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The value of (2^(14) + 2^(15) + 2^(16) + 2^(17))/5 is [#permalink]
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09 May 2011, 06:51
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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
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Re: The value of (2^(14) + 2^(15) + 2^(16) + 2^(17))/5 is [#permalink]
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09 May 2011, 07:31
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) 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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14 Apr 2012, 14:50
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]
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15 Apr 2012, 07:47
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]
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Re: The value of (2^(14) + 2^(15) + 2^(16) + 2^(17))/5 is [#permalink]
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09 Oct 2013, 20:41
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))/5 is [#permalink]
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09 Oct 2013, 21:15
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]
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21 Oct 2013, 09:50
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 Comments please!



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Re: The value of (2^(14) + 2^(15) + 2^(16) + 2^(17))/5 is [#permalink]
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26 Feb 2014, 02:56
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 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]
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30 Jun 2014, 18:31
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]
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12 Sep 2014, 01:53
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)????



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Re: The value of (2^(14) + 2^(15) + 2^(16) + 2^(17))/5 is [#permalink]
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27 Apr 2015, 13:47
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Re: The value of (2^(14) + 2^(15) + 2^(16) + 2^(17))/5 is [#permalink]
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06 Jun 2016, 08:45
(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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21 Jul 2016, 10:41
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: The 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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22 Aug 2016, 15:15
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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Re: The value of (2^(14) + 2^(15) + 2^(16) + 2^(17))/5 is [#permalink]
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22 Aug 2016, 15:22
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.
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The value of (2^(14) + 2^(15) + 2^(16) + 2^(17))/5 is [#permalink]
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27 May 2017, 09:27
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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14 Aug 2017, 11:29
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 anticipating experts' sage advice ....



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Re: The value of (2^(14) + 2^(15) + 2^(16) + 2^(17))/5 is [#permalink]
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20 Sep 2017, 10:34
Attached is a visual that should help.
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Re: The value of (2^(14) + 2^(15) + 2^(16) + 2^(17))/5 is [#permalink]
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08 Oct 2017, 06:43
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




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