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2+2+2^2.... MBA.com CAT

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sarahmailings
 Post subject: 2+2+2^2.... MBA.com CAT
 Post Posted: Mon Nov 01, 2010 7:50 pm 
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Course Students


Posts: 7
Hi,

I've run into trouble with another MBA.com CAT question.

2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8

a)2^9
b)2^10
c)2^16
d)2^35
e)2^37


Generally, when I run into exponent problems that involve base addition that I can't solve I try and factor. But that didn't get me too far in this problem - maybe I've done something wrong. I eventually guessed D under time constraints, but the correct answer is A.

I couldn't find much in the number properties guide to help me. Most of the similar examples involve adding bases with equivalent exponents. A similar approach might help here, but I'm not sure where to start.

I'm grateful for any suggestions.

Thanks.
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graphica
 Post subject: Re: 2+2+2^2.... MBA.com CAT
 Post Posted: Wed Nov 03, 2010 9:14 am 
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Students


Posts: 5
It is a bit lengthy but can done.

2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 = ?

Rewrite the first 2+2 as 2^2

Therefore

2^2[1+1+2+2^2+2^3+2^4+2^5+2^6] Now making 1+1+2=2^2
2^2[2^2{1+1+2+2^2+2^3+2^4}] Now making 1+1+2=2^2
2^2[2^2{2^2(1+1+2+2^2)}] Now making 1+1+2=2^2
2^2[2^2{2^2(2^2+2^2)}] Now making 1+1+2=2^2
2^2[2^2{2^2(2^2(1+1))}] Now making 1+1=2
Finally it comes to
2^2 X 2^2 X 2^2 X 2^2 X 2

Adding the powers since the base is the same makes it
2^2+2+2+2+1 = 2^9

I hope it helps.
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mschwrtz
 Post subject: Re: 2+2+2^2.... MBA.com CAT
 Post Posted: Fri Nov 05, 2010 1:20 am 
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ManhattanGMAT Staff


Posts: 506
Alternatively you could look for a pattern.

2+2=2^2

2+2+2^2=2^3

so you can see that each term in the expression is equal to the sum of all the previous terms, so that adding each term is doubling the previous sum. Doubling=multiplying by 2=increasing the power by 1.
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atul.prasad
 Post subject: Re: 2+2+2^2.... MBA.com CAT
 Post Posted: Sun Nov 14, 2010 3:15 pm 
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Students


Posts: 34
Lets rephrase the question:

2 + 2 + 2^2 + 2^3... 2^8 as

2 + (sum of first 8 terms of a Geometric progression with factor 2 and the first term also as 2)

Sum of n terms of a GP is a (r^n -1 )/(r-1)
where a is the first term, r is the factor and n is the number of terms
On substituting we get:
2 + 2(2^8-1)/(2-1)
= 2 + 2^9 - 2
= 2 ^ 9
(A is the answer)
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jnelson0612
 Post subject: Re: 2+2+2^2.... MBA.com CAT
 Post Posted: Wed Nov 17, 2010 4:14 pm 
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ManhattanGMAT Staff


Posts: 1857
atul, once again, excellent work!

Thank you,

_________________
Jamie Nelson
ManhattanGMAT Instructor
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