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The value of (2^(-14) + 2^(-15) + 2^(-16) + 2^(-17))/5 is

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The value of (2^(-14) + 2^(-15) + 2^(-16) + 2^(-17))/5 is [#permalink] New post 14 Apr 2012, 12:56
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The value of (2^(-14) + 2^(-15) + 2^(-16) + 2^(-17))/5 is how many times the value of 2^(-17)?

A. 3/2
B. 5/2
C. 3
D. 4
E. 5
[Reveal] Spoiler: OA

Last edited by Bunuel on 14 Apr 2012, 13:51, edited 1 time in total.
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Re: The value of (2^-14)+(2^-15)+(2^-16) + (2^-17) is how ... [#permalink] New post 14 Apr 2012, 13:50
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andih wrote:
The value of (2^-14)+(2^-15)+(2^-16) + (2^-17) is how times the value of 2^-17?

A. 3/2

B. 5/2

C. 3

D. 4

E. 5


Original question reads:
The value of (2^(-14) + 2^(-15) + 2^(-16) + 2^(-17))/5 is how many times the value of 2^(-17)?

We need to find the value of: \frac{\frac{1}{5}*(2^{-14}+2^{-15}+2^{-16}+2^{-17})}{ 2^{-17}}=\frac{\frac{1}{5}*(\frac{1}{2^{14}}+\frac{1}{2^{15}}+\frac{1}{2^{16}}+\frac{1}{2^{17}})}{\frac{1}{2^{17}}}.

Now, \frac{\frac{1}{5}*(\frac{1}{2^{14}}+\frac{1}{2^{15}}+\frac{1}{2^{16}}+\frac{1}{2^{17}})}{\frac{1}{2^{17}}}=\frac{2^{17}}{5}*(\frac{1}{2^{14}}+\frac{1}{2^{15}}+\frac{1}{2^{16}}+\frac{1}{2^{17}})=\frac{1}{5}*(2^3+2^2+2+1)=\frac{1}{5}*15=3.

Answer: C.
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Re: The value of (2^(-14) + 2^(-15) + 2^(-16) + 2^(-17))/5 is [#permalink] New post 15 Apr 2012, 06:47
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if you take 2^(-17) common in the numerator, you will have 2^(-17) { 8 + 4 + 2 + 1} which equals 15.
This 15 cancels with 5 in the denominator and leaves {3} 2^-(17). Slightly quicker this way i feel.
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Re: The value of (2^(-14) + 2^(-15) + 2^(-16) + 2^(-17))/5 is [#permalink] New post 02 Jul 2013, 00:17
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Re: The value of (2^-14)+(2^-15)+(2^-16) + (2^-17) is how ... [#permalink] New post 09 Oct 2013, 19:41
Bunuel wrote:
andih wrote:
The value of (2^-14)+(2^-15)+(2^-16) + (2^-17) is how times the value of 2^-17?

A. 3/2

B. 5/2

C. 3

D. 4

E. 5


Original question reads:
The value of (2^(-14) + 2^(-15) + 2^(-16) + 2^(-17))/5 is how many times the value of 2^(-17)?

We need to find the value of: \frac{\frac{1}{5}*(2^{-14}+2^{-15}+2^{-16}+2^{-17})}{ 2^{-17}}=\frac{\frac{1}{5}*(\frac{1}{2^{14}}+\frac{1}{2^{15}}+\frac{1}{2^{16}}+\frac{1}{2^{17}})}{\frac{1}{2^{17}}}.

Now, \frac{\frac{1}{5}*(\frac{1}{2^{14}}+\frac{1}{2^{15}}+\frac{1}{2^{16}}+\frac{1}{2^{17}})}{\frac{1}{2^{17}}}=\frac{2^{17}}{5}*(\frac{1}{2^{14}}+\frac{1}{2^{15}}+\frac{1}{2^{16}}+\frac{1}{2^{17}})=\frac{1}{5}*(2^3+2^2+2+1)=\frac{1}{5}*15=3.

Answer: C.


Why do we divide by 2^-17?

Thanks,
C
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Re: The value of (2^-14)+(2^-15)+(2^-16) + (2^-17) is how ... [#permalink] New post 09 Oct 2013, 20:15
runningguy wrote:
Bunuel wrote:
andih wrote:
The value of (2^-14)+(2^-15)+(2^-16) + (2^-17) is how times the value of 2^-17?

A. 3/2

B. 5/2

C. 3

D. 4

E. 5


Original question reads:
The value of (2^(-14) + 2^(-15) + 2^(-16) + 2^(-17))/5 is how many times the value of 2^(-17)?

We need to find the value of: \frac{\frac{1}{5}*(2^{-14}+2^{-15}+2^{-16}+2^{-17})}{ 2^{-17}}=\frac{\frac{1}{5}*(\frac{1}{2^{14}}+\frac{1}{2^{15}}+\frac{1}{2^{16}}+\frac{1}{2^{17}})}{\frac{1}{2^{17}}}.

Now, \frac{\frac{1}{5}*(\frac{1}{2^{14}}+\frac{1}{2^{15}}+\frac{1}{2^{16}}+\frac{1}{2^{17}})}{\frac{1}{2^{17}}}=\frac{2^{17}}{5}*(\frac{1}{2^{14}}+\frac{1}{2^{15}}+\frac{1}{2^{16}}+\frac{1}{2^{17}})=\frac{1}{5}*(2^3+2^2+2+1)=\frac{1}{5}*15=3.

Answer: C.


Why do we divide by 2^-17?

Thanks,
C

It is given in the question.

We need to find "how many times the value of 2^(-17)" which means the entire expression is divided by 2^(-17). The quotient is the answer

Hope it is clear
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Re: The value of (2^(-14) + 2^(-15) + 2^(-16) + 2^(-17))/5 is [#permalink] New post 21 Oct 2013, 08:50
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andih wrote:
The value of 2^{-14} + 2^{-15} + 2^{-16} + 2^{-17}/5 is how many times the value of 2^{-17}?

A. 3/2
B. 5/2
C. 3
D. 4
E. 5


2^{-14} + 2^{-15} + 2^{-16} + 2^{-17}/5 -----> Factor out from the nominator 2^{-17}
2^{-17}(2^3+2^2+2^1+1)/5
2^{-17}(8+4+2+1)/5
2^{-17}*15/5
2^{-17}*3

Therefore, the equation is 3 times the value of 2^{-17} and our answer is
[Reveal] Spoiler:
C


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Re: The value of (2^(-14) + 2^(-15) + 2^(-16) + 2^(-17))/5 is [#permalink] New post 26 Feb 2014, 01:56
suk1234 wrote:
andih wrote:
The value of 2^{-14} + 2^{-15} + 2^{-16} + 2^{-17}/5 is how many times the value of 2^{-17}?

A. 3/2
B. 5/2
C. 3
D. 4
E. 5


2^{-14} + 2^{-15} + 2^{-16} + 2^{-17}/5 -----> Factor out from the nominator 2^{-17}
2^{-17}(2^3+2^2+2^1+1)/5
2^{-17}(8+4+2+1)/5
2^{-17}*15/5
2^{-17}*3

Therefore, the equation is 3 times the value of 2^{-17} and our answer is
[Reveal] Spoiler:
C


Comments please!



How many times the value of 2^{-17} means just multiply the complete equation by 2^17 (Please note the power sign has been changed) & we get the answer

(8+4+2+1) / 5 = 3 = Answer = C
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Re: The value of (2^(-14) + 2^(-15) + 2^(-16) + 2^(-17))/5 is [#permalink] New post 30 Jun 2014, 17:31
The question asked
the value of (2^(-14) + 2^(-15) + 2^(-16) + 2^(-17))/5 is how many times the value of 2^(-17)?

Lets say (2^(-14) + 2^(-15) + 2^(-16) + 2^(-17))/5 = x* 2^(-17) --> (X times of 2^(-17)), So basically we need to find what is x ?

looks like we need to simplify the exponents to make given values in form desire one ..

lets Simplify Given Part , if we take 2^(-17) from numerator the simplified numerator will be ..

2^(-17)(2^(3) + 2^(2) + 2^(1) + 2^(0) )/5 = x*2^(-17)

why 2^(3) + 2^(2) ..... ? because if we want to make 2^(-17) = 2^(-14) we required to add 2^(3) positive power . same for other...


now divide 2^(-17) both side , x = (2^(3) + 2^(2) + 2^(1) + 2^(0) )/5 => x= (8+4+2+1)/5 => x =15/5 => x=3 Answer is C.
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Re: The value of (2^(-14) + 2^(-15) + 2^(-16) + 2^(-17))/5 is [#permalink] New post 12 Sep 2014, 00:53
hi according to answer 2^17 (Please note the power sign has been changed) & we get the answer

(8+4+2+1) / 5 = 3

how you reach this (8+4+2+1)????
Re: The value of (2^(-14) + 2^(-15) + 2^(-16) + 2^(-17))/5 is   [#permalink] 12 Sep 2014, 00:53
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