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A sequence of 10 integers is as follows: 2, 4, 8, 16, 32 ... If the re

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A sequence of 10 integers is as follows: 2, 4, 8, 16, 32 ... If the re  [#permalink]

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New post 21 Jun 2019, 00:25
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A sequence of 10 integers is as follows: 2, 4, 8, 16, 32 ... If the reciprocal of the 10th term is x, then x should be in which of the following ranges?


(A) \(0.000001 < x < 0.00001\)

(B) \(0.00001 < x < 0.0001\)

(C) \(0.0001 < x < 0.001\)

(D) \(0.001 < x < 0.01\)

(E) \(0.01 < x < 0.1\)

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Re: A sequence of 10 integers is as follows: 2, 4, 8, 16, 32 ... If the re  [#permalink]

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New post 21 Jun 2019, 00:34
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Bunuel wrote:
A sequence of 10 integers is as follows: 2, 4, 8, 16, 32 ... If the reciprocal of the 10th term is x, then x should be in which of the following ranges?


(A) \(0.000001 < x < 0.00001\)

(B) \(0.00001 < x < 0.0001\)

(C) \(0.0001 < x < 0.001\)

(D) \(0.001 < x < 0.01\)

(E) \(0.01 < x < 0.1\)


Series is in GP
1st term, a = 2
ratio, r = 2
10th term, x = a*\(r^9\) = 2*\(2^9\) = 1024
Reciprocal of x = 1/1024
\(\frac{1}{10000}\) < \(\frac{1}{1024}\) < \(\frac{1}{1000}\)
--> 0.0001 < x < 0.001

IMO Option C

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Re: A sequence of 10 integers is as follows: 2, 4, 8, 16, 32 ... If the re  [#permalink]

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New post 21 Jun 2019, 00:49
Tenth term in the GP is ar^9=2^10; X=1/2^10; 1/1024; So Xmust be 0.000something (>1) so IMO C
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Re: A sequence of 10 integers is as follows: 2, 4, 8, 16, 32 ... If the re  [#permalink]

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New post 21 Jun 2019, 11:32
1/2^10 = 1/1024 would fall under the range ; \(0.0001 < x < 0.001\)
IMO C

Bunuel wrote:
A sequence of 10 integers is as follows: 2, 4, 8, 16, 32 ... If the reciprocal of the 10th term is x, then x should be in which of the following ranges?


(A) \(0.000001 < x < 0.00001\)

(B) \(0.00001 < x < 0.0001\)

(C) \(0.0001 < x < 0.001\)

(D) \(0.001 < x < 0.01\)

(E) \(0.01 < x < 0.1\)
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A sequence of 10 integers is as follows: 2, 4, 8, 16, 32 ... If the re  [#permalink]

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New post 21 Jun 2019, 15:08
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Not sure where the question is from, but a sequence question can simply never ask you to "guess" the next values in a sequence only by giving you a list of a few numbers. A sequence beginning 2, 4, 8, 16, 32, ... might be the sequence in which the nth term is 2^n -- that's what it looks like. But it could be an infinite number of other sequences as well. It could be that the nth term is given by this rule:

2^n + (n-1)(n-2)(n-3)(n-4)(n-5)

for example, which is equal to 2^n for the first five terms, and is not equal to 2^n for any other terms. So as the question is written, there's no way to guess what the sequence even is, and no way to answer the question. If this were a real GMAT problem, it would provide an algebraic rule, or a description in words, that lets you work out the tenth term without any potential ambiguity.
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A sequence of 10 integers is as follows: 2, 4, 8, 16, 32 ... If the re   [#permalink] 21 Jun 2019, 15:08
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