GMAT Changed on April 16th - Read about the latest changes here

 It is currently 24 Apr 2018, 01:42

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 44638
Amit and Ian paint a wall in alternating shifts. First Amit paints alo [#permalink]

### Show Tags

17 Sep 2015, 00:51
1
KUDOS
Expert's post
5
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

62% (01:58) correct 38% (02:43) wrong based on 117 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.
[Reveal] Spoiler: OA

_________________
Senior Manager
Joined: 12 Mar 2013
Posts: 284
Re: Amit and Ian paint a wall in alternating shifts. First Amit paints alo [#permalink]

### Show Tags

17 Sep 2015, 01:12
1
KUDOS
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
Joined: 16 Apr 2015
Posts: 44
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

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

### Show Tags

17 Sep 2015, 13:21
4
KUDOS
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)

SVP
Joined: 08 Jul 2010
Posts: 2067
Location: India
GMAT: INSIGHT
WE: Education (Education)
Re: Amit and Ian paint a wall in alternating shifts. First Amit paints alo [#permalink]

### Show Tags

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

_________________

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
Joined: 02 Sep 2009
Posts: 44638
Re: Amit and Ian paint a wall in alternating shifts. First Amit paints alo [#permalink]

### Show Tags

20 Sep 2015, 21:55
1
KUDOS
Expert's post
3
This post was
BOOKMARKED
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)
$$\frac{1}{2}*\frac{2}{3}*\frac{1}{2}*\frac{2}{3}*\frac{1}{2}*\frac{2}{3} *\frac{1}{2}=\frac{1}{54}$$.

_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 6644
Re: Amit and Ian paint a wall in alternating shifts. First Amit paints alo [#permalink]

### Show Tags

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