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

Question

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

CareerGeek · Accepted Answer

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

Pls Hit Kudos if you like the solution

Lampard42 · Answer

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

Archit3110 · Answer

1/2^10 = 1/1024 would fall under the range ;  0.0001 < x < 0.001 
IMO C

IanStewart · Answer

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.

MV94 · Answer

The reciprocal of a number with K digits has K-1 leading zeros (unless it is 10^n, in which case it has K-2 leading zeros).

2^10 = 1024 -> 4 digits.

Therefore n has 3 leading zeros.

Must be C.

ScottTargetTestPrep · Answer

Solution:
 
We see that 2 = 2^1, 4 = 2^2, 8 = 2^3, etc. In other words, the nth term of the sequence is 2^n. Thus, the 10th term is 2^10 = 1,024, and since x is the reciprocal of the 10th term, then x = 1/1,024, which has a value between 1/10,000 = 0.0001 and 1/1,000 = 0.001.

Answer: C

CEdward · Answer

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) \(0.01 < x < 0.1\)

dhruvie · Answer

5th term of the GP is 32, 10th term will be 32*32.

Reciprocal will be 1/(32*32)

1/30 = 0.0333..., 1/(30*30) = 0.00111...

But the number will be smaller than 0.00111... since denominator is 32*32 not 30*30.

Hence between 0.001 and 0.0001 -  OPTION C.

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

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