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Math Expert V
Joined: 02 Sep 2009
Posts: 58344
If x − 1/2^6 − 1/2^7 − 1/2^8 = 2/2^9, then x =  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 76% (01:52) correct 24% (02:34) wrong based on 182 sessions

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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

Kudos for a correct solution.

Source: Chili Hot GMAT

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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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8
$$x - \frac{1}{2^6} - \frac{1}{2^7} - \frac{1}{2^8} = \frac{2}{2^9}$$

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

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

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

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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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1
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
Math Expert V
Joined: 02 Sep 2009
Posts: 58344
Re: If x − 1/2^6 − 1/2^7 − 1/2^8 = 2/2^9, then x =  [#permalink]

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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

Kudos for a correct solution.

Source: Chili Hot GMAT

The correct answer is 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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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.

D
Manager  Joined: 26 Feb 2015
Posts: 110
Re: If x − 1/2^6 − 1/2^7 − 1/2^8 = 2/2^9, then x =  [#permalink]

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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?
Math Expert V
Joined: 02 Sep 2009
Posts: 58344
Re: If x − 1/2^6 − 1/2^7 − 1/2^8 = 2/2^9, then x =  [#permalink]

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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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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

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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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x= (2/2^9) +(1/2)^8 + (1/2)^7 + (1/2)^6
x =( 1/2^8) + ( 1/2^8)+ (1/2)^7 + (1/2)^6
x= (2/2^8) + (1/2)^7 + (1/2)^6
x = (1/2^7) +(1/2)^7 + (1/2)^6
x = (2/2^7) + (1/2)^6
x= (1/2)^6 + (1/2)^6
x = (2/2^6)
x = 1/2^5

Hence answer is D
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SVP  P
Joined: 03 Jun 2019
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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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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

Kudos for a correct solution.

Source: Chili Hot GMAT

Given: $$x - \frac{1}{2^6} - \frac{1}{2^7} - \frac{1}{2^8} = \frac{2}{2^9}$$

Asked: x = ?

$$x - \frac{1}{2^6} - \frac{1}{2^7} - \frac{1}{2^8} = \frac{2}{2^9}$$

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

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

$$x = \frac{1}{2^5}-\frac{1}{2^6} + \frac{1}{2^6}-\frac{1}{2^7} +\frac{1}{2^7}-\frac{1}{2^8} + \frac{1}{2^8}$$

$$x = \frac{1}{2^5}$$

IMO D
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E-mail : kinshook.chaturvedi@gmail.com If x − 1/2^6 − 1/2^7 − 1/2^8 = 2/2^9, then x =   [#permalink] 18 Aug 2019, 07:23
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