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Express 2^20-2^19-2^18-2^17 as a power of 2.

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Math Revolution GMAT Instructor
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Express 2^20-2^19-2^18-2^17 as a power of 2.  [#permalink]

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New post 22 Mar 2019, 00:39
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

81% (01:08) correct 19% (01:11) wrong based on 43 sessions

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[GMAT math practice question]

Express \(2^{20}-2^{19}-2^{18}-2^{17}\) as a power of \(2\).

\(A. 2^{15}\)
\(B. 2^{16}\)
\(C. 2^{17}\)
\(D. 2^{18}\)
\(E. 2^{19}\)

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Re: Express 2^20-2^19-2^18-2^17 as a power of 2.  [#permalink]

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New post 22 Mar 2019, 02:40
1
1
Take 2^17 common. Then 2^17(8-4-2-1) = 2^17.

C is the answer
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Re: Express 2^20-2^19-2^18-2^17 as a power of 2.  [#permalink]

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New post 22 Mar 2019, 09:56
MathRevolution wrote:
[GMAT math practice question]

Express \(2^{20}-2^{19}-2^{18}-2^{17}\) as a power of \(2\).

\(A. 2^{15}\)
\(B. 2^{16}\)
\(C. 2^{17}\)
\(D. 2^{18}\)
\(E. 2^{19}\)


Test an analogous case with easier values:
2⁴ - 2³ - 2² - = 16 - 8 - 4 - 2 =
The matching blue portions imply the following:
2²⁰ - 2¹⁹ - 2¹⁸ - 2¹⁷ = 2¹⁷

.
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Math Revolution GMAT Instructor
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Express 2^20-2^19-2^18-2^17 as a power of 2.  [#permalink]

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New post 24 Mar 2019, 18:21
=>

\(2^{20}-2^{19}-2^{18}-2^{17}\)
\(=2^32^{17}- 2^22^{17}-2^12^{17}-2^{17}\)
\(= 2^{17} (8-4-2-1)\)
\(= 2^{17}(1)\)
\(= 2^{17}\)

Therefore, the answer is C.
Answer: C
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Express 2^20-2^19-2^18-2^17 as a power of 2.   [#permalink] 24 Mar 2019, 18:21
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