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

 It is currently 17 Feb 2019, 12:08

### 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 February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Free GMAT Algebra Webinar

February 17, 2019

February 17, 2019

07:00 AM PST

09:00 AM PST

Attend this Free Algebra Webinar and learn how to master Inequalities and Absolute Value problems on GMAT.
• ### Valentine's day SALE is on! 25% off.

February 18, 2019

February 18, 2019

10:00 PM PST

11:00 PM PST

We don’t care what your relationship status this year - we love you just the way you are. AND we want you to crush the GMAT!

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

Author Message
TAGS:

### Hide Tags

Director
Joined: 26 Feb 2006
Posts: 846
A and B working together can finish a job in d days. If A  [#permalink]

### Show Tags

Updated on: 15 Apr 2012, 23:35
9
00:00

Difficulty:

15% (low)

Question Stats:

80% (02:17) correct 20% (02:52) wrong based on 515 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?

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

Originally posted by Himalayan on 14 Jul 2007, 17:58.
Last edited by Bunuel on 15 Apr 2012, 23:35, edited 2 times in total.
Edited the question and added the OA
Math Expert
Joined: 02 Sep 2009
Posts: 52906
Re: A and B working together can finish a job in d days. If A  [#permalink]

### Show Tags

15 Apr 2012, 23:36
5
1
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

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: $$\frac{1}{15+5}+\frac{1}{15+45}=\frac{1}{20}+\frac{1}{60}=\frac{1}{15}$$.

_________________
Intern
Joined: 28 Aug 2012
Posts: 46
Concentration: Operations, Marketing
GMAT 1: 510 Q36 V25
GPA: 4
WE: Information Technology (Other)
Re: A and B working together can finish a job in d days. If A  [#permalink]

### Show Tags

25 Dec 2012, 20:21
5
6
There is always a trick to such Qs when your given A+B= x days , A= x+ something , B=x+ something .
To find X , use the formula X=$$\sqrt{ab}$$

X=$$\sqrt{5*45}$$
X= 15 days

##### General Discussion
Manager
Joined: 12 Feb 2012
Posts: 124
Re: A and B working together can finish a job in d days. If A  [#permalink]

### Show Tags

Updated on: 15 Apr 2012, 17:39
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.

Originally posted by alphabeta1234 on 15 Apr 2012, 17:29.
Last edited by alphabeta1234 on 15 Apr 2012, 17:39, edited 1 time in total.
Manager
Joined: 12 Mar 2012
Posts: 233
Concentration: Operations, Strategy
Re: A and B working together can finish a job in d days. If A  [#permalink]

### Show Tags

15 Apr 2012, 17:36
5
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

1/(d+5) +1/(d+45)= 1/d
=> (2d+50)d = (d+5)*(d+45)
=> d^2 = 9*5*5
=> d= 15

hence option C.
_________________

Practice Practice and practice...!!

If there's a loophole in my analysis--> suggest measures to make it airtight.

Manager
Status: I will not stop until i realise my goal which is my dream too
Joined: 25 Feb 2010
Posts: 188
Schools: Johnson '15
Re: A and B working together can finish a job in d days. If A  [#permalink]

### Show Tags

15 Apr 2012, 20:40
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

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)

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

Satyameva Jayate - Truth alone triumphs

Manager
Joined: 22 Nov 2010
Posts: 221
Location: India
GMAT 1: 670 Q49 V33
WE: Consulting (Telecommunications)
Re: A and B working together can finish a job in d days. If A  [#permalink]

### Show Tags

23 Jan 2013, 22:56
3
thinktank wrote:
There is always a trick to such Qs when your given A+B= x days , A= x+ something , B=x+ something .
To find X , use the formula X=$$\sqrt{ab}$$

X=$$\sqrt{5*45}$$
X= 15 days

What is the source of this trick? good one though.it can reduce the time to ans tremendously
_________________

YOU CAN, IF YOU THINK YOU CAN

Intern
Joined: 28 Aug 2012
Posts: 46
Concentration: Operations, Marketing
GMAT 1: 510 Q36 V25
GPA: 4
WE: Information Technology (Other)
Re: A and B working together can finish a job in d days. If A  [#permalink]

### Show Tags

24 Jan 2013, 00:47
I was going through this 9th grade math text book to pick up on my basics, found a number of shortcuts there
Manager
Joined: 18 Oct 2011
Posts: 86
Location: United States
Concentration: Entrepreneurship, Marketing
GMAT Date: 01-30-2013
GPA: 3.3
Re: A and B working together can finish a job in d days. If A  [#permalink]

### Show Tags

24 Jan 2013, 11:16
1
1/A = 1/(d+5)
1/B = 1/(d+45)

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

When you do the math you end up with d^2 = 225. Therefore, d=15
Math Expert
Joined: 02 Sep 2009
Posts: 52906
Re: A and B working together can finish a job in d days. If A  [#permalink]

### Show Tags

25 Jan 2013, 04:40
chiccufrazer1 wrote:
:shock: at bunuel..but solving for d is mathematically correct..then why is it that our answer is C

_________________
Manager
Joined: 23 Sep 2015
Posts: 82
Concentration: General Management, Finance
GMAT 1: 680 Q46 V38
GMAT 2: 690 Q47 V38
GPA: 3.5
Re: A and B working together can finish a job in d days. If A  [#permalink]

### Show Tags

08 Nov 2015, 21:40
can someone show the steps (expanded form) on how to solve for d from the formula

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

thanks
Manager
Joined: 03 Jan 2015
Posts: 74
Re: A and B working together can finish a job in d days. If A  [#permalink]

### Show Tags

23 Dec 2015, 05:03
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

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: $$\frac{1}{15+5}+\frac{1}{15+45}=\frac{1}{20}+\frac{1}{60}=\frac{1}{15}$$.

Could you please show the expanded form as to how to solve for d please? Thank you.
CEO
Joined: 20 Mar 2014
Posts: 2629
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: A and B working together can finish a job in d days. If A  [#permalink]

### Show Tags

23 Dec 2015, 05:13
1
saiesta wrote:
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

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: $$\frac{1}{15+5}+\frac{1}{15+45}=\frac{1}{20}+\frac{1}{60}=\frac{1}{15}$$.

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.

Thus d= 15 is the only acceptable solution.

Hope this helps.
CEO
Joined: 20 Mar 2014
Posts: 2629
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: A and B working together can finish a job in d days. If A  [#permalink]

### Show Tags

23 Dec 2015, 05:14
1
GMATDemiGod wrote:
can someone show the steps (expanded form) on how to solve for d from the formula

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

thanks

Refer to a-and-b-working-together-can-finish-a-job-in-d-days-if-a-48822.html#p1621558
Intern
Joined: 08 Feb 2015
Posts: 4
Re: A and B working together can finish a job in d days. If A  [#permalink]

### Show Tags

22 Jun 2016, 13:32
thinktank wrote:
There is always a trick to such Qs when your given A+B= x days , A= x+ something , B=x+ something .
To find X , use the formula X=$$\sqrt{ab}$$

X=$$\sqrt{5*45}$$
X= 15 days

Was there an explanation to this trick ? Thanks
Director
Joined: 04 Jun 2016
Posts: 568
GMAT 1: 750 Q49 V43
Re: A and B working together can finish a job in d days. If A  [#permalink]

### Show Tags

22 Jul 2016, 09:55
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

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

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

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

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

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

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

$$2d^2+50d=d^2+5d+45+225$$

$$2d^2+50d=d^2+50d+225$$

$$2d^2-d^2=225$$

$$d^2=225$$

$$d=\sqrt{225}$$

$$d=15$$

_________________

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. .. 16 March 2017 - I am back but for all purposes please consider me semi-retired.

Intern
Joined: 18 Apr 2018
Posts: 16
Re: A and B working together can finish a job in d days. If A  [#permalink]

### Show Tags

05 Sep 2018, 03:37
EMPOWERgmatRichC would love your thoughts on this one
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13540
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: A and B working together can finish a job in d days. If A  [#permalink]

### Show Tags

05 Sep 2018, 19:51
1
Hi All,

Since we have two entities working on a job together, we're dealing with a Work Formula question.

Work = (A)(B)/(A+B) where A and B are the two individual times it takes to complete the job.

We're told that it takes two people D days to complete a task - and the individual times are (D+5) days and (D+45) days. From the answer choices, we know that D is an INTEGER... so we're going to end up reducing a fraction to an integer. This question is perfect for TESTing THE ANSWERS.

Notice how we're adding A and B in the denominator; that sum will almost certainly be a nice 'round' number - again, since the fraction reduces to "D" - so the correct answer is likely A, B or C. Let's TEST Answer C first...

IF....
D=15 days...
then the two individual rates are 20 days and 60 days.
When we plug those two values into the Work Formula, what do we end up with....?
(20)(60)/(20+60) =
1200/80 =
15
That is an exact match for the value of D, so this MUST be the answer.

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Intern
Joined: 18 Apr 2018
Posts: 16
Re: A and B working together can finish a job in d days. If A  [#permalink]

### Show Tags

06 Sep 2018, 03:41
1
EMPOWERgmatRichC wrote:
Hi All,

Since we have two entities working on a job together, we're dealing with a Work Formula question.

Work = (A)(B)/(A+B) where A and B are the two individual times it takes to complete the job.

We're told that it takes two people D days to complete a task - and the individual times are (D+5) days and (D+45) days. From the answer choices, we know that D is an INTEGER... so we're going to end up reducing a fraction to an integer. This question is perfect for TESTing THE ANSWERS.

Notice how we're adding A and B in the denominator; that sum will almost certainly be a nice 'round' number - again, since the fraction reduces to "D" - so the correct answer is likely A, B or C. Let's TEST Answer C first...

IF....
D=15 days...
then the two individual rates are 20 days and 60 days.
When we plug those two values into the Work Formula, what do we end up with....?
(20)(60)/(20+60) =
1200/80 =
15
That is an exact match for the value of D, so this MUST be the answer.

GMAT assassins aren't born, they're made,
Rich

Seems like I didn't have the intuition to start with testing C. I started testing B and D as that what I usually do, and ended up wasting too much time.
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2779
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: A and B working together can finish a job in d days. If A  [#permalink]

### Show Tags

06 Sep 2018, 03:51
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

Rate of A & B together = Rate of A + rate of B

i.e. 1/d = 1/(d+5) + 1/(d+45)

d must be a multiple of 5 for this equation to be true so check with a few values d = 5, 10, 15, 20 etc.

1/15 = 1/20 + 1/60
hence d = 15 fits

_________________

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

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Re: A and B working together can finish a job in d days. If A   [#permalink] 06 Sep 2018, 03:51

Go to page    1   2    Next  [ 21 posts ]

Display posts from previous: Sort by