

x = 16/2^9

x = 2^4/2^9

x = 1/2^5

Answer: D
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Re: If x − 1/2^6 − 1/2^7 − 1/2^8 = 2/2^9, then x =  [#permalink]

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Re: If x − 1/2^6 − 1/2^7 − 1/2^8 = 2/2^9, then x =   [#permalink] 29 Mar 2019, 21:13
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