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

It is currently 16 Oct 2018, 09:35

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

R and S can complete a certain job in 6 and 4 days respectively, while

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

Hide Tags

e-GMAT Representative
User avatar
P
Joined: 04 Jan 2015
Posts: 2063
R and S can complete a certain job in 6 and 4 days respectively, while  [#permalink]

Show Tags

New post Updated on: 13 Aug 2018, 05:58
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

45% (01:33) correct 55% (01:19) wrong based on 168 sessions

HideShow timer Statistics

Solve Time and Work Problems Efficiently using Efficiency Method! - Exercise Question #2

R and S can complete a certain job in 6 and 4 days respectively, while they work individually. What will be the least number of days they will take to complete the same job, if they work on alternate days?

    A. 2.2 days
    B. 2.67 days
    C. 4.4 days
    D. 4.67 days
    E. 5 days



To solve question 3: Question 3

To read the article: Solve Time and Work Problems Efficiently using Efficiency Method!

_________________








Register for free sessions
Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Must Read Articles
Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com


Originally posted by EgmatQuantExpert on 23 May 2018, 04:13.
Last edited by EgmatQuantExpert on 13 Aug 2018, 05:58, edited 2 times in total.
Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3182
Location: India
GPA: 3.12
Premium Member CAT Tests
Re: R and S can complete a certain job in 6 and 4 days respectively, while  [#permalink]

Show Tags

New post 23 May 2018, 05:28
1
2
EgmatQuantExpert wrote:
Solve Time and Work Problems Efficiently using Efficiency Method! - Exercise Question #2

R and S can complete a certain job in 6 and 4 days respectively, while they work individually. What will be the least number of days they will take to complete the same job, if they work on alternate days?

    A. 2.2 days
    B. 2.67 days
    C. 4.4 days
    D. 4.67 days
    E. 5 days


Since R and S can complete a certain job in 6 and 4 days respectively,
let's assume the total work done to be done as 24 units(A number that works with individual rates of 6 and 4).

The individual rates are R - 4 units/day and S - 6 units/day.

Working alternatively, R and S do 4+6+4+6 = 20 units of the work in 4 days.

We are left with 4 units of work to do on the 5th day.
On the fifth day,
if R does the 4 units of work, it takes R 1 day to complete the work.
if S does the 4 units of work, it takes S \(\frac{4}{6}\) or 0.67 day.
The minimum amount of time is taken if S does the work on the fifth day. Since they work alternatively,
S must have done work on the first and third day and R on the second and fourth day.

Therefore, the total time taken for R and S to complete the work is 4.67 days(Option D)
_________________

You've got what it takes, but it will take everything you've got

Senior Manager
Senior Manager
User avatar
D
Joined: 12 Feb 2015
Posts: 488
Premium Member CAT Tests
Re: R and S can complete a certain job in 6 and 4 days respectively, while  [#permalink]

Show Tags

New post 26 May 2018, 11:51
LCM of 6 & 4 is 12 [Final answer does not change but this may be important for other questions as this amounts to a silly mistake]

Also in your solution you have to specifically assume who is doing the work first? Since the question stem is asking the "least" time, then the person who works faster will start the work first. The order mentioned by you assumes RSRS (4+6+4+6 = 20). If this is the assumption then on the fifth day R will work again and he will take entire day to complete 4 units. Which means the answer in this case comes to (E) 4+1= 5 days, which is the wrong answer as the stem asks you to find out the "least time". (Your final answer is right, I am just clarifying the logic behind your answer because someone could ignore the order and commit a silly mistake as the trap answer in one of the options)

Hence the correct order is S works on the first day because he does more units per day followed by R the next day. This gives us the following order of SRSR completing 20 units in first 4 days. On the 5th day S works for 2/3rd of the day as his individual rate is 6 units per day but he needs to complete only 4 units for which only 2/3 day or .67 day is required. Hence the answer is 4+.67=4.67 days.

pushpitkc wrote:
EgmatQuantExpert wrote:
Solve Time and Work Problems Efficiently using Efficiency Method! - Exercise Question #2

R and S can complete a certain job in 6 and 4 days respectively, while they work individually. What will be the least number of days they will take to complete the same job, if they work on alternate days?

    A. 2.2 days
    B. 2.67 days
    C. 4.4 days
    D. 4.67 days
    E. 5 days


Since R and S can complete a certain job in 6 and 4 days respectively,
let's assume the total work done to be done as 24 units(LCM of 6 and 4).

The individual rates are R - 4 units/day and S - 6 units/day.

Working alternatively, R and S do 4+6+4+6 = 20 units of the work in 4 days.

We are left with 4 units of work to do on the 5th day.
On the fifth day,
if R does the 4 units of work, it takes R 1 day to complete the work.
if S does the 4 units of work, it takes S \(\frac{4}{6}\) or 0.67 day.
The minimum amount of time is taken if S does the work on the fifth day.

Therefore, the total time taken for R and S to complete the work is 4.67 days(Option D)

_________________

"Please hit :thumbup: +1 Kudos if you like this post" :student_man:

_________________
Manish :geek:

"Only I can change my life. No one can do it for me"

Senior Manager
Senior Manager
User avatar
D
Joined: 12 Feb 2015
Posts: 488
Premium Member CAT Tests
Re: R and S can complete a certain job in 6 and 4 days respectively, while  [#permalink]

Show Tags

New post 26 May 2018, 12:13
1
Since R and S can complete a certain job in 6 and 4 days respectively,
let's assume the total work done to be done as 12 units (LCM of 6 and 4).

The individual rates are R - 2 units/day and S - 3 units/day.

Since the question stem is asking the "least" time, then the person who works faster will start the work first. S works on the first day because he does more units per day followed by R the next day. This gives us the following order of SRSR completing 10 units in first 4 days. On the 5th day S works at his individual rate of 3 units per day but he needs to complete only 2 units for the entire work to be completed for which only 2/3 of the day or 0.67 day is required. Hence the answer is 4+.67=4.67 days.

Correct Answer: Option D

PS: Someone could ignore the order and commit a silly mistake as the trap answer is E which is one of the options.
_________________

"Please hit :thumbup: +1 Kudos if you like this post" :student_man:

_________________
Manish :geek:

"Only I can change my life. No one can do it for me"

Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3182
Location: India
GPA: 3.12
Premium Member CAT Tests
Re: R and S can complete a certain job in 6 and 4 days respectively, while  [#permalink]

Show Tags

New post 26 May 2018, 12:17
CAMANISHPARMAR wrote:
Since R and S can complete a certain job in 6 and 4 days respectively,
let's assume the total work done to be done as 12 units (LCM of 6 and 4).

The individual rates are R - 2 units/day and S - 3 units/day.

Since the question stem is asking the "least" time, then the person who works faster will start the work first. S works on the first day because he does more units per day followed by R the next day. This gives us the following order of SRSR completing 10 units in first 4 days. On the 5th day S works at his individual rate of 3 units per day but he needs to complete only 2 units for the entire work to be completed for which only 2/3 of the day or 0.67 day is required. Hence the answer is 4+.67=4.67 days.

Correct Answer: Option D

PS: Someone could ignore the order and commit a silly mistake as the trap answer is E which is one of the options.


Thanks for noticing and notifying CAMANISHPARMAR

Have made the necessary changes in my solution.
_________________

You've got what it takes, but it will take everything you've got

e-GMAT Representative
User avatar
P
Joined: 04 Jan 2015
Posts: 2063
Re: R and S can complete a certain job in 6 and 4 days respectively, while  [#permalink]

Show Tags

New post 26 May 2018, 12:44
1
1

Solution



Given:
In this question, it is given that
    • R and S can complete a certain job in 6 days and 4 days respectively, when they work individually.


To find:
    • We need to find out the least number of days they will take to complete the job, if they work on alternate days.

Approach and Working:
As R and S take 6 days and 4 days respectively while working individually, we can assume the total work to be LCM (6, 4) = 12 units
    • In 6 days, R can complete 12 units of work
      • Hence, in 1-day R can complete \(\frac{12}{6}\) = 2 units of work
    • Similarly, in 4 days, S can complete 12 units of work
      • Hence, in 1-day S can complete \(\frac{12}{4}\) = 3 units of work
    As they work on alternate days, the work that they will complete in a span of 2 days = (2 + 3) = 5 units
    • Therefore, in the first 4 days, they will complete 5 * 2 = 10 units of the total work
Hence, remaining work = (12 – 10) units = 2 units

Now to ensure that the completion of work happens in the least possible day, the person, who is more efficient among the 2, should work on the 5th day
Among R and S, we know S is more efficient, and therefore, S should work on the 5th day to ensure the work gets completed at earliest
    • As S can complete 3 units of work in 1 day, to complete 2 units of work, S will take = \(\frac{2}{3}\) days = 0.67 days
Hence, the least total number of days needed to complete the work = (4 + 0.67) days = 4.67 days

Hence, the correct answer is option D.

Answer: D

Important Observation


    • As they are working in alternate days, only one person is working in a day.
      • Hence, to ensure the job gets completed in least number of days, we need to ensure the more efficient person(S) works on the last day.
    • This also indicates that S should start the work on day 1, to ensure S works in the final day.

_________________








Register for free sessions
Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Must Read Articles
Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

GMATH Teacher
User avatar
S
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 360
Re: R and S can complete a certain job in 6 and 4 days respectively, while  [#permalink]

Show Tags

New post 28 Sep 2018, 08:53
EgmatQuantExpert wrote:

R and S can complete a certain job in 6 and 4 days respectively, while they work individually. What will be the least number of days they will take to complete the same job, if they work on alternate days?

    A. 2.2 days
    B. 2.67 days
    C. 4.4 days
    D. 4.67 days
    E. 5 days

Let´s imagine the job is defined by exactly 12 identical tasks (LCM(6,4) = 12).

R does 2 tasks/day, while S does 3 tasks/day.

FOCUS: minimize the number of days to do the 12 tasks... S is more efficient, let´s make HIM/HER start as soon as possible! (*)

In four days, we have 3+2+3+2 = 10 tasks done.

At the beginning of the 5th day, it is S who works (*) and using UNITS CONTROL, one of the most powerful tools of our course, we have:

\(2\,\,\,{\rm{tasks}}\,\,\,\left( {{{1\,\,{\rm{day}}} \over {3\,\,{\rm{tasks}}}}\,\,\,\matrix{
\nearrow \cr
\nearrow \cr

} } \right)\,\,\,\,\, = \,\,\,{2 \over 3}\,\,{\rm{day}}\)

Obs.: arrows indicate licit converter.

\({\rm{?}}\,\,{\rm{ = }}\,\,{\rm{4}}{2 \over 3}\,\,{\rm{days}}\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________

Fabio Skilnik :: http://www.GMATH.net (Math for the GMAT)
Course release PROMO : finish our test drive till 31/Oct with (at least) 60 correct answers out of 92 (12-questions Mock included) to gain a 60% discount!

CEO
CEO
User avatar
D
Joined: 12 Sep 2015
Posts: 2996
Location: Canada
Re: R and S can complete a certain job in 6 and 4 days respectively, while  [#permalink]

Show Tags

New post 28 Sep 2018, 09:27
Top Contributor
EgmatQuantExpert wrote:
R and S can complete a certain job in 6 and 4 days respectively, while they work individually. What will be the least number of days they will take to complete the same job, if they work on alternate days?

    A. 2.2 days
    B. 2.67 days
    C. 4.4 days
    D. 4.67 days
    E. 5 days


Let's assign a "nice" value to the job, a value that works well with the given values (6 days and 4 days ).
So, let's say the ENTIRE job is to make 24 widgets

R can complete a certain job in 6 days
In other words, R can make 24 widgets in 6 days
So, R can make 4 widgets per day

S can complete a certain job in 4 days
In other words, S can make 24 widgets in 4 days
So, S can make 6 widgets per day

What will be the least number of days they will take to complete the same job, if they work on alternate days?
To MINIMIZE the time, the fastest worker (worker S) should go first.

DAY 1: Worker S makes 6 widgets (running total of widgets made at the end of day 1 = 6)
DAY 2: Worker R makes 4 widgets (running total of widgets made at the end of day 2 = 10)
DAY 3: Worker S makes 6 widgets (running total of widgets made at the end of day 3 = 16)
ASIDE: at this point, we can see that it will take more than 3 days to complete the job (ELIMINATE answer choices A and B)
DAY 4: Worker R makes 4 widgets (running total of widgets made at the end of day 4 = 20)

At this point, R and S have made 20 of the 24 needed widgets
So, on day 5, worker S need only make 4 widgets.

We already know that S can make 6 widgets per day, so it will take LESS THAN ONE day to make the remaining 4 widgets (ELIMINATE answer choice E)
We can also conclude that, in 1/2 a day, S can make only 3 widgets. So, it will take MORE THAN 1/2 a day to make the remaining 4 widgets. (ELIMINATE answer choice C)

Answer: D

Cheers,
Brent
_________________

Brent Hanneson – GMATPrepNow.com
Image
Sign up for our free Question of the Day emails

Manager
Manager
User avatar
S
Joined: 03 Mar 2017
Posts: 149
CAT Tests
R and S can complete a certain job in 6 and 4 days respectively, while  [#permalink]

Show Tags

New post 28 Sep 2018, 23:33
The catch here is that you are not given the order. Although if any of them starts,after 2 days work completed will be 5/12.
Similarly after another 2 days work done will be 5/12 again. Now we are left with(1/6) work.
Here we have to decide the order. If we start with R on the first day, then it is his turn on the 5th day and he will take the whole day since his rate is 1/6.
Since we are asked to find the least amount of time, we should start with S and therefore answer will be D.

Very good question. Not so difficult but tricky.Read question carefully.
_________________

--------------------------------------------------------------------------------------------------------------------------
All the Gods, All the Heavens, and All the Hells lie within you.

GMAT Club Bot
R and S can complete a certain job in 6 and 4 days respectively, while &nbs [#permalink] 28 Sep 2018, 23:33
Display posts from previous: Sort by

R and S can complete a certain job in 6 and 4 days respectively, while

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


Copyright

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®.