1/2^10 + 1/2^11 + 1/2^12 + 1/2^12

Question

\frac{1}{2^{10}} + \frac{1}{2^{11}} + \frac{1}{2^{12}} + \frac{1}{2^{12}}

A.  \frac{1}{2^7}

B.  \frac{1}{2^8}

C.  \frac{1}{2^9}

D.  \frac{1}{2^{13}}

E.  \frac{1}{2^{45}}

PS21160

BrentGMATPrepNow · Accepted Answer

Key property:  \frac{1}{x^n} = x^{-n}   
For example,  \frac{1}{5^8} = 5^{-8}

So, we can rewrite our sum as follows:  2^{-10} + 2^{-11} + 2^{-12} + 2^{-12}

Factor out  2^{-12}  to get:  2^{-12}(2^2 + 2^1 + 1 + 1)

Evaluate to get:  2^{-12}(4 + 2 + 1 + 1)

Simplify:  2^{-12}(8)

Rewrite as follows:  (2^{-12})(2^3)

Apply the product law to get:  2^{-9}

Rewrite as:  \frac{1}{2^{9}}

Answer: C

Cheers, 
Brent

yashikaaggarwal · Answer

=> (1/2^10)+(1/2^11)+(1/2^12)+(1/2^12)
Using LCM
=> (1*4/2^10*4)+(1*2/2^11*2)+(1/2^12)+(1/2^12)
=> (4/2^12)+(2/2^12)+(1/2^12)+(1/2^12)
=> (4+2+1+1)/(2^12)
=> 8/2^12
=> 2^3/2^12
=> 1/2^9

Answer is C

Posted from my mobile device

Archit3110 · Answer

given 
 \frac{1}{2^{10}} + \frac{1}{2^{11}} + \frac{1}{2^{12}} + \frac{1}{2^{12}} 
can be written as
1/2^10 * ( 1+1/2+1/4+1/4 ) 
or say
1/2^10 * 8/4 ; 1/2^10 * 2 ; 
1/2^9
OPTION C

ScottTargetTestPrep · Answer

First, let’s obtain the common denominator of 2^12. We obtain:

(2^2/2^2)(1/2^10) + (2/2)1/2^11) + 1/2^12 + 1/2^12

2^2/2^12 + 2/2^12 + 1/2^12 + 1/2^12 = 8/2^12 = 2^3/2^12 = 1/2^9

Answer: C

CrackverbalGMAT · Answer

Let try another approach:
The max value in the series is 1/2^10 and the rest of the terms are less than 1/2^10.

since there are 4 terms , we can say that SUM < 4 * 1/2^10
i.e. SUM < 1/2^8

The min value in the series is 1/2^12 and the rest of the terms are greater than 1/2^10.
SUM > 4 * 1/2^12
SUM > 1/2^10

We can conclude that 1/2^10 < SUM < 1/2^8

When we analyze the options, we can see that all options are in decreasing order and only 1/2^9 is in our range.

Option C is the right answer.

Thanks,
Clifin J Francis
GMAT SME

DanTheGMATMan · Answer

Adding exponents- factor out!:

https://www.youtube.com/watch?v=arCYLvpdcGE

ablatt4 · Answer

2^-10(1+2^-1+2^-2+2^-2)

2^-10(2)=2^9

1/2^10 + 1/2^11 + 1/2^12 + 1/2^12

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1/2^10 + 1/2^11 + 1/2^12 + 1/2^12

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