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Intern  Joined: 04 May 2011
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The value of (2^(-14) + 2^(-15) + 2^(-16) + 2^(-17))/5 is  [#permalink]

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Question Stats: 79% (01:41) correct 21% (02:19) wrong based on 2514 sessions

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The value of $$\frac{2^{(-14)} + 2^{(-15)} + 2^{(-16)} + 2^{(-17)}}{5}$$ is how many times the value of $$2^{(-17)}$$?

A. 3/2
B. 5/2
C. 3
D. 4
E. 5
Math Expert V
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Posts: 59588
Re: The value of (2^(-14) + 2^(-15) + 2^(-16) + 2^(-17))/5 is  [#permalink]

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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

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

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GMAT 1: 680 Q44 V39 Re: The value of (2^(-14) + 2^(-15) + 2^(-16) + 2^(-17))/5 is  [#permalink]

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21
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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.
##### General Discussion
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Re: The value of (2^(-14) + 2^(-15) + 2^(-16) + 2^(-17))/5 is  [#permalink]

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5
2^-14+2^-15+2^-16+2^-17/5

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

= = 2^-17 * 15/5 = 3(2^-17)

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Re: The value of (2^(-14) + 2^(-15) + 2^(-16) + 2^(-17))/5 is  [#permalink]

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Re: The value of (2^(-14) + 2^(-15) + 2^(-16) + 2^(-17))/5 is  [#permalink]

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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

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

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))/5 is  [#permalink]

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1
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

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

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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Posts: 45
Re: The value of (2^(-14) + 2^(-15) + 2^(-16) + 2^(-17))/5 is  [#permalink]

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12
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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

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Re: The value of (2^(-14) + 2^(-15) + 2^(-16) + 2^(-17))/5 is  [#permalink]

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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

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]

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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)?

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]

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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)????
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See attachment
Time: 30 Seconds
Attachments Solution.PNG [ 4.04 KiB | Viewed 55603 times ]

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Re: The value of (2^(-14) + 2^(-15) + 2^(-16) + 2^(-17))/5 is  [#permalink]

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(2^-14 + 2^-15 + 2^-16 + 2^-17)/5 = 2^-17*(2^3 + 2^2 + 2 + 1) / 5
= 2^-17 * (15)/5 = 2^-17 * 3

Correct Option: C
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Re: The value of (2^(-14) + 2^(-15) + 2^(-16) + 2^(-17))/5 is  [#permalink]

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carollu wrote:
The value of $$\frac{2^{(-14)} + 2^{(-15)} + 2^{(-16)} + 2^{(-17)}}{5}$$ is how many times the value of $$2^{(-17)}$$?

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

We start by translating the question. We are asked (2^-14) + (2^-15) + (2^-16) + (2^-17) is how times the value of 2^-17. We can express it as the following: _________________

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Re: The value of (2^(-14) + 2^(-15) + 2^(-16) + 2^(-17))/5 is  [#permalink]

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I think we can solve it another way.
please expert correct me if I am wrong.
2^(-17)* (2^3+2^2+2^1+1)/5 = 2^(-17)*(8+4+2+1)/5
2^(-17)*(15)/5 = 2^(-17)*(3)
So finally, (2^(-14) + 2^(-15) + 2^(-16) + 2^(-17))/5 is 3 time 2^(-17).
I think It is simple and direct. but one should get the idea. It is wordy and looks complicated and let me be scared.
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GMAT 1: 790 Q51 V49 GRE 1: Q170 V170 Re: The value of (2^(-14) + 2^(-15) + 2^(-16) + 2^(-17))/5 is  [#permalink]

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4
1
Riffing on Scott's solution above. Instead of 'pulling out' a 2^-17, you can multiply both sides by 2^17 to simplify all of the exponents.
Attachments gmatclub 2-17.png [ 27.9 KiB | Viewed 47475 times ]

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

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Is it possible for us to just assume that 2^$${-14}$$ + 2^ $${-15}$$ .... is the same as 2^$${-1}$$ + 2^ $${-2}$$+ 2^ $${-3}$$+ 2^ $${-4}$$ /5?

for me it worked well.... then we need to know how much is 2^ $${-4}$$ from that expression

it will give us $$(\frac{1}{2}+\frac{1}{4}+ \frac{1}{8}+ \frac{1}{16})/5$$ which is equal to 15/80 -> or 3/16........ which is 3 times 2^ $${-4}$$
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The value of (2^(-14) + 2^(-15) + 2^(-16) + 2^(-17))/5 is  [#permalink]

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carollu wrote:
The value of $$\frac{2^{(-14)} + 2^{(-15)} + 2^{(-16)} + 2^{(-17)}}{5}$$ is how many times the value of $$2^{(-17)}$$?

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

hi

what is wrong with below ...?

2^-14( 1 + 1/2 + 1/4 + 1/8)

= 2^-14 x 15/8 x 1/5

= 2^-14 x 3/8

now it is 2^-14 x 3/8 x 1/2^17..

= 3 times

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Re: The value of (2^(-14) + 2^(-15) + 2^(-16) + 2^(-17))/5 is  [#permalink]

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Top Contributor
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Attached is a visual that should help.
Attachments Screen Shot 2017-09-20 at 10.31.39 AM.png [ 98.14 KiB | Viewed 27744 times ]

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GMAT 1: 720 Q49 V40 Re: The value of (2^(-14) + 2^(-15) + 2^(-16) + 2^(-17))/5 is  [#permalink]

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carollu wrote:
The value of $$\frac{2^{(-14)} + 2^{(-15)} + 2^{(-16)} + 2^{(-17)}}{5}$$ is how many times the value of $$2^{(-17)}$$?

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

I found the following answer to be the most simplest,

$$\frac{2^{(-14)} + 2^{(-15)} + 2^{(-16)} + 2^{(-17)}}{5}$$ = $$\frac{2^{(-14)} (1+2^{(-1)}+2^{(-2)}+2^{(-3)})}{5}$$

= {2^(-14) [(2^3)+(2^2)+2+1]/(2^3)} / 5

= {2^(-17) [8+4+2+1] / 5

= 2^(-17) * 3

Ans C Re: The value of (2^(-14) + 2^(-15) + 2^(-16) + 2^(-17))/5 is   [#permalink] 08 Oct 2017, 06:43

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