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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

A and B working together can finish a job in d days. If A [#permalink]

Show Tags

14 Jul 2007, 18:58

5

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

25% (medium)

Question Stats:

77% (05:42) correct
23% (02:23) wrong based on 457 sessions

HideShow timer Statistics

A and B working together can finish a job in d days. If A works alone and completes the job, he will take d + 5 days. If B works alone and completes the same job, he will take d + 45 days. What is d?

Re: A and B working together can finish a job in d days. If A [#permalink]

Show Tags

15 Apr 2012, 18:29

Sorry to revisit an old post but this was a toughy! Its not a necessary condition that d be an integer.

So working together they can do the job is d days. Let \(r_1\) be the rate of A Let \(r_2\) be the rate of B

Working together their rates to do the job is Equation1: \((r_1+r_2)d=1 (job)\)

A working alone can do the job by Equation2: \((r_1)(d+5)=1 (job)\)

B working alone can do the job by Equation3: \((r_2)(d+45)=1 (job)\)

Now set the first equation to the second equation

\((r_1+r_2)d=1 = (r_1)(d+5)\) solve for d to get \(d=5(r_1/r_2)\)

Now set equation1 to equation2

\((r_1)(d+5)=1 =(r_2)(d+45)\) solve to get \(r_1/r_2=(d+45)/(d+5)\)

Now substitute \(d=5(r_1/r_2)=5((d+45)/(d+5))\)

to get \(d(d+5)=5(d+45)\)

which leads you to \(d^2=5*45\). Which is equal to \(d=15\) when you square root both sides (of couse d must be positive, were talking about days here!).

Again, tough problem. If anyone has an easier method let us know.

Last edited by alphabeta1234 on 15 Apr 2012, 18:39, edited 1 time in total.

Re: A and B working together can finish a job in d days. If A [#permalink]

Show Tags

15 Apr 2012, 18:36

4

This post received KUDOS

Himalayan wrote:

A and B working together can finish a job in d days. If A works alone and completes the job, he will take d + 5 days. If B works alone and completes the same job, he will take d + 45 days. What is d?

Re: A and B working together can finish a job in d days. If A [#permalink]

Show Tags

15 Apr 2012, 21:40

Himalayan wrote:

A and B working together can finish a job in d days. If A works alone and completes the job, he will take d + 5 days. If B works alone and completes the same job, he will take d + 45 days. What is d?

(1) 25 (2) 60 (3) 15 (4) 14 (5) 13

Please solve it with your intellectual prowess!

take the total work as X

so both A & B can do it in d days, A alone in d+5 and B alone in d+45

rate calculation is total rate = sum of individual rates

X/d = X/(d+5) + X/(d+45)

we can remove X, then the equation becomes as below

1/d = 1/(d+5) + 1/(d+45)

simplification leads to

d^2 = 225

d= + or - 15

u cannot have days in negative right as it should take some time to do a task...hence 15 is the answer...

Note: Give me kudos if my approach is right , else help me understand where i am missing.. I want to bell the GMAT Cat
_________________

Regards, Harsha

Note: Give me kudos if my approach is right , else help me understand where i am missing.. I want to bell the GMAT Cat

A and B working together can finish a job in d days. If A works alone and completes the job, he will take d + 5 days. If B works alone and completes the same job, he will take d + 45 days. What is d?

(1) 25 (2) 60 (3) 15 (4) 14 (5) 13

Please solve it with your intellectual prowess!

If A works alone and completes the job, he will take d + 5 days --> the rate of A is \(\frac{1}{d+5}\) job/day; If B works alone and completes the job, he will take d + 45 days --> the rate of B is \(\frac{1}{d+45}\) job/day;

Since A and B working together can finish a job in d days, then their combined rate is \(\frac{1}{d}\) job/day;

So, \(\frac{1}{d+5}+\frac{1}{d+45}=\frac{1}{d}\). At this point it's MUCH better to substitute the values from the answer choices rather than to solve for \(d\).

Answer choice C fits: \(\frac{1}{15+5}+\frac{1}{15+45}=\frac{1}{20}+\frac{1}{60}=\frac{1}{15}\).

Re: A and B working together can finish a job in d days. If A [#permalink]

Show Tags

17 Jun 2014, 09:59

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: A and B working together can finish a job in d days. If A [#permalink]

Show Tags

18 Aug 2015, 09:21

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: A and B working together can finish a job in d days. If A [#permalink]

Show Tags

23 Dec 2015, 06:03

Bunuel wrote:

Himalayan wrote:

A and B working together can finish a job in d days. If A works alone and completes the job, he will take d + 5 days. If B works alone and completes the same job, he will take d + 45 days. What is d?

(1) 25 (2) 60 (3) 15 (4) 14 (5) 13

Please solve it with your intellectual prowess!

If A works alone and completes the job, he will take d + 5 days --> the rate of A is \(\frac{1}{d+5}\) job/day; If B works alone and completes the job, he will take d + 45 days --> the rate of B is \(\frac{1}{d+45}\) job/day;

Since A and B working together can finish a job in d days, then their combined rate is \(\frac{1}{d}\) job/day;

So, \(\frac{1}{d+5}+\frac{1}{d+45}=\frac{1}{d}\). At this point it's MUCH better to substitute the values from the answer choices rather than to solve for \(d\).

Answer choice C fits: \(\frac{1}{15+5}+\frac{1}{15+45}=\frac{1}{20}+\frac{1}{60}=\frac{1}{15}\).

Answer: C.

Could you please show the expanded form as to how to solve for d please? Thank you.

A and B working together can finish a job in d days. If A works alone and completes the job, he will take d + 5 days. If B works alone and completes the same job, he will take d + 45 days. What is d?

(1) 25 (2) 60 (3) 15 (4) 14 (5) 13

Please solve it with your intellectual prowess!

If A works alone and completes the job, he will take d + 5 days --> the rate of A is \(\frac{1}{d+5}\) job/day; If B works alone and completes the job, he will take d + 45 days --> the rate of B is \(\frac{1}{d+45}\) job/day;

Since A and B working together can finish a job in d days, then their combined rate is \(\frac{1}{d}\) job/day;

So, \(\frac{1}{d+5}+\frac{1}{d+45}=\frac{1}{d}\). At this point it's MUCH better to substitute the values from the answer choices rather than to solve for \(d\).

Answer choice C fits: \(\frac{1}{15+5}+\frac{1}{15+45}=\frac{1}{20}+\frac{1}{60}=\frac{1}{15}\).

Answer: C.

Could you please show the expanded form as to how to solve for d please? Thank you.

1 thing I would mention here as Bunuel has mentioned as well, you need to be intelligent to pick your battles in GMAT. It is not about finding the correct answer but you also need to make sure that you do not spend more time than what you should be spending.

Putting in the values in the options after you get 1/(d+5) + 1/(d+45) = 1/d , is the fastest way to solve this equation.

But for the sake of your question, look below for the solution:

1/(d+5) + 1/(d+45) = 1/d ---> \(\frac{(2d+50)}{(d+5)(d+45)} = \frac{1}{d}\) ---> \(2d^2+50d=d^2+50d+225\) ---> \(d^2=225\) --->\(d = \pm 15\), you can not have d < 0 as the number of days can only be >0.

Re: A and B working together can finish a job in d days. If A [#permalink]

Show Tags

22 Jul 2016, 10:55

Himalayan wrote:

A and B working together can finish a job in d days. If A works alone and completes the job, he will take d + 5 days. If B works alone and completes the same job, he will take d + 45 days. What is d?

A. 25 B. 60 C. 15 D. 14 E. 13

Please solve it with your intellectual prowess!

Rate of \(A=\frac{1}{(d+5)}\)

Rate of \(B=\frac{1}{(d+45)}\)

Rate of \(A+B= \frac{1}{d}\)

Rate of \(A+B= \frac{1}{(d+45)} + \frac{1}{(d+5)}\)

\(\frac{2d+50}{(d+5)(d+45)}=\frac{1}{d}\)

\((2d+50)d= (d+5)(d+45)\)

\(2d^2+50d=d^2+5d+45+225\)

\(2d^2+50d=d^2+50d+225\)

\(2d^2-d^2=225\)

\(d^2=225\)

\(d=\sqrt{225}\)

\(d=15\)

Answer is C
_________________

Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly. FINAL GOODBYE :- 17th SEPTEMBER 2016.

gmatclubot

Re: A and B working together can finish a job in d days. If A
[#permalink]
22 Jul 2016, 10:55

Hey, guys, So, I’ve decided to run a contest in hopes of getting the word about the site out to as many applicants as possible this application season...

Whether you’re an entrepreneur, aspiring business leader, or you just think that you may want to learn more about business, the thought of getting your Masters in Business Administration...

Term 1 has begun. If you're confused, wondering what my post on the last 2 official weeks was, that was pre-term. What that means is that the school...