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What is the value of (2^8 + 2^9 + 2^{10}+ 2^{11}) / 32?

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New post 28 Jan 2019, 01:42
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[GMAT math practice question]

What is the value of \(\frac{(2^8 + 2^9 + 2^{10}+ 2^{11})}{32}\)?

\(A. 80\)
\(B. 96\)
\(C. 100\)
\(D. 120\)
\(E. 160\)

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Re: What is the value of (2^8 + 2^9 + 2^{10}+ 2^{11}) / 32?  [#permalink]

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New post 28 Jan 2019, 01:46
\(\frac{2^8 (1+2^1+2^2+2^3)}{2^5}\) = 15*8 = 120

D is the answer.
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Re: What is the value of (2^8 + 2^9 + 2^{10}+ 2^{11}) / 32?  [#permalink]

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New post 28 Jan 2019, 01:46
MathRevolution wrote:
[GMAT math practice question]

What is the value of \(\frac{(2^8 + 2^9 + 2^{10}+ 2^{11})}{32}\)?

\(A. 80\)
\(B. 96\)
\(C. 100\)
\(D. 120\)
\(E. 160\)



\(\frac{(2^8 + 2^9 + 2^{10}+ 2^{11})}{32}\)?

2^8* ( 1+2+4+8) / 2^5

=> 120
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Re: What is the value of (2^8 + 2^9 + 2^{10}+ 2^{11}) / 32?  [#permalink]

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New post 28 Jan 2019, 01:54
MathRevolution wrote:
[GMAT math practice question]

What is the value of \(\frac{(2^8 + 2^9 + 2^{10}+ 2^{11})}{32}\)?

\(A. 80\)
\(B. 96\)
\(C. 100\)
\(D. 120\)
\(E. 160\)


\(\frac{(2^8 + 2^9 + 2^{10}+ 2^{11})}{32}\)

\(\frac{2^8(1+2+2^{2}+2^{3})}{32}\)

\(\frac{2^8(1+2+4+8)}{32}\)

\(\frac{2^8(15)}{2^{5}}\)

\(15(2^{8}*2^{-5})\)

\(15(2^{8-5}) = 15(2^{3}) = 15*8 = 120\)

Answer D
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Re: What is the value of (2^8 + 2^9 + 2^{10}+ 2^{11}) / 32?  [#permalink]

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New post 30 Jan 2019, 02:23
=>

\(\frac{(2^8 + 2^9 + 2^{10} + 2^{11})}{32}\)
\(= \frac{(2^8 + 2^82^1 + 2^82^2 + 2^82^3)}{2^5}\)
\(= \frac{2^8(1 + 2^1 + 2^2 + 2^3)}{2^5}\)
\(= 2^3(1+2+4+8)\)
\(= 8*15\)
\(= 120\)

Therefore, the answer is D.
Answer: D
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Re: What is the value of (2^8 + 2^9 + 2^{10}+ 2^{11}) / 32?   [#permalink] 30 Jan 2019, 02:23
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