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If 2^k – 2^(k+1) + 2^(k–1) = 2km, what is the value of m?

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If 2^k – 2^(k+1) + 2^(k–1) = 2km, what is the value of m?  [#permalink]

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New post 26 Aug 2018, 06:29
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Re: If 2^k – 2^(k+1) + 2^(k–1) = 2km, what is the value of m?  [#permalink]

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New post 26 Aug 2018, 06:41
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i guess expression should be ...= 2^km or (2^K)m because after solving you get 2^k/-2=2km where m can not have any constant value
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Re: If 2^k – 2^(k+1) + 2^(k–1) = 2km, what is the value of m?  [#permalink]

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New post 26 Aug 2018, 06:53
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Re: If 2^k – 2^(k+1) + 2^(k–1) = 2km, what is the value of m?  [#permalink]

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New post 26 Aug 2018, 07:32
Bunuel wrote:
If \(2^k - 2^{k+1} + 2^{k-1} = 2^k*m\), what is the value of m?


(A) \(-1\)

(B) \(\frac{-1}{2}\)

(C) \(\frac{1}{2}\)

(D) \(1\)

(E) \(2\)


Factorize the similar terms..
\(2^k - 2^{k+1} + 2^{k-1} = 2^k*m.........2^{k-1}(2-2^2+1)=2^km......
..2-4+1=2m........m=\frac{-1}{2}\)
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Re: If 2^k – 2^(k+1) + 2^(k–1) = 2km, what is the value of m?  [#permalink]

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New post 26 Aug 2018, 08:45
Bunuel wrote:
If \(2^k - 2^{k+1} + 2^{k-1} = 2^k*m\), what is the value of m?


(A) \(-1\)

(B) \(\frac{-1}{2}\)

(C) \(\frac{1}{2}\)

(D) \(1\)

(E) \(2\)


\(2^k - 2^{k+1} + 2^{k-1} = 2^k*m\)

Or, \(2^k - 2^k*2^1 + 2^k*2^{-1} = 2^k*m\)

Or, \(2^k ( - 2^1 + 2^{-1}) = 2^k*m\)

Or, \(-2 + \frac{1}{2} = m\)

Or, \(m = \frac{-1}{2}\) , Answer must be (B)
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Re: If 2^k – 2^(k+1) + 2^(k–1) = 2km, what is the value of m?  [#permalink]

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New post 26 Aug 2018, 10:34
Bunuel wrote:
If \(2^k - 2^{k+1} + 2^{k-1} = 2^k*m\), what is the value of m?


(A) \(-1\)

(B) \(\frac{-1}{2}\)

(C) \(\frac{1}{2}\)

(D) \(1\)

(E) \(2\)


Since RHS of the expression contains a multiple of \(2^k\), it seems we have to factor out \(2^k\) from LHS, so that the term containing variable(k) would cancel out.

Factoring out \(2^k\), we have

\(2^k(1-2+2^{-1})=2^k*m\)
Or, \(-1+\frac{1}{2}=m\) (Dividing both sides by \(2^k\))
Or, \(m=\frac{-1}{2}\)

Ans. (B)
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Re: If 2^k – 2^(k+1) + 2^(k–1) = 2km, what is the value of m?  [#permalink]

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New post 26 Aug 2018, 10:38
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Bunuel wrote:
If \(2^k - 2^{k+1} + 2^{k-1} = 2^k*m\), what is the value of m?


(A) \(-1\)

(B) \(\frac{-1}{2}\)

(C) \(\frac{1}{2}\)

(D) \(1\)

(E) \(2\)
Answer is B
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Re: If 2^k – 2^(k+1) + 2^(k–1) = 2km, what is the value of m?   [#permalink] 26 Aug 2018, 10:38
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