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# If n is a positive integer greater than 1, then 2^{n-1} + 2^

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If n is a positive integer greater than 1, then 2^{n-1} + 2^ [#permalink]  06 Sep 2013, 23:46
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Question Stats:

87% (01:39) correct 13% (01:29) wrong based on 79 sessions
If n is a positive integer greater than 1, then $$2^{n-1} + 2^n =$$

A) $$3^n$$
B) $$2^n+1$$
C) $$2^{2n-1}$$
D) $$2^{n(n-1)}$$
E) $$3*2^{n-1}$$
[Reveal] Spoiler: OA

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Last edited by fozzzy on 07 Sep 2013, 05:31, edited 1 time in total.
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Concentration: Finance, Strategy
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Kudos [?]: 51 [2] , given: 4

Re: if n is a positive integer greater than 1, then 2^{n-1} + 2^ [#permalink]  07 Sep 2013, 02:18
2
KUDOS
fozzzy wrote:
if n is a positive integer greater than 1, then $$2^{n-1} + 2^n =$$
A) $$3^n$$
B) $$2^n+1$$
C) $$2^{2n-1}$$
D) $$2^{n(n-1)}$$
E) $$3*2^{n-1}$$

2^n-1+2^n
=>2^n-1(1+2)
=>2^n-1(3)
=>3*2^n-1
Option E
Director
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Kudos [?]: 622 [0], given: 543

Re: If n is a positive integer greater than 1, then 2^{n-1} + 2^ [#permalink]  07 Sep 2013, 23:27
I didn't understand the manipulation. Could you elaborate...
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Kudos [?]: 57184 [1] , given: 8808

Re: If n is a positive integer greater than 1, then 2^{n-1} + 2^ [#permalink]  08 Sep 2013, 04:19
1
KUDOS
Expert's post
fozzzy wrote:
I didn't understand the manipulation. Could you elaborate...

If n is a positive integer greater than 1, then $$2^{n-1} + 2^n =$$

A) $$3^n$$
B) $$2^n+1$$
C) $$2^{2n-1}$$
D) $$2^{n(n-1)}$$
E) $$3*2^{n-1}$$

Factor out $$2^{n-1}$$:

$$2^{n-1}(1+2)=3*2^{n-1}$$ (notice that $$2^{n-1}*2=2^n$$).

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if-5-x-5-x-3-124-5-y-what-is-y-in-terms-of-x-109080.html

Hope this helps.
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Posts: 902
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Kudos [?]: 622 [0], given: 543

Re: If n is a positive integer greater than 1, then 2^{n-1} + 2^ [#permalink]  08 Sep 2013, 04:32
Here is what I did

$$2^n . 2^{-1}+ 2^n$$

we then get $$2^n [ \frac{1}{2} + 1]$$

$$2^n [ \frac{3}{2}]$$ --------> I stopped over here

so basically this step is valid-----> $$2^n . 2^{-1} [3]$$

Add the exponents we get $$2^{n-1}[3]$$
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Re: If n is a positive integer greater than 1, then 2^{n-1} + 2^   [#permalink] 08 Sep 2013, 04:32
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