November 14, 2018 November 14, 2018 07:00 PM PST 08:00 PM PST Join the webinar and learn timemanagement tactics that will guarantee you answer all questions, in all sections, on time. Save your spot today! Nov. 14th at 7 PM PST November 15, 2018 November 15, 2018 10:00 PM MST 11:00 PM MST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299)
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50544

Question Stats:
55% (01:10) correct 45% (01:03) wrong based on 117 sessions
HideShow timer Statistics



Math Expert
Joined: 02 Sep 2009
Posts: 50544

Re M1705
[#permalink]
Show Tags
16 Sep 2014, 00:00
Official Solution:The value of \(\frac{1}{2} + (\frac{1}{2})^2 + (\frac{1}{2})^3 + ... + (\frac{1}{2})^{20}\) is between? A. \(\frac{1}{2}\) and \(\frac{2}{3}\) B. \(\frac{2}{3}\) and \(\frac{3}{4}\) C. \(\frac{3}{4}\) and \(\frac{9}{10}\) D. \(\frac{9}{10}\) and \(\frac{10}{9}\) E. \(\frac{10}{9}\) and \(\frac{3}{2}\) We have the sum of a geometric progression with the first term equal to \(\frac{1}{2}\) and the common ratio also equal to \(\frac{1}{2}\). Now, the sum of infinite geometric progression with common ratio \(r \lt 1\), is \(sum=\frac{b}{1r}\), where \(b\) is the first term. So, if we had infinite geometric progression instead of just 20 terms then its sum would be \(Sum=\frac{\frac{1}{2}}{1\frac{1}{2}}=1\). Which means that the sum of this sequence will never exceed 1. Also since we have a large enough number of terms (20), the sum will be very close to 1, so we can safely choose answer choice D. One can also use direct formula. We have geometric progression with \(b=\frac{1}{2}\), \(r=\frac{1}{2}\) and \(n=20\); \(S_n=\frac{b(1r^n)}{(1r)}\), so: \(S_{20}=\frac{\frac{1}{2}(1\frac{1}{2^{20}})}{(1\frac{1}{2})}=1\frac{1}{2^{20}}\). Since \(\frac{1}{2^{20}}\) is very small number then \(1\frac{1}{2^{20}}\) will be less than 1 but very close to it. Answer: D
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 11 Sep 2013
Posts: 157
Concentration: Finance, Finance

M1705
[#permalink]
Show Tags
Updated on: 09 Nov 2015, 08:28
In case we forget formula we can do it by following approximation 1/2=.50 1/2^2 =.250 1/2^3= .125 ............. .50+.250+.125 = .875 So we are sure that by other decimal number value we will be very close to 1 but less than 1
Only option D shows that
Originally posted by Raihanuddin on 27 Nov 2014, 15:19.
Last edited by Raihanuddin on 09 Nov 2015, 08:28, edited 1 time in total.



Verbal Forum Moderator
Joined: 15 Apr 2013
Posts: 184
Location: India
Concentration: General Management, Marketing
GMAT Date: 11232015
GPA: 3.6
WE: Science (Other)

Re: M1705
[#permalink]
Show Tags
21 Aug 2015, 19:38
Dear Buenel,
As per your explanation, answer should be C not D.
In (D) 10/9 is actually greater than 01.
Please suggest if I am wrong. Please assist.



Math Expert
Joined: 02 Sep 2009
Posts: 50544

Re: M1705
[#permalink]
Show Tags
22 Aug 2015, 03:58



Verbal Forum Moderator
Joined: 15 Apr 2013
Posts: 184
Location: India
Concentration: General Management, Marketing
GMAT Date: 11232015
GPA: 3.6
WE: Science (Other)

Thanks for quick feedback.
The whole issue with D was that 10/9 is 1.11... Which is greater than 1?
Please clarify



Math Expert
Joined: 02 Sep 2009
Posts: 50544

Re: M1705
[#permalink]
Show Tags
22 Aug 2015, 04:05



Verbal Forum Moderator
Joined: 15 Apr 2013
Posts: 184
Location: India
Concentration: General Management, Marketing
GMAT Date: 11232015
GPA: 3.6
WE: Science (Other)

OK
Thanks a lot



Manager
Joined: 08 Jul 2015
Posts: 56
GPA: 3.8
WE: Project Management (Energy and Utilities)

I actually forgot the formula when I had this question so I did the most native manual way I can: 1/2 + 1/4 = 3/4 + 1/8 = 7/8 + 1/16 = 15/16 Stop here: 15/16 > 9/10 and since the rhythm of the series we can see that the sum will always <1 > correct ans: D
_________________
[4.33] In the end, what would you gain from everlasting remembrance? Absolutely nothing. So what is left worth living for? This alone: justice in thought, goodness in action, speech that cannot deceive, and a disposition glad of whatever comes, welcoming it as necessary, as familiar, as flowing from the same source and fountain as yourself. (Marcus Aurelius)



Current Student
Joined: 03 Apr 2016
Posts: 83
Location: India
Concentration: Operations, General Management
WE: Analyst (Computer Software)

Re: M1705
[#permalink]
Show Tags
09 Jul 2016, 13:46
is GP even asked in GMAT?



Current Student
Joined: 28 Aug 2016
Posts: 90
Concentration: Strategy, General Management

Re: M1705
[#permalink]
Show Tags
08 Oct 2016, 15:26
Linhbiz wrote: I actually forgot the formula when I had this question so I did the most native manual way I can: 1/2 + 1/4 = 3/4 + 1/8 = 7/8 + 1/16 = 15/16 Stop here: 15/16 > 9/10 and since the rhythm of the series we can see that the sum will always <1 > correct ans: D I didn't even know the formula but took the same approach. I was able to solve the problem within 1 minute.



Intern
Joined: 22 Nov 2014
Posts: 29

Re: M1705
[#permalink]
Show Tags
22 Dec 2016, 05:16
shashanksagar wrote: is GP even asked in GMAT? havent seen a single sum



Intern
Joined: 26 May 2016
Posts: 20

Raihanuddin wrote: In case we forget formula we can do it by following approximation 1/2=.50 1/2^2 =.250 1/2^3= .125 ............. .50+.250+.125 = .875 So we are sure that by other decimal number value we will be very close to 1 but less than 1
Only option D shows that To be sure, I added 1/2, 1/4,1/8 and 1/16 to to get 0.875 + 0.0625 > 0.93 and since the further we go, the smaller fractions we add, we should be close to 0.99 Hence D



Intern
Joined: 25 Apr 2017
Posts: 3

Re: M1705
[#permalink]
Show Tags
16 Jun 2017, 05:28
I agree that option D is the closest in terms of the correct answer,but the range is wrong as 10/9 is greater than 1. So I had eliminated that option at first glance. I think none of the options in this question is correct.



Math Expert
Joined: 02 Sep 2009
Posts: 50544

Re: M1705
[#permalink]
Show Tags
16 Jun 2017, 05:33



Manager
Joined: 12 Nov 2016
Posts: 72

Re: M1705
[#permalink]
Show Tags
28 Jun 2017, 18:21
Bunuel wrote: WillGetIt wrote: Thanks for which feedback.
The whole issue with D was that 10/9 is 1.11... Which is greater than 1?
Please clarify Note that the question asks about the range, not the exact value of the expression. If the value of the expression were 0.9999999 wouldn't it still be correct to say that it's between 0.9 and 1000000000000000000000000? Bunuel, yes the values can be considered that way. But also we in this range there are values which are greater than 1 and we know for sure it cannot be greater than 1. How do we justify that...what if the value of the expression is 1.00000000009 or 1.10, wouldn't it be greater than 1? Pls clarify



Math Expert
Joined: 02 Sep 2009
Posts: 50544

Re: M1705
[#permalink]
Show Tags
28 Jun 2017, 20:21
Chets25 wrote: Bunuel wrote: WillGetIt wrote: Thanks for which feedback.
The whole issue with D was that 10/9 is 1.11... Which is greater than 1?
Please clarify Note that the question asks about the range, not the exact value of the expression. If the value of the expression were 0.9999999 wouldn't it still be correct to say that it's between 0.9 and 1000000000000000000000000? Bunuel, yes the values can be considered that way. But also we in this range there are values which are greater than 1 and we know for sure it cannot be greater than 1. How do we justify that...what if the value of the expression is 1.00000000009 or 1.10, wouldn't it be greater than 1? Pls clarify How does this matter? Say x = 10. Wouldn't it be correct to say that it's between 1000000 and 10000000000000?
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 08 Sep 2016
Posts: 32

Re: M1705
[#permalink]
Show Tags
30 Jun 2017, 03:46
Hi,
I understood that you did it without using the formula...but can u please explain how did u arrive ta the answer in details
I understood until point u get 15/16..after that how did u arrive at the answer?
Thanks in advance!



Intern
Joined: 08 Sep 2016
Posts: 32

Re: M1705
[#permalink]
Show Tags
30 Jun 2017, 03:47
Rookie84 wrote: Linhbiz wrote: I actually forgot the formula when I had this question so I did the most native manual way I can: 1/2 + 1/4 = 3/4 + 1/8 = 7/8 + 1/16 = 15/16 Stop here: 15/16 > 9/10 and since the rhythm of the series we can see that the sum will always <1 > correct ans: D I didn't even know the formula but took the same approach. I was able to solve the problem within 1 minute. Hi, I understood that you did it without using the formula...but can u please explain how did u arrive ta the answer in details I understood until point u get 15/16..after that how did u arrive at the answer? Thanks in advance!



Intern
Joined: 17 Nov 2016
Posts: 2

Re: M1705
[#permalink]
Show Tags
27 Nov 2017, 08:18
I did it by approximation 20*(1/2)^10= 5/256 =1/11 =.09 hence option D







Go to page
1 2
Next
[ 21 posts ]



