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

Question

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

PareshGmat · Accepted Answer

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

desaichinmay22 · Answer

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

Bunuel · Answer

The correct answer is D.

intheend14 · Answer

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

erikvm · Answer

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?

Bunuel · Answer

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} .

ScottTargetTestPrep · Answer

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

brains · Answer

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

Kinshook · Answer

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

monk123 · Answer

we can multiply 2^9 on both sides- 
 
2^9 x - 2^9/2^6 - 2^9/2^7 - 2^9/2^8 = (2^9*2/2^9) 
 2^9 x - 2^3 - 2^2 - 2 = 2     (taking 2 on right side) 
 2^9 x - 2^3 - 2^2 = 4 
 2^2 ( 2^7 x - 2 - 1 ) = 2^2  
 2^7 x -3 = 1   (taking 2^2on right side) 
 2^7 x= 4 
 x = 2^2 / 2^7 
 x = 2^-5 
 x = (1/2)^5

ANSWER (D)

BlueRocketAsh · Answer

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

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

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