Last visit was: 18 Jun 2025, 10:44 It is currently 18 Jun 2025, 10:44
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
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 18 June 2025
Posts: 102,118
Own Kudos:
Given Kudos: 93,918
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,118
Kudos: 733,445
 [38]
1
Kudos
Add Kudos
37
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 18 June 2025
Posts: 102,118
Own Kudos:
Given Kudos: 93,918
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,118
Kudos: 733,445
 [12]
4
Kudos
Add Kudos
8
Bookmarks
Bookmark this Post
General Discussion
User avatar
Nightmare007
Joined: 26 Aug 2016
Last visit: 05 Aug 2020
Posts: 438
Own Kudos:
Given Kudos: 204
Location: India
Concentration: Operations, International Business
GMAT 1: 690 Q50 V33
GMAT 2: 700 Q50 V33
GMAT 3: 730 Q51 V38
GPA: 4
WE:Information Technology (Consulting)
Products:
GMAT 3: 730 Q51 V38
Posts: 438
Kudos: 425
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 18 June 2025
Posts: 102,118
Own Kudos:
733,445
 [1]
Given Kudos: 93,918
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,118
Kudos: 733,445
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Nightmare007
Hi Bunuel,
Can you spot my error

(A+B)/AB = 1/6.

Statement 1 : A + B = 25
AB = 150.

A-B = ((A+B)^2 - 4AB)^1/2
A-B = constant.
A+B = 25

Can't we get statement 1 enough.

???

From (1) we get two solutions: A = 10 and B = 15 OR A = 15 and B = 10.
avatar
aliakberza
Joined: 11 Feb 2018
Last visit: 21 Feb 2020
Posts: 41
Own Kudos:
Given Kudos: 148
Posts: 41
Kudos: 110
Kudos
Add Kudos
Bookmarks
Bookmark this Post
chetan2u Bunuel

Hi. Could someone please explain why \(\frac{1}{B}+\frac{1}{B+5}=\frac{1}{6}\) as a solution to st-2 is not a valid equation. Solving this yields b=3, but clearly \(\frac{1}{3}+\frac{1}{8}\) is not equal to \(\frac{1}{6}\), which led me to believe I had done sth else wrong or was applying the incorrect methodology altogether. Appreciate your help please.
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 18 Jun 2025
Posts: 11,303
Own Kudos:
Given Kudos: 333
Status:Math and DI Expert
Products:
Expert
Expert reply
Posts: 11,303
Kudos: 41,246
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi..
You are going wrong in finding solution..
The solutions will be 10 and -3..
(1/b)+(1/(b+5))=1/6..
6(b+5+b)=b^2+5b...12b+30=b^2+5b...
b^2-7b-30=0....(b-10)(b+3)=0..
So b=10 and -3

Hope it helps

Posted from my mobile device
User avatar
Oppenheimer1945
Joined: 16 Jul 2019
Last visit: 17 Jun 2025
Posts: 797
Own Kudos:
Given Kudos: 223
Location: India
GMAT Focus 1: 645 Q90 V76 DI80
GPA: 7.81
Kudos
Add Kudos
Bookmarks
Bookmark this Post
chetan2u GMATinsight Bunuel
how are we getting this slution for st 1? We are getting A=10 and -5 . Why would we randomly consider other variations

Bunuel
Nightmare007
Hi Bunuel,
Can you spot my error

(A+B)/AB = 1/6.

Statement 1 : A + B = 25
AB = 150.

A-B = ((A+B)^2 - 4AB)^1/2
A-B = constant.
A+B = 25

Can't we get statement 1 enough.

???

From (1) we get two solutions: A = 10 and B = 15 OR A = 15 and B = 10.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 18 June 2025
Posts: 102,118
Own Kudos:
733,445
 [1]
Given Kudos: 93,918
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,118
Kudos: 733,445
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
samagra21
chetan2u GMATinsight Bunuel
how are we getting this slution for st 1? We are getting A=10 and -5 . Why would we randomly consider other variations

Bunuel
Nightmare007
Hi Bunuel,
Can you spot my error

(A+B)/AB = 1/6.

Statement 1 : A + B = 25
AB = 150.

A-B = ((A+B)^2 - 4AB)^1/2
A-B = constant.
A+B = 25

Can't we get statement 1 enough.

???

From (1) we get two solutions: A = 10 and B = 15 OR A = 15 and B = 10.

For (1) we have 1/A + 1/B = 1/6 and A + B = 25. After substituting B = 25 - A into 1/A + 1/B = 1/6 we get 1/A + 1/(25 - A) = 1/6, which gives A^2 -25A + 150 = 0, which gives A = 10 or A = 15. But as explained in the solution, you don't really need to do all that if you recognize that for (1) we have no way of distinguishing machines A and B from one another and thus we have to get two solutions for A and B: \(A \lt B\) and \(A \gt B\).
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 18 June 2025
Posts: 102,118
Own Kudos:
733,445
 [1]
Given Kudos: 93,918
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,118
Kudos: 733,445
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
User avatar
joe123x
Joined: 03 Oct 2022
Last visit: 25 Dec 2023
Posts: 85
Own Kudos:
Given Kudos: 53
GMAT 1: 610 Q40 V34
GMAT 1: 610 Q40 V34
Posts: 85
Kudos: 16
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Official Solution:


Machine A and B working together at their constant rates can complete a certain task in 6 days. In how many days, working alone, can machine A complete the task?

Let A and B be the times needed for machines A and B to complete the task working alone, respectively. Thus, we have \(\frac{1}{A}+\frac{1}{B}=\frac{1}{6}\).

(1) The average (arithmetic mean) of the respective times A and B would each take to complete the task working alone is 12.5 days.

This implies that \(A+B=2*12.5=25\). However, since we do not know which machine is faster (we cannot differentiate between A and B), even if we substitute B with \(25-A\) into \(\frac{1}{A}+\frac{1}{B}=\frac{1}{6}\) to get \(\frac{1}{A} + \frac{1}{25-A} = \frac{1}{6}\) and solve, we must get two different answers for A and B: \(A \lt B\) and \(A \gt B\). Not sufficient.

(2) It would take machine A 5 more days to complete the task alone than it would take machine B to complete the task.

This implies that \(A=B+5\). Substituting this into the equation, we get \(\frac{1}{A}+\frac{1}{A-5}=\frac{1}{6}\). We can solve for \(A\) to get \(A=2\) or \(A=15\). However, \(A=2\) cannot be true since it would make \(B\) negative, so \(A = 15\) is the only valid solution. Sufficient.


Answer: B

while I did answer B.

I couldn't get to solve \(\frac{1}{A}+\frac{1}{A-5}=\frac{ 1}{6}\)

could you please explain how did we get A=2, A= 15? I understand that we will get a quadratic.
but the one I got is: \(A^2-5A-6=0 \)
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 18 June 2025
Posts: 102,118
Own Kudos:
733,445
 [2]
Given Kudos: 93,918
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,118
Kudos: 733,445
 [2]
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
joe123x
Bunuel
Official Solution:


Machine A and B working together at their constant rates can complete a certain task in 6 days. In how many days, working alone, can machine A complete the task?

Let A and B be the times needed for machines A and B to complete the task working alone, respectively. Thus, we have \(\frac{1}{A}+\frac{1}{B}=\frac{1}{6}\).

(1) The average (arithmetic mean) of the respective times A and B would each take to complete the task working alone is 12.5 days.

This implies that \(A+B=2*12.5=25\). However, since we do not know which machine is faster (we cannot differentiate between A and B), even if we substitute B with \(25-A\) into \(\frac{1}{A}+\frac{1}{B}=\frac{1}{6}\) to get \(\frac{1}{A} + \frac{1}{25-A} = \frac{1}{6}\) and solve, we must get two different answers for A and B: \(A \lt B\) and \(A \gt B\). Not sufficient.

(2) It would take machine A 5 more days to complete the task alone than it would take machine B to complete the task.

This implies that \(A=B+5\). Substituting this into the equation, we get \(\frac{1}{A}+\frac{1}{A-5}=\frac{1}{6}\). We can solve for \(A\) to get \(A=2\) or \(A=15\). However, \(A=2\) cannot be true since it would make \(B\) negative, so \(A = 15\) is the only valid solution. Sufficient.


Answer: B

while I did answer B.

I couldn't get to solve \(\frac{1}{A}+\frac{1}{A-5}=\frac{ 1}{6}\)

could you please explain how did we get A=2, A= 15? I understand that we will get a quadratic.
but the one I got is: \(A^2-5A-6=0 \)

Sure.

    \(\frac{1}{A}+\frac{1}{A-5}=\frac{1}{6}\);

    \(\frac{A - 5 + A}{A(A-5)}=\frac{1}{6}\);

    \(\frac{2A-5}{A(A-5)}=\frac{1}{6}\);

    \(12A-30 = A(A-5)\);

    \(12A-30 = A^2-5A\);

    \(A^2 - 17A+ 30 = 0\);

    \(A=2\) or \(A=15\).
User avatar
BottomJee
User avatar
Retired Moderator
Joined: 05 May 2019
Last visit: 09 Jun 2025
Posts: 996
Own Kudos:
Given Kudos: 1,009
Affiliations: GMAT Club
Location: India
GMAT Focus 1: 645 Q82 V81 DI82
GMAT 1: 430 Q31 V19
GMAT 2: 570 Q44 V25
GMAT 3: 660 Q48 V33
GPA: 3.26
WE:Engineering (Manufacturing)
Products:
GMAT Focus 1: 645 Q82 V81 DI82
GMAT 3: 660 Q48 V33
Posts: 996
Kudos: 1,174
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I think this is a high-quality question and I agree with explanation.
User avatar
einstein801
Joined: 23 Jan 2024
Last visit: 18 Feb 2025
Posts: 181
Own Kudos:
Given Kudos: 138
Posts: 181
Kudos: 128
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Please explain how you get 2 solutions from (1):

A^2-25A+150 = (A+5)(A-30). --> A=-5 or 30.
Bunuel
Nightmare007
Hi Bunuel,
Can you spot my error

(A+B)/AB = 1/6.

Statement 1 : A + B = 25
AB = 150.

A-B = ((A+B)^2 - 4AB)^1/2
A-B = constant.
A+B = 25

Can't we get statement 1 enough.

???
From (1) we get two solutions: A = 10 and B = 15 OR A = 15 and B = 10.
­
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 18 June 2025
Posts: 102,118
Own Kudos:
Given Kudos: 93,918
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,118
Kudos: 733,445
Kudos
Add Kudos
Bookmarks
Bookmark this Post
unicornilove
Please explain how you get 2 solutions from (1):

A^2-25A+150 = (A+5)(A-30). --> A=-5 or 30.
Bunuel
Nightmare007
Hi Bunuel,
Can you spot my error

(A+B)/AB = 1/6.

Statement 1 : A + B = 25
AB = 150.

A-B = ((A+B)^2 - 4AB)^1/2
A-B = constant.
A+B = 25

Can't we get statement 1 enough.

???
From (1) we get two solutions: A = 10 and B = 15 OR A = 15 and B = 10.
­
­A^2 -25A + 150 = 0

(A - 10)(A - 15) = 0

A = 10 or A = 15.
 
Moderators:
Math Expert
102118 posts
Founder
40930 posts