\(\dfrac12, \dfrac14, \dfrac18, \dfrac1{16}, \dfrac1{32}, \ldots\)
In the sequence above each term after the first one-half the previous term. If \(x\) is the tenth term of the sequence, then \(x\) satisfies which of the following inequalities?
A) \(0.1 < x < 1\)
B) \(0.01 < x < 0.1\)
C) \(0.001 < x < 0.01\)
D) \(0.0001 < x < 0.001\)
E) \(0.00001 < x < 0.0001\)
[spoiler]OA=D[/spoiler]
Source: GMAT Prep
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
In the sequence above each term after the first one-half the previous term. If \(x\) is the tenth term of the sequence,
This topic has expert replies
GMAT/MBA Expert
-
Jay@ManhattanReview
- GMAT Instructor
- Posts: 3008
- Joined: Mon Aug 22, 2016 6:19 am
- Location: Grand Central / New York
- Thanked: 470 times
- Followed by:34 members
Given that the terms are \(\dfrac12, \dfrac14, \dfrac18, \dfrac1{16}, \dfrac1{32}, \ldots\), we can write them asVJesus12 wrote: ↑Tue Jun 30, 2020 8:08 am\(\dfrac12, \dfrac14, \dfrac18, \dfrac1{16}, \dfrac1{32}, \ldots\)
In the sequence above each term after the first one-half the previous term. If \(x\) is the tenth term of the sequence, then \(x\) satisfies which of the following inequalities?
A) \(0.1 < x < 1\)
B) \(0.01 < x < 0.1\)
C) \(0.001 < x < 0.01\)
D) \(0.0001 < x < 0.001\)
E) \(0.00001 < x < 0.0001\)
[spoiler]OA=D[/spoiler]
Source: GMAT Prep
\(\dfrac12, \dfrac1{2^2}, \dfrac1{2^3}, \dfrac1{2^4}, \dfrac1{2^5}, \ldots\)
Thus, the 10th term = \( x = \dfrac1{2^{10}} = \dfrac1{1,024} < \left[\dfrac1{1,000} = \dfrac1{10^3} = 0.001 \right]\)
Similarly, the 10th term = \( x = \dfrac1{2^{10}} = \dfrac1{1,024} > \left[\dfrac1{10,000} = \dfrac1{10^4} = 0.0001 \right]\)
The correct answer is D.
Correct answer: D
Hope this helps!
-Jay
_________________
Manhattan Review GMAT Prep
Locations: Manhattan GRE | LSAT Practice Questions | SAT Practice Test | GMAT Info | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
