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

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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!

Originally posted by Himalayan on 14 Jul 2007, 18:58.
Last edited by Bunuel on 16 Apr 2012, 00:35, edited 2 times in total.
Edited the question and added the OA
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Re: A and B working together can finish a job in d days. If A  [#permalink]

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New post 16 Apr 2012, 00:36
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

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

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New post 25 Dec 2012, 21:21
4
5
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 8-)

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

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New post Updated on: 15 Apr 2012, 18:39
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, 18:29.
Last edited by alphabeta1234 on 15 Apr 2012, 18:39, edited 1 time in total.
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Re: A and B working together can finish a job in d days. If A  [#permalink]

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New post 15 Apr 2012, 18:36
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

Please solve it with your intellectual prowess!


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

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New post 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...

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

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New post 23 Jan 2013, 23:56
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 8-)

Answer : [C]


What is the source of this trick? good one though.it can reduce the time to ans tremendously
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Re: A and B working together can finish a job in d days. If A  [#permalink]

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New post 24 Jan 2013, 01:47
I was going through this 9th grade math text book to pick up on my basics, found a number of shortcuts there :)
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Re: A and B working together can finish a job in d days. If A  [#permalink]

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New post 24 Jan 2013, 12:16
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
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Re: A and B working together can finish a job in d days. If A  [#permalink]

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

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New post 08 Nov 2015, 22:40
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
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Re: A and B working together can finish a job in d days. If A  [#permalink]

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

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New post 23 Dec 2015, 06:13
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

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.

Thus d= 15 is the only acceptable solution.

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

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New post 23 Dec 2015, 06:14
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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
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Re: A and B working together can finish a job in d days. If A  [#permalink]

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New post 22 Jun 2016, 14:32
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 8-)

Answer : [C]


Was there an explanation to this trick ? Thanks
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Re: A and B working together can finish a job in d days. If A  [#permalink]

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

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New post 05 Sep 2018, 04:37
EMPOWERgmatRichC would love your thoughts on this one
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Re: A and B working together can finish a job in d days. If A  [#permalink]

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New post 05 Sep 2018, 20:51
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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.

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

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New post 06 Sep 2018, 04:41
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.

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

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New post 06 Sep 2018, 04:51
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

Please solve it with your intellectual prowess!


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

Answer: option C
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