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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 [#permalink]

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14 Jul 2007, 17:58
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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

[Reveal] Spoiler: OA

Last edited by Bunuel on 15 Apr 2012, 23:35, 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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15 Apr 2012, 17:29
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, 17:39, 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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15 Apr 2012, 17:36
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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.
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Re: A and B working together can finish a job in d days. If A [#permalink]

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

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15 Apr 2012, 23:36
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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: $$\frac{1}{15+5}+\frac{1}{15+45}=\frac{1}{20}+\frac{1}{60}=\frac{1}{15}$$.

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

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25 Dec 2012, 20:21
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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

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

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23 Jan 2013, 22:56
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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
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Re: A and B working together can finish a job in d days. If A [#permalink]

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

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24 Jan 2013, 11:16
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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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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

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17 Jun 2014, 08:59
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18 Aug 2015, 08:21
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Re: A and B working together can finish a job in d days. If A [#permalink]

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

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

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23 Dec 2015, 05:13
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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.
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Re: A and B working together can finish a job in d days. If A [#permalink]

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23 Dec 2015, 05:14
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Re: A and B working together can finish a job in d days. If A [#permalink]

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

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

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

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

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

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

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

$$d^2=225$$

$$d=\sqrt{225}$$

$$d=15$$

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Re: A and B working together can finish a job in d days. If A   [#permalink] 22 Jul 2016, 09:55
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