Oct 14 08:00 PM PDT  11:00 PM PDT Join a 4day FREE online boot camp to kick off your GMAT preparation and get you into your dream bschool in R2.**Limited for the first 99 registrants. Register today! Oct 15 12:00 PM PDT  01:00 PM PDT Join this live GMAT class with GMAT Ninja to learn to conquer your fears of long, kooky GMAT questions. Oct 16 08:00 PM PDT  09:00 PM PDT EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299) Oct 19 07:00 AM PDT  09:00 AM PDT Does GMAT RC seem like an uphill battle? eGMAT is conducting a free webinar to help you learn reading strategies that can enable you to solve 700+ level RC questions with at least 90% accuracy in less than 10 days. Sat., Oct 19th at 7 am PDT Oct 20 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58335

If n is a positive integer, is (1/2)^n > 0.125 ?
[#permalink]
Show Tags
21 Aug 2019, 08:34
Question Stats:
65% (01:32) correct 35% (01:27) wrong based on 68 sessions
HideShow timer Statistics
Competition Mode Question If n is a positive integer, is \((\frac{1}{2})^n > 0.125\) ? (1) \(n > 3\) (2) \((\frac{1}{2})^{n  1} < 0.25\)
Official Answer and Stats are available only to registered users. Register/ Login.
_________________



SVP
Joined: 03 Jun 2019
Posts: 1682
Location: India

Re: If n is a positive integer, is (1/2)^n > 0.125 ?
[#permalink]
Show Tags
Updated on: 21 Aug 2019, 08:55
Quote: If n is a positive integer, is \((\frac{1}{2})^n>0.125?\)
(1) n>3
(2) \((\frac{1}{2})^n−1<0.25\) Given: n is a positive integer Asked: Is \((\frac{1}{2})^n>0.125?\) \(0.125 = (\frac{1}{2})^3\) Is \((\frac{1}{2})^n>0.125\) Mean Is n<3? (1) n>3 If n>3 => \((\frac{1}{2})^n<0.125\) SUFFICIENT (2) \((\frac{1}{2})^{n−1}<0.25\) n1>2 n>3 If n>3 => \((\frac{1}{2})^n<0.125\) SUFFICIENT IMO D
_________________
"Success is not final; failure is not fatal: It is the courage to continue that counts." Please provide kudos if you like my post. Kudos encourage active discussions. My GMAT Resources:  Efficient LearningAll you need to know about GMAT quantTele: +911140396815 Mobile : +919910661622 Email : kinshook.chaturvedi@gmail.com
Originally posted by Kinshook on 21 Aug 2019, 08:46.
Last edited by Kinshook on 21 Aug 2019, 08:55, edited 3 times in total.



Manager
Joined: 08 Jan 2018
Posts: 145
Location: India
Concentration: Operations, General Management
WE: Project Management (Manufacturing)

Re: If n is a positive integer, is (1/2)^n > 0.125 ?
[#permalink]
Show Tags
21 Aug 2019, 08:51
IMOD
n is a positive integer Check : 1/2 ^ n> 0.125 ?
0.125 = 1/2 ^ 3 So, Check (1/2)^n > (1/2)^3
(1) n>3 If n>3, (1/2)^n < (1/2)^3 Sufficient
(2) 1/2 ^ (n−1) <0.25 1/2 ^ (n−1) < (1/2)^2 n1 > 2 n>3 If n>3, (1/2)^n < (1/2)^3 Sufficient



Senior Manager
Status: Whatever it takes!
Joined: 10 Oct 2018
Posts: 381
GPA: 4

If n is a positive integer, is (1/2)^n > 0.125 ?
[#permalink]
Show Tags
Updated on: 22 Aug 2019, 09:00
n = positive integer We need to find whether \((\frac{1}{2})^n > 0.125\)? =\((\frac{1}{2})^n > (\frac{125}{1000})\)? =\((\frac{1}{2})^n > (\frac{1}{8})\)? =\((\frac{1}{2})^n > (\frac{1}{2})^3\)? indirectly asking whether n<3? (1) n>3 Any number greater than 3 would always give NO. Example: when n=4 => \((\frac{1}{2})^4 > (\frac{1}{2})^3\)? NO when n=5 => \((\frac{1}{2})^5 > (\frac{1}{2})^3\)? NO Hence n always has to be less than 3, i.e, n<3 SUFFICIENT! (2) \((\frac{1}{2})^{(n1)} < 0.25\) \((\frac{1}{2})^{(n1)} < (\frac{25}{100})\) \((\frac{1}{2})^{(n1)} < (\frac{1}{2})^2\) n1 > 2 (sign changes here) n>3.............same as statement 1, always no! SUFFICIENT IMO OPTION D
_________________
Originally posted by EncounterGMAT on 21 Aug 2019, 09:03.
Last edited by EncounterGMAT on 22 Aug 2019, 09:00, edited 2 times in total.



Intern
Joined: 26 May 2019
Posts: 2

Re: If n is a positive integer, is (1/2)^n > 0.125 ?
[#permalink]
Show Tags
21 Aug 2019, 09:04
n should be less than 3 to make sure \((1/2)^n > 0.125\) as (1/2)^n > (1/2)^3 => n < 3 (Fractional value decreases as power increases)
1) This is sufficient as n > 3, so answer is NO
2) With the same logic, n 1 > 2 => n > 3 , sufficient as it would result in answer NO
Answer is D



GMAT Club Legend
Joined: 18 Aug 2017
Posts: 4976
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)

Re: If n is a positive integer, is (1/2)^n > 0.125 ?
[#permalink]
Show Tags
21 Aug 2019, 09:22
If n is a positive integer, is (12)n>0.125(12)n>0.125 ? (1) n>3 (2) (12)n−1<0.25 simplify given expression we get (1/2)^n>(1/2)^3 only possible when n=1,2 #1 n>3 sufficient #2 (12)n−1<0.25 solve we get (1/2)^n1<(1/2)^2 possible when n>3 sufficient IMO D
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.



Manager
Joined: 15 Jun 2019
Posts: 203

Re: If n is a positive integer, is (1/2)^n > 0.125 ?
[#permalink]
Show Tags
21 Aug 2019, 09:38
statement 1 gives n>3 so 1/2^3 = .125 so if n >3 then it will be lesser than .125 which is clear no so sufficient statement 2 1/2 ^(n1) 1/2^n/1/2^1 multiply both side by 1/2 gives 1/2 ^n > .125 which is nothing but question so not sufficient hence ans is A
_________________
please do correct my mistakes that itself a big kudo for me,
thanks



Senior Manager
Joined: 07 Mar 2019
Posts: 311
Location: India
WE: Sales (Energy and Utilities)

Re: If n is a positive integer, is (1/2)^n > 0.125 ?
[#permalink]
Show Tags
21 Aug 2019, 09:48
If n is a positive integer, is \((\frac{1}{2})^n > 0.125\) ? (1) n > 3 (2) \(\frac{1}{2}^(n−1)\) < 0.25 \((\frac{1}{2})^n > 0.125\) \((\frac{1}{2})^n > (\frac{1}{8})\) [Also \(0.125 = (0.5)^3\)] \((\frac{1}{2})^n > (\frac{1}{2})^3\) n > 3 [Since n >0] Statement 1) n > 3 Yes n > 3 SUFFICIENT Statement 2) \(\frac{1}{2}^(n−1)\) < 0.25 \(\frac{1}{2}^(n−1)\) < \((0.5)^2\) n  1 < 2 [Since n >0] n < 3 No, n > 3 SUFFICIENT Answer (D).
_________________
Ephemeral Epiphany..!
GMATPREP1 590(Q48,V23) March 6, 2019 GMATPREP2 610(Q44,V29) June 10, 2019 GMATPREPSoft1 680(Q48,V35) June 26, 2019



Senior Manager
Joined: 25 Jul 2018
Posts: 253

Re: If n is a positive integer, is (1/2)^n > 0.125 ?
[#permalink]
Show Tags
21 Aug 2019, 11:07
If n is a positive integer, is \((\frac{1}{2})^{n}\) > 0.125 ?
\((\frac{1}{2})^{n}\) > \(\frac{1}{8}\)
\((\frac{1}{2})^{n}\) > \((\frac{1}{2})^{3}\)
is n < 3 ???
Statement1: n>3 > Always NO. Sufficient
Statement2: \((\frac{1}{2})^{n−1}\) < 0.25
\((\frac{1}{2})^{n1}\) < \((\frac{1}{2})^2\) n1 > 2 n >3 Always YES Sufficient
The answer is D.



Manager
Joined: 12 Aug 2017
Posts: 51

Re: If n is a positive integer, is (1/2)^n > 0.125 ?
[#permalink]
Show Tags
21 Aug 2019, 11:38
Given: n >=1 Analysis: (1/2)^n > 0.125 (1/2)^n > 1/8 => n>3 St.1 : n>3 Sufficient St.2 : (1/2)^n * 2 < 1/4 (1/2)^n < 1/8 n < 3 => Sufficient. D ans.
_________________
The key is not the will to win, it's the will to prepare to win that is important !!



Intern
Joined: 10 Aug 2019
Posts: 16

Re: If n is a positive integer, is (1/2)^n > 0.125 ?
[#permalink]
Show Tags
21 Aug 2019, 11:43
1st Statement n>3 , (1/2)^4 = 0.0625 Insuff. for the question being.
2nd Statement (1/2)^n1 <0.25 If n= 1,2,3 then statement false. Insuff. for the question being
But (1) + (2) n>3 and (1/2)^n1 <0.25 n=4 , the answer comes to be 0.125<0.25 Hence together Sufficient.
IMO C



Senior Manager
Joined: 18 May 2019
Posts: 339

Re: If n is a positive integer, is (1/2)^n > 0.125 ?
[#permalink]
Show Tags
21 Aug 2019, 12:00
We know from the question stem that n is a positive integer. We are to find if (0.5)^n > (0.5)^3. This means we are simply asked if n>3.
Statement 1 says n>3. Clearly it is sufficient since we can answer that n>3 or that for all integers values n={4,5,5,...}, (0.5)^n is not greater than 0.125.
Statement 2: (0.5)^(n1) < (0.5)^2 This means that n1 < 2 hence n<3. And for all positive values of n<3 (1,2), (0.5)^n > 0.125. Hence we can answer yes to the question posed. Statement 2 is also sufficient on its own.
Answer is therefore D.
Posted from my mobile device



Director
Joined: 24 Nov 2016
Posts: 559
Location: United States

Re: If n is a positive integer, is (1/2)^n > 0.125 ?
[#permalink]
Show Tags
21 Aug 2019, 12:38
Quote: If n is a positive integer, is (1/2)^n>0.125 ?
(1) n>3 (2) (1/2)^(n−1)<0.25 \((1/2)^n>1/8…2^{(n)}>2^{(3)}…n>3…n<3\) so, find if \(n<3\) (1) n>3: sufic. (2) (1/2)^(n−1)<0.25: \((1/2)^{(n1)}>1/4…2^{((n1))}>2^{(2)}…(n1)>2…n>3…n<3\); sufic. Answer (D)




Re: If n is a positive integer, is (1/2)^n > 0.125 ?
[#permalink]
21 Aug 2019, 12:38






