GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 21 Aug 2018, 13:09

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.

Close

Request Expert Reply

Confirm Cancel

Amit and Ian paint a wall in alternating shifts. First Amit paints alo

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 48109
Amit and Ian paint a wall in alternating shifts. First Amit paints alo  [#permalink]

Show Tags

New post 17 Sep 2015, 00:51
2
4
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

60% (01:57) correct 40% (02:41) wrong based on 122 sessions

HideShow timer Statistics

Amit and Ian paint a wall in alternating shifts. First Amit paints alone, then Ian paints alone, then Amit paints alone, etc. During each of his shifts, Amit paints 1/2 of the remaining unpainted area of the wall, while Ian paints 1/3 of the remaining unpainted area of the wall during each of his shifts. If Amit goes first, what fraction of the wall's area will remain unpainted after Amit has completed his 4th shift?

A. 1/27
B. 1/54
C. 1/81
D. 1/162
E. 1/216


Kudos for a correct solution.

_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Senior Manager
Senior Manager
User avatar
P
Joined: 12 Mar 2013
Posts: 293
Reviews Badge CAT Tests
Re: Amit and Ian paint a wall in alternating shifts. First Amit paints alo  [#permalink]

Show Tags

New post 17 Sep 2015, 01:12
1
Bunuel wrote:
Amit and Ian paint a wall in alternating shifts. First Amit paints alone, then Ian paints alone, then Amit paints alone, etc. During each of his shifts, Amit paints 1/2 of the remaining unpainted area of the wall, while Ian paints 1/3 of the remaining unpainted area of the wall during each of his shifts. If Amit goes first, what fraction of the wall's area will remain unpainted after Amit has completed his 4th shift?

A. 1/27
B. 1/54
C. 1/81
D. 1/162
E. 1/216


Kudos for a correct solution.



Let total work is 1

amit's 1st shift: 1/2 (paint left: 1-1/2= 1/2)
Ian 1st shift: (1/2)*(1/3)= 1/6 (paint left: 1-(1/2 +1/6) = 1/3
Amint's 2nd shift: (1/3)*(1/2)= 1/6 (paint left: 1/3 - 1/6 = 1/6
Ian 2nd shift: 1/6*1/3= 1/18 (paint left: 1/6-1/18 = 1/9
amit's 3rd shift: 1/9*1/2=1/18 (paint left: 1/9-1/18 = 1/18
Ian 3rd shift:....... (paint left: 1/18*2/3 = 1/27
amit's 4th shift:.....(paint left: 1/27*1/2 = 1/54
Remain paintings: 1/54 ( i used short cut at the last sections)
_________________

We Shall Overcome... One day...

Intern
Intern
avatar
Joined: 16 Apr 2015
Posts: 42
Concentration: Operations, Strategy
Schools: UFlorida '18, UFL '17
Re: Amit and Ian paint a wall in alternating shifts. First Amit paints alo  [#permalink]

Show Tags

New post 17 Sep 2015, 06:57
took me 3 minutes to solve this.any shortcuts??
Manager
Manager
avatar
Joined: 29 Jul 2015
Posts: 159
GMAT ToolKit User
Re: Amit and Ian paint a wall in alternating shifts. First Amit paints alo  [#permalink]

Show Tags

New post 17 Sep 2015, 13:21
4
Bunuel wrote:
Amit and Ian paint a wall in alternating shifts. First Amit paints alone, then Ian paints alone, then Amit paints alone, etc. During each of his shifts, Amit paints 1/2 of the remaining unpainted area of the wall, while Ian paints 1/3 of the remaining unpainted area of the wall during each of his shifts. If Amit goes first, what fraction of the wall's area will remain unpainted after Amit has completed his 4th shift?

A. 1/27
B. 1/54
C. 1/81
D. 1/162
E. 1/216


Kudos for a correct solution.


Work remaining after amit completes his shift will be 1/2.
Ian will complete 1/3 of this work. So,work remaining after Ian completes his shift will be 2/3 of the work remaining after Amit completes his shift.
Fraction of the work which is unfinished after amit completes his 4th shift will be

\(\frac{1}{2}\)*\(\frac{2}{3}\)*\(\frac{1}{2}\)*\(\frac{2}{3}\)*\(\frac{1}{2}\)*\(\frac{2}{3}\)*\(\frac{1}{2}\) = \(\frac{1}{54}\)
(Each color indicates different shift)

Answer:- B
SVP
SVP
User avatar
P
Joined: 08 Jul 2010
Posts: 2139
Location: India
GMAT: INSIGHT
WE: Education (Education)
Reviews Badge
Re: Amit and Ian paint a wall in alternating shifts. First Amit paints alo  [#permalink]

Show Tags

New post 18 Sep 2015, 04:51
Bunuel wrote:
Amit and Ian paint a wall in alternating shifts. First Amit paints alone, then Ian paints alone, then Amit paints alone, etc. During each of his shifts, Amit paints 1/2 of the remaining unpainted area of the wall, while Ian paints 1/3 of the remaining unpainted area of the wall during each of his shifts. If Amit goes first, what fraction of the wall's area will remain unpainted after Amit has completed his 4th shift?

A. 1/27
B. 1/54
C. 1/81
D. 1/162
E. 1/216


Kudos for a correct solution.


Fraction of area unpainted after FIRST shift of Amit = 1-(1/2) = 1/2

Fraction of area unpainted after FIRST shift of Ian = (1/2)-(1/3)(1/2) = (2/3)(1/2)

Fraction of area unpainted after SECOND shift of Amit = (1/2)(2/3)(1/2)

Fraction of area unpainted after SECOND shift of Ian = (2/3)(1/2)(2/3)(1/2)

Fraction of area unpainted after THIRD shift of Amit = (1/2)(2/3)(1/2)(2/3)(1/2)

Fraction of area unpainted after THIRD shift of Ian = (2/3)(1/2)(2/3)(1/2)(2/3)(1/2)

Fraction of area unpainted after FORTH shift of Amit = (1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2) = 1/54

Answer: option B
_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 48109
Re: Amit and Ian paint a wall in alternating shifts. First Amit paints alo  [#permalink]

Show Tags

New post 20 Sep 2015, 21:55
2
2
Bunuel wrote:
Amit and Ian paint a wall in alternating shifts. First Amit paints alone, then Ian paints alone, then Amit paints alone, etc. During each of his shifts, Amit paints 1/2 of the remaining unpainted area of the wall, while Ian paints 1/3 of the remaining unpainted area of the wall during each of his shifts. If Amit goes first, what fraction of the wall's area will remain unpainted after Amit has completed his 4th shift?

A. 1/27
B. 1/54
C. 1/81
D. 1/162
E. 1/216


Kudos for a correct solution.


ECONOMIST GMAT TUTOR OFFICIAL SOLUTION:

The issue of this question is (efficiently) finding out a term in a sequence. The terms in this sequence are the fractions of unpainted wall area. To find out how to calculate the terms, start writing them down and look for a pattern.

The first term - the fraction of unpainted area after Amit's first shift is 1/2.

In the next shift, Ian paints a 1/3 of the unpainted area, i.e., a 1/3 of 1/2. But how much is left unpainted? Ian leaves 2/3 of the 1/2 unpainted. Thus, the second term is (2/3)(1/2).

In the following shift, (Amit's second shift,) half of the unpainted area is painted, or, in other words, half of unpainted area remains unpainted, hence, the third term is (1/2)(2/3)(1/2). Continue the pattern from here until after Amit's 4th shift.

The final expression after Amit's 4th shift (labeled Amit (4)):

Amit(1) Ian Amit(2) Ian Amit(3) Ian Amit(4)
\(\frac{1}{2}*\frac{2}{3}*\frac{1}{2}*\frac{2}{3}*\frac{1}{2}*\frac{2}{3}
*\frac{1}{2}=\frac{1}{54}\).

Answer: B.
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 7776
Premium Member
Re: Amit and Ian paint a wall in alternating shifts. First Amit paints alo  [#permalink]

Show Tags

New post 09 Dec 2017, 08:53
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 Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: Amit and Ian paint a wall in alternating shifts. First Amit paints alo &nbs [#permalink] 09 Dec 2017, 08:53
Display posts from previous: Sort by

Amit and Ian paint a wall in alternating shifts. First Amit paints alo

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.