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4 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 =
[#permalink]
12 May 2021, 08:53
12 May 2021, 08:53
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90% (01:36) correct
10% (01:31) wrong based on 10 sessions
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\(4 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 =\)
A. 2^7
B. 2^8
C. 2^16
D. 2^28
E. 2^29
A. 2^7
B. 2^8
C. 2^16
D. 2^28
E. 2^29
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Joined: 10 Apr 2015
Posts: 6218
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Re: 4 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 =
[#permalink]
12 May 2021, 09:02
12 May 2021, 09:02
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Carcass wrote:
\(4 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 =\)
A. 2^7
B. 2^8
C. 2^16
D. 2^28
E. 2^29
A. 2^7
B. 2^8
C. 2^16
D. 2^28
E. 2^29
Look for a pattern
4 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 = 4 + 4 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7
= 8 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7
= 2^3 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7
Now examine the following...
2^3 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 = 8 + 8 + 2^4 + 2^5 + 2^6 + 2^7
= 16 + 2^4 + 2^5 + 2^6 + 2^7
= 2^4 + 2^4 + 2^5 + 2^6 + 2^7
And then...
2^4 + 2^4 + 2^5 + 2^6 + 2^7 = 16 + 16 + 2^5 + 2^6 + 2^7
= 32 + 2^5 + 2^6 + 2^7
= 2^5 + 2^5 + 2^6 + 2^7
In general, 2^n + 2^n = 2^(n+1)
This should make sense since 2^n + 2^n = 2^n(1 + 1) = (2^n)(2^1) = 2^(n+1)
So, continuing with the pattern, we get a TOTAL SUM of 2^8
Answer: B
gmatclubot
Re: 4 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 = [#permalink]
12 May 2021, 09:02
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