Last visit was: 18 Nov 2025, 21:07 It is currently 18 Nov 2025, 21:07
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
EgmatQuantExpert
User avatar
e-GMAT Representative
Joined: 04 Jan 2015
Last visit: 02 Apr 2024
Posts: 3,663
Own Kudos:
20,162
 [37]
Given Kudos: 165
Expert
Expert reply
Posts: 3,663
Kudos: 20,162
 [37]
Question of the Week - 43 (While working individually, each of A, B) Updated on: 18 Apr 2019, 02:19
Originally posted by EgmatQuantExpert on 12 Apr 2019, 03:56.
Last edited by chetan2u on 18 Apr 2019, 02:19, edited 1 time in total.
Corrected the question
1
Kudos
Add Kudos
36
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

95% (hard)

Question Stats:

33% (03:13) correct 67% (03:01) wrong based on 233 sessions

History

Date
Time
Result
Not Attempted Yet
e-GMAT Question of the Week #43


While working individually, each of A, B, C and D can produce 60 units of a certain item in a, b, c and d hours respectively, where a, b, c, d are consecutive integers in increasing order. If A and C together can produce 60 units in more than 2 hours, then which of the following can be the time they will take to produce 60 units, if all are working together?

    A. 28.2 minutes
    B. 46.75 minutes
    C. 60 minutes
    D. 63.15 minutes
    E. 79 minutes

ShowHide Answer
Official Answer
E
Most Helpful Reply
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 15 Nov 2025
Posts: 11,238
Own Kudos:
43,696
 [7]
Given Kudos: 335
Status:Math and DI Expert
Location: India
Concentration: Human Resources, General Management
GMAT Focus 1: 735 Q90 V89 DI81
Products:
My Reviews
Expert
Expert reply
GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,238
Kudos: 43,696
 [7]
Question of the Week - 43 (While working individually, each of A, B) 12 Apr 2019, 05:12
2
Kudos
Add Kudos
5
Bookmarks
Bookmark this Post
EgmatQuantExpert
e-GMAT Question of the Week #43


While working individually, each of A, B, C and D can produce 60 units of a certain item in a, b, c and d hours respectively, where a, b, c, d are consecutive integers in increasing order. If A and C together can produce 60 units in more than 2 hours, then which of the following cannot be the time they will take to produce 60 units, if all are working together?

    A. 28.2 minutes
    B. 46.75 minutes
    C. 60 minutes
    D. 63.15 minutes
    E. 79 minutes

Show more

so a, b, c and d can be written as a, a+1, a+2 and a+3...

If A and C together can produce 60 units in more than 2 hours...\(\frac{1}{a}+\frac{1}{c}<\frac{1}{2}\)...
Just substitute a..
a as 1.. c is 3.. \(1+(\frac{1}{3})=\frac{4}{3} >\frac{1}{2}\)
a as 3.. c is 5...\((\frac{1}{3})+(\frac{1}{5})=\frac{8}{15}>\frac{1}{2}\)
So, minimum value of a is 4..

Thus the least time all four will take is if a, b, c, and d are 4, 5, 6 and 7...
\(\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}=\frac{5*6*7+4*6*7+4*5*7+4*5*6}{4*5*6*7}=\frac{210+168+140+120}{840}=\frac{638}{840}.......\)..
so time = 840/638 hrs = \(\frac{840*60}{638}\) minutes = 78.99 minutes..
So, the least value is 78.99..
Thus all choices A to D are not possible..

E


EgmatQuantExpert, please relook what are you looking for.. which of the following cannot or can be the time they will take to produce 60 units
General Discussion
User avatar
fra
User avatar
Joined: 29 Oct 2013
Last visit: 20 Aug 2019
Posts: 16
Own Kudos:
56
Given Kudos: 12
Posts: 16
Kudos: 56
Question of the Week - 43 (While working individually, each of A, B) 12 Apr 2019, 05:52
Kudos
Add Kudos
Bookmarks
Bookmark this Post
chetan2u
EgmatQuantExpert
e-GMAT Question of the Week #43


While working individually, each of A, B, C and D can produce 60 units of a certain item in a, b, c and d hours respectively, where a, b, c, d are consecutive integers in increasing order. If A and C together can produce 60 units in more than 2 hours, then which of the following cannot be the time they will take to produce 60 units, if all are working together?

    A. 28.2 minutes
    B. 46.75 minutes
    C. 60 minutes
    D. 63.15 minutes
    E. 79 minutes


so a, b, c and d can be written as a, a+1, a+2 and a+3...

If A and C together can produce 60 units in more than 2 hours...\(\frac{1}{a}+\frac{1}{c}<\frac{1}{2}\)...
Just substitute a..
a as 1.. c is 3.. \(1+(\frac{1}{3})=\frac{4}{3} >\frac{1}{2}\)
a as 3.. c is 5...\((\frac{1}{3})+(\frac{1}{5})=\frac{8}{15}>\frac{1}{2}\)
So, minimum value of a is 4..

Thus the least time all four will take is if a, b, c, and d are 4, 5, 6 and 7...
\(\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}=\frac{5*6*7+4*6*7+4*5*7+4*5*6}{4*5*6*7}=\frac{210+168+140+120}{840}=\frac{638}{840}.......\)..
so time = 840/638 hrs = \(\frac{840*60}{638}\) minutes = 78.99 minutes..
So, the least value is 78.99..
Thus all choices A to D are not possible..

E


EgmatQuantExpert, please relook what are you looking for.. which of the following cannot or can be the time they will take to produce 60 units
Show more


Is there a typo in the question? It says which of the following "cannot" be the time taken.

Posted from my mobile device
User avatar
Archit3110
User avatar
Major Poster
Joined: 18 Aug 2017
Last visit: 18 Nov 2025
Posts: 8,423
Own Kudos:
4,979
 [1]
Given Kudos: 243
Status:You learn more from failure than from success.
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1: 545 Q79 V79 DI73
GMAT Focus 2: 645 Q83 V82 DI81
GPA: 4
WE:Marketing (Energy)
GMAT Focus 2: 645 Q83 V82 DI81
Posts: 8,423
Kudos: 4,979
 [1]
Question of the Week - 43 (While working individually, each of A, B) 12 Apr 2019, 10:35
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
given a,b,c,d are consective integers
so a=x ,b=x+1, c= x+2, d= x+3
also given
1/a + 1/c>1/2
use hit and trial to see at which value of x we get 1/a + 1/c>1/2
only at a=4 and c=6 we get >1/2
so a=4,b=5,c=6,d=7
working together
1/4+1/5+1/6+1/7 = 5*6*7+4*6*7+4*5*7+4*5*6/ (4*5*6*7 )
solve we get
638/840 ; time 840*60/638 = ~79 mins
IMO E

EgmatQuantExpert
e-GMAT Question of the Week #43


While working individually, each of A, B, C and D can produce 60 units of a certain item in a, b, c and d hours respectively, where a, b, c, d are consecutive integers in increasing order. If A and C together can produce 60 units in more than 2 hours, then which of the following cannot be the time they will take to produce 60 units, if all are working together?

    A. 28.2 minutes
    B. 46.75 minutes
    C. 60 minutes
    D. 63.15 minutes
    E. 79 minutes

Show more
avatar
vijay282001
avatar
Current Student
Joined: 23 Mar 2013
Last visit: 08 Sep 2021
Posts: 28
Own Kudos:
7
 [2]
Given Kudos: 30
Location: United States
Schools: Stern PT Fall '24 (A) Tepper PT '24 (A)
Schools: Stern PT Fall '24 (A) Tepper PT '24 (A)
Posts: 28
Kudos: 7
 [2]
Question of the Week - 43 (While working individually, each of A, B) Updated on: 13 Apr 2019, 05:08
Originally posted by vijay282001 on 12 Apr 2019, 18:56.
Last edited by vijay282001 on 13 Apr 2019, 05:08, edited 1 time in total.
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
a + c > 2 and a<b<c<d,
means, a will take at least 4 hours to complete the work
in an hour, units of work completed,

for A, 60*1/4 = 15
B, 60*1/5 = 12
C, 60*1/6=10
D, 60*1/7 ~ 8

Total work = 15+12+10+8 = 45
remaining work= 60-45= 15 which 4th of total, so would need additional 4th of an hour, i.e. 15mins,

in all the minimum time would be greater than, 60 + 15 = 75, the only answer which is greater than 75, is E
User avatar
pushpitkc
User avatar
Joined: 26 Feb 2016
Last visit: 19 Feb 2025
Posts: 2,803
Own Kudos:
6,063
 [1]
Given Kudos: 47
Location: India
GPA: 3.12
Posts: 2,803
Kudos: 6,063
 [1]
Question of the Week - 43 (While working individually, each of A, B) 13 Apr 2019, 01:44
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
EgmatQuantExpert

While working individually, each of A, B, C and D can produce 60 units of a certain item in a, b, c and d hours respectively, where a, b, c, d are consecutive integers in increasing order. If A and C together can produce 60 units in more than 2 hours, then which of the following cannot be the time they will take to produce 60 units, if all are working together?

    A. 28.2 minutes
    B. 46.75 minutes
    C. 60 minutes
    D. 63.15 minutes
    E. 79 minutes

Show more

For work to complete in 2 hours or less, A and C must complete half the work in an hour. The combined rate
of work of A and C cannot be greater than 30 units in an hour. B and D will complete more than 30 units/hr.
With increasing time, the rate at which they individually complete the work decreases.

Let us assume that A completes the work at 15 units/hr. A will take 4 hours (\(\frac{60}{15} = 4\))

Since the time at which they individually complete work is in consecutive order,
B will take 5 hours and the work done by A in an hour is \(\frac{60}{5} = 12\) units.
C will take 6 hours and the work done by A in an hour is \(\frac{60}{6} = 10\) units.
D will take 7 hours and the work done by A in an hour is \(\frac{60}{7} = 8.5\) units. (approximately)
In an hour, they will complete a total of \(15 + 12 + 10 + 8.5 = 45.5\) units.

Therefore, the time take to complete the work is \(\frac{60}{45.5} = 1.32\) hours (or) 79 minutes(Option E)
User avatar
effatara
User avatar
Joined: 09 Nov 2015
Last visit: 17 Jul 2024
Posts: 195
Own Kudos:
461
Given Kudos: 96
Posts: 195
Kudos: 461
Question of the Week - 43 (While working individually, each of A, B) Updated on: 22 Apr 2019, 01:16
Originally posted by effatara on 18 Apr 2019, 02:17.
Last edited by effatara on 22 Apr 2019, 01:16, edited 2 times in total.
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Because of the structure of the question, we can devise a shortcut to solving this problem – one that takes only a few seconds - by employing a bit of logic:

In solving questions like this we have to fix a minimum or a maximum time for the value to be determined (in this case, the time that all four will take to complete the job). In this particular case, however, we can only fix a minimum time because there is no maximum limit set: A & C could take a 100 or even a million hours to complete the job. It follows that when A, B, C and D all work together there is no maximum time limit and we can only fix a minimum value since there is a fixed relationship between the times that each take to finish the job while working alone.
It stands to reason that the minimum time in which A, B, C and D can complete the work must lie between the highest value (E) and the second highest value (D) thus making E the only possible answer because, if the minimum time is less (i.e. between any two of the lesser answer choices), all the answer choices which are more than the minimum time become possible. For example, if the minimum time is 50 minutes (i.e. between B and C), that would make C, D and E all possible but the question allows for only one correct answer. If the minimum time was more than 79 minutes (E) then the correct answer would have been "None" which is not among the answer choices. So the correct answer can only be E. On the other hand, if the minimum time is less than (A), all the options (A) through (E) could be possible and the correct answer would be "All" which is also not among the given options.
This shortcut could be prevented by changing the structure of the question to allow for more than one correct answer (e.g. D and E, A only, E only, all five, none, etc.).
avatar
archer90
avatar
Joined: 05 Feb 2014
Last visit: 16 Jan 2020
Posts: 9
Posts: 9
Kudos: 0
Question of the Week - 43 (While working individually, each of A, B) 20 Apr 2019, 21:37
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi everyone,

I'm a bit confused and I was hoping to get some clarification on this.

I see an answer that states:
(1/a + a/c) > 1/2
Why does a has to be at least 4? If a were to be 1, (1/1 + 1/3) is indeed greater than 1/2.

Another answer states the opposite:
(1/a + 1/c) < 1/2
In this case, I do understand that a must be at least 4, but why are we posing (1/a + 1/c) less than 1/2 when we know that it takes a+c at least 2 hours to build 60 units?

Thanks so much for helping!
Mike
User avatar
hadimadi
User avatar
Joined: 26 Oct 2021
Last visit: 03 Dec 2022
Posts: 114
Own Kudos:
31
Given Kudos: 94
Posts: 114
Kudos: 31
Question of the Week - 43 (While working individually, each of A, B) 15 Jan 2022, 05:28
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi,

let w,x,y,z be the respective work rates with x=a+1, y=a+2,..., we get from the text:

60/(w+y)>2
30>w+y, because w=60/a and y=60/(a+2) we get
30>60/a+60/(a+2), expanding RHS
30>(120a+120)/(a^2+2a)
30a^2+60a>120a+120, dividing by 30
a^2+2a>4a+4
a^2-2a>4
a(a-2)>4

a is an integer -> a>=4 -> the least possible work rates are w=60/4, x=60/5, ..., so the least time in hours they require to get the job done is given by:

60/(w+x+y+z)=420/319

-> 60*420/319=78.99min -> (E)
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,587
Own Kudos:
1,079
Posts: 38,587
Kudos: 1,079
Question of the Week - 43 (While working individually, each of A, B) 12 Jul 2024, 05:17
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Moderators:
Bunuel
Math Expert
105355 posts
Krunaal
Tuck School Moderator
805 posts