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

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Joined: 02 Sep 2009
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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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26 Aug 2018, 06:29
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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) $$2$$

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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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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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26 Aug 2018, 06:53
alitariquet wrote:
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

Its' 2^k*m. Edited. Thank you.
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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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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..
$$2^k - 2^{k+1} + 2^{k-1} = 2^k*m.........2^{k-1}(2-2^2+1)=2^km...... ..2-4+1=2m........m=\frac{-1}{2}$$
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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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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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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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) $$2$$
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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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