NEW HERE? LEARN MORE
closeclose
Last visit was: 24 Apr 2024, 19:14 It is currently 24 Apr 2024, 19:14
Decision Tracker
My Rewards
New posts
New comers' posts

Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

In the sequence above each term after

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
avatar
HarveyKlaus
Manager
Manager
Joined: 18 Feb 2015
Posts: 71
Own Kudos [?]: 567 [41]
Given Kudos: 15
Send PM
In the sequence above each term after [#permalink] New post   Updated on: 30 Jun 2017, 03:39
1
Kudos
40
Bookmarks
00:00
A
B
C
D
E

Difficulty:

25% (medium)

Question Stats:

72% (01:41) correct 28% (01:55) wrong based on 899 sessions
Hide Show timer Statistics
1/2, 1/4, 1/8, 1/16, 1/32, ....

In the sequence above each term after 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
ShowHide Answer
Official Answer
D

Originally posted by HarveyKlaus on 10 Jul 2016, 02:35.
Last edited by abhimahna on 30 Jun 2017, 03:39, edited 1 time in total.
Edited the question
Most Helpful Reply
avatar
shashanksst94
Intern
Intern
Joined: 02 Feb 2016
Posts: 1
Own Kudos [?]: 16 [10]
Given Kudos: 67
Send PM
Re: In the sequence above each term after [#permalink] New post   10 Jul 2016, 07:31
8
Kudos
2
Bookmarks
In the Sequence notice that the sequence is just the 1/(2^n) ...
so for 1st term=1/2^1=1/2
2nd term=1/(2^2)1/4, 3rd term=1/(2^3)=1/8 and so on...
Thus the 10th term will be 1/(2^10)=1/1024
Roughly, 1/1024 can be 1/1000=0.001 but since denominator is a bit more than 1000 therefore the actual value will be a bit less than 0.001.

thus the ans will lie btw. 0.0001 and 0.001.(D)
User avatar
G
msk0657
Retired Moderator
Joined: 26 Nov 2012
Posts: 473
Own Kudos [?]: 493 [8]
Given Kudos: 46
Send PM
Re: In the sequence above each term after [#permalink] New post   10 Jul 2016, 06:23
5
Kudos
3
Bookmarks
HarveyKlaus wrote:
Hi all,
I am not able to solve this question by the normal sequence formula. Can someone please help? Thanks

1/2, 1/4, 1/8, 1/16, 1/32, ....

In the sequence above each term after 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


Hi,

This is how I tried.

We are asked to find the tenth term of the series 1/2, 1/4, 1/8, 1/16, 1/32, ....

If you observe that denominator is power of 2 i.e. \(2^1\), \(2^2\),\(2^3\).... then tenth term will be 2^10.

Here 2^10 = 1024

Then 1/1024 = 0.024. Now check where this number fits in and this value is greater than 0.001. So C is eliminated.

Then only D satisfies this condition.
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6821
Own Kudos [?]: 29915 [7]
Given Kudos: 799
Location: Canada
Send PM
Re: In the sequence above each term after [#permalink] New post   11 Dec 2021, 07:25
3
Kudos
4
Bookmarks
Expert Reply
Top Contributor
HarveyKlaus wrote:
1/2, 1/4, 1/8, 1/16, 1/32, ....

In the sequence above each term after 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


We can think of the terms as follows....
term_1 = 1/2
term_2 = (1/2)(1/2) = (1/2)²
term_3 = (1/2)(1/2)(1/2) = (1/2)³
term_4 = (1/2)(1/2)(1/2)(1/2) = (1/2)⁴
.
.
.
term_n = (1/2)(1/2)(1/2)(1/2) = (1/2)^n

So, term_10 = (1/2)¹⁰ = 1/2¹⁰ = 1/1,024

We get: 1/10,000 < 1/1,024 < 1/1,000
In other words: 0.0001 < 1/1,024 < 0.01

Answer: D
General Discussion
User avatar
B
syahasa2
Manager
Manager
Joined: 26 Mar 2016
Posts: 58
Own Kudos [?]: 53 [0]
Given Kudos: 61
Location: Greece
GMAT 1: 710 Q51 V34
GPA: 2.9
Send PM
Reviews Badge
Re: In the sequence above each term after [#permalink] New post   10 Jul 2016, 06:39
It's just about calculating the tenth term which is 2^10=1024.
Then you should be able to define where this number fits.
avatar
drbyrnes
Intern
Intern
Joined: 16 Jan 2017
Posts: 1
Own Kudos [?]: [0]
Given Kudos: 0
Send PM
Re: In the sequence above each term after [#permalink] New post   03 Jun 2017, 13:23
msk0657 wrote:
Hi,

This is how I tried.

We are asked to find the tenth term of the series 1/2, 1/4, 1/8, 1/16, 1/32, ....

If you observe that denominator is power of 2 i.e. \(2^1\), \(2^2\),\(2^3\).... then tenth term will be 2^10.

Here 2^10 = 1024

Then 1/1024 = 0.024. Now check where this number fits in and this value is greater than 0.001. So C is eliminated.

Then only D satisfies this condition.


What is your approach to solve for 2^10 and 1/1024?
User avatar
L
generis
Senior SC Moderator
Joined: 22 May 2016
Posts: 5330
Own Kudos [?]: 35486 [2]
Given Kudos: 9464
Send PM
CAT Tests
Re: In the sequence above each term after [#permalink] New post   06 Jun 2017, 13:04
2
Kudos
Expert Reply
msk0657 wrote:
HarveyKlaus wrote:

1/2, 1/4, 1/8, 1/16, 1/32, ....

In the sequence above each term after 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


Hi,

This is how I tried.

We are asked to find the tenth term of the series 1/2, 1/4, 1/8, 1/16, 1/32, ....

If you observe that denominator is power of 2 i.e. \(2^1\), \(2^2\),\(2^3\).... then tenth term will be 2^10.

Here 2^10 = 1024

Then 1/1024 = 0.024. Now check where this number fits in and this value is greater than 0.001. So C is eliminated.

Then only D satisfies this condition.


Then 1/1024 = 0.024
msk0657 , how did you get this value?

On a calculator it comes out as .0009765625.
User avatar
P
ocelot22
Manager
Manager
Joined: 16 Oct 2011
Posts: 171
Own Kudos [?]: 125 [1]
Given Kudos: 545
GMAT 1: 640 Q38 V40
GMAT 2: 650 Q44 V36
GMAT 3: 570 Q31 V38
GMAT 4: 720 Q49 V40
GPA: 3.75
Send PM
Reviews Badge
Re: In the sequence above each term after [#permalink] New post   16 Jan 2019, 16:21
1
Kudos
HarveyKlaus wrote:
1/2, 1/4, 1/8, 1/16, 1/32, ....

In the sequence above each term after 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


When comparing powers of some value to either powers of 10 or some decimal with a trailing 1 (which is also a power of 10), one approach is to rewrite our term, to get it as close to a power of 10 as possible. For (1/2)^10, a base of 1/8 is gonna be as close to 1/10 as we can get. Then (1/2)^10 = 1/(2^3 *2^3 *2^3 *2) = (1/8)^3*1/2 is approximately
(1/10)^3 *1/2 = .001*1/2 = approximately .0005, which falls between .0001 and .001. The answer is D
User avatar
G
jfranciscocuencag
Manager
Manager
Joined: 12 Sep 2017
Posts: 239
Own Kudos [?]: 117 [0]
Given Kudos: 132
Send PM
In the sequence above each term after [#permalink] New post   20 Jan 2019, 11:50
msk0657 wrote:
HarveyKlaus wrote:
Hi all,
I am not able to solve this question by the normal sequence formula. Can someone please help? Thanks

1/2, 1/4, 1/8, 1/16, 1/32, ....

In the sequence above each term after 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


Hi,

This is how I tried.

We are asked to find the tenth term of the series 1/2, 1/4, 1/8, 1/16, 1/32, ....

If you observe that denominator is power of 2 i.e. \(2^1\), \(2^2\),\(2^3\).... then tenth term will be 2^10.

Here 2^10 = 1024

Then 1/1024 = 0.024. Now check where this number fits in and this value is greater than 0.001. So C is eliminated.

Then only D satisfies this condition.


Hello msk0657 !

How did you get this result?

Then 1/1024 = 0.024

Kind regards!
User avatar
S
sanjna2023
Manager
Manager
Joined: 17 Feb 2017
Posts: 82
Own Kudos [?]: 37 [0]
Given Kudos: 629
Location: India
Schools: IESE '25 (A) INSEAD Aug'23 intake (A$) ISB '24 (A) HEC Sep'24 Intake (D)
GMAT 1: 680 Q48 V35
GPA: 4
WE:Consulting (Consulting)
Send PM
Reviews Badge
In the sequence above each term after [#permalink] New post   09 Sep 2020, 08:31
We calculate 2^10 = 1024

Thus,

1/1000 > 1/1024
0.001 > 1/1024

Only option D fits with this calculation so we can easily select the same.
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32657
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: In the sequence above each term after [#permalink] New post   26 Feb 2023, 15:35
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: In the sequence above each term after [#permalink]
26 Feb 2023, 15:35
Moderators:
Bunuel
Math Expert
92900 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions