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What is the value of [m]2 + 2^1 + 2^2 + 2^3...........2^{18}[/m]? A)
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11 May 2021, 03:46
11 May 2021, 03:46
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What is the value of \(2 + 2^1 + 2^2 + 2^3...........2^{18}\)?
A) \(2^{19}\)
B) \(2^{171}\)
C) \(2^{172}\)
D) \(2^{18!}\)
E) \(2 + 2^{18!}\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A) \(2^{19}\)
B) \(2^{171}\)
C) \(2^{172}\)
D) \(2^{18!}\)
E) \(2 + 2^{18!}\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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Re: What is the value of [m]2 + 2^1 + 2^2 + 2^3...........2^{18}[/m]? A)
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11 May 2021, 05:52
11 May 2021, 05:52
1
Carcass wrote:
What is the value of \(2 + 2^1 + 2^2 + 2^3...........2^{18}\)?
A) \(2^{19}\)
B) \(2^{171}\)
C) \(2^{172}\)
D) \(2^{18!}\)
E) \(2 + 2^{18!}\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A) \(2^{19}\)
B) \(2^{171}\)
C) \(2^{172}\)
D) \(2^{18!}\)
E) \(2 + 2^{18!}\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
One approach is to start listing values and look for a pattern (I'll let others do that)
We can also solve the question quickly by eliminating 4 of the answer choices.
Notice what would happen if we took the sum 2 + 2^1 + 2^2 + 2^3 + . . . . 2^17 + 2^18 replaced each value with 2^18
The NEW sum would definitely be bigger than the ORIGINAL sum
That is: 2 + 2^1 + 2^2 + 2^3 + . . . . 2^17 + 2^18 < 2^18 + 2^18 + 2^18 + 2^18 . . . + 2^18 + 2^18
Notice that the NEW sum is the sum of nineteen 2^18's
So, we can write: 2 + 2^1 + 2^2 + 2^3 + . . . . 2^17 + 2^18 < (19 )(2^18)
Now notice that 19 < 2^5, so we can write: 2 + 2^1 + 2^2 + 2^3 + . . . . 2^17 + 2^18 < (19 )(2^18) < (2^4 )(2^18)
Simplify the right-most expression to get: 2 + 2^1 + 2^2 + 2^3 + . . . . 2^17 + 2^18 < (19 )(2^18) < 2^22
So, we can conclude that: 2 + 2^1 + 2^2 + 2^3 + . . . . 2^17 + 2^18 < 2^22
Only answer choice A is less than 2^22
gmatclubot
Re: What is the value of [m]2 + 2^1 + 2^2 + 2^3...........2^{18}[/m]? A) [#permalink]
11 May 2021, 05:52
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