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# GMAT Diagnostic Test Question 30

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GMAT Diagnostic Test Question 30 [#permalink]  06 Jun 2009, 22:12
Expert's post
GMAT Diagnostic Test Question 30
Field: word problems (work problems)
Difficulty: 750

Painters A and B can paint a house working alone in 20 and 30 days respectively. They started painting a house together but then A left after a number of days but then rejoined B before the job was completed. If B worked alone for 5 days and then A and B together completed the work in 4 days, after how many days of working together, did A leave B?

A. 4
B. 5
C. 6
D. 7
E. 8
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Last edited by bb on 29 Sep 2013, 20:30, edited 1 time in total.
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Re: GMAT Diagnostic Test Question 30 [#permalink]  06 Jul 2009, 08:25
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Explanation:

The rates of work of A and B will be $$\frac{1}{20}$$ and $$\frac{1}{30}$$ respectively. The rate of working together will be $$\frac{1}{20}*\frac{1}{30}=\frac{5}{60}=\frac{1}{12}$$. Now we need to calculate what part of the work was done by A and B together before A left. To do that we subtract the amount of work finished by B alone in 5 days and A+B together in 4 last days from 1:

$$1 - \frac{1}{30}*5 - \frac{1}{12}*4 = 1 - \frac{1}{6} - \frac{1}{3} = \frac{1}{2}$$

Exactly half of the work was finished by A and B prior to A's leaving. Now we can find the number of days A and B were working before A left:

$$\frac{1}{12}*x=\frac{1}{2}$$

$$x=6$$

They were working for 6 days together before A left.
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Last edited by bb on 29 Sep 2013, 20:30, edited 1 time in total.
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Re: GMAT Diagnostic Test Question 30 [#permalink]  22 Aug 2009, 15:19
Fantastic explanation. It took me 6:22 mins to do exactly the same.
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Re: GMAT Diagnostic Test Question 30 [#permalink]  22 Aug 2009, 15:41
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Together A and B can do the work in (1/20 + 1/30 = 5/60) = 12 days.

B alone worked for 5 days i.e. B completed 5/30 = 1/6 th work.

A and B worked together for 4 days i.e they completed 4/12 = 1/3 rd work.

Total work left = 1 - (work completed by B) - (work completed by A and B)
= 1 - 1/6 -1/3
= 1/2

We know that A and B can work together for 12 days to finish the work.
To complete 1/2 the work it will take them 6 days.

Ans = 6 (A and B must have worked for 6 days before A left and then re joined.)

Time taken = 2 mins.
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Re: GMAT Diagnostic Test Question 30 [#permalink]  22 Aug 2009, 20:51
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suppose the painting speed of these two people are m and n, and A left B after worked x days together.

20m=30n
(m+n)*x+5n+(m+n)*4=20m

x=6

within 1 minute.
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Re: GMAT Diagnostic Test Question 30 [#permalink]  31 Aug 2009, 09:48
IMHO:

Compared to the other rate questions on this sufficiency test, I have no idea why it's leveled at "750." This seemed a lot easier that the other word problems.
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Re: GMAT Diagnostic Test Question 30 [#permalink]  18 Sep 2009, 21:45
I agree with stilite. This was comparably easier than the other work problems.
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Re: GMAT Diagnostic Test Question 30 [#permalink]  13 Nov 2009, 14:36
A = 1/20 = 5%.
B = 1/30 = 3 1/3%.
4(A+B) = 4(8 1/3%) = 33 1/3%.
5B = 16 2/3%.

100% - (4(A+B) + 5B) = 50%.
50% divided by 8 1/3% = 6
implies 6 days
implies C.

Takes maybe a minute this way.
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Re: GMAT Diagnostic Test Question 30 [#permalink]  22 Dec 2009, 00:51
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I would change question 30 with question 29 in their difficulty level.
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Re: GMAT Diagnostic Test Question 30 [#permalink]  03 Jan 2010, 11:15
__________X ______ Y=5_______ Z=4
A =20 ------------- --------------
B= 30 -------------- -------------- ---------------

Let’s set the equation
A+B can finish the job in 12 days
1/30 + 1/20 = 1/total days
Total days = 12

X/ (A+B) + Y/B + Z/ (A+B) = 1
X/12 + 5/30 + 4/12 = 1
X/12 = 1 -1/6 – 1/3
X = 6
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Re: GMAT Diagnostic Test Question 30 [#permalink]  07 Jan 2010, 15:09
I solved the problem based on a method some one used to solve question 29.

x= total number of days A and B worked together before A left.

The equation should be

total work done by A + total work done by B = complete work

(X + 4)/20 + (X+ 4 + 5days B worked alone)/30 = 1

(X + 4)/20 + (X+9)/30 = 1

solve for X and we get the answer.
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Re: GMAT Diagnostic Test Question 30 [#permalink]  04 Feb 2010, 19:19
The difficulty level of question 30 and 29 should be reversed. I like this question though. Its along similar lines as question 29. I got both of them right. This took me some time to solve though. Made some silly calculation mistake is why.
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Re: GMAT Diagnostic Test Question 30 [#permalink]  25 Mar 2010, 11:18
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bb wrote:
GMAT Diagnostic Test Question 30
Field: word problems (work problems)
Difficulty: 750
 Rating:

Painters A and B can paint a house working alone in 20 and 30 days respectively. They started painting a house together but then A left after a number of days but then rejoined B before the job was completed. If B worked alone for 5 days and then A and B together completed the work in 4 days, after how many days of working together, did A leave B?

A. 4
B. 5
C. 6
D. 7
E. 8

Let A and B need to paint 600 feet of wall (multiple of 20 and 30)

A does 30feet per day and B does 20feet per day.

Now we know B worked alone for 5 days so work done is 100feet
A&B worked together for 4 days at end that gives 200feet

work remaining is 600-100-200=300 to be done be A&B together which gives 6 days.

This way i solved only in 45 seconds.

Hope this helps.
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Re: GMAT Diagnostic Test Question 30 [#permalink]  25 Apr 2010, 13:32
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+1, really nice and it does not look like a difficult one.

mustdoit wrote:
bb wrote:
GMAT Diagnostic Test Question 30
Field: word problems (work problems)
Difficulty: 750
 Rating:

Let A and B need to paint 600 feet of wall (multiple of 20 and 30)

A does 30feet per day and B does 20feet per day.

Now we know B worked alone for 5 days so work done is 100feet
A&B worked together for 4 days at end that gives 200feet

work remaining is 600-100-200=300 to be done be A&B together which gives 6 days.

This way i solved only in 45 seconds.

Hope this helps.

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Re: GMAT Diagnostic Test Question 30 [#permalink]  18 Jun 2010, 07:16
dzyubam wrote:
Explanation:
 Rating:

The rates of work of A and B will be $$\frac{1}{20}$$ and $$\frac{1}{30}$$ respectively. The rate of working together will be $$\frac{1}{20}*\frac{1}{30}=\frac{5}{60}=\frac{1}{12}$$. Now we need to calculate what part of the work was done by A and B together before A left. To do that we subtract the amount of work finished by B alone in 5 days and A+B together in 4 last days from 1:

$$1 - \frac{1}{30}*5 - \frac{1}{12}*4 = 1 - \frac{1}{6} - \frac{1}{3} = \frac{1}{2}$$

Exactly half of the work was finished by A and B prior to A's leaving. Now we can find the number of days A and B were working before A left:

$$\frac{1}{12}*x=\frac{1}{2}$$

$$x=6$$

They were working for 6 days together before A left.

In your solution, shouldn't the total work be (1/20)+ (1/30) which equals 5/60.
I think you have a typo, when you wrote * instead of +.

Anyways, thank you for the solution.
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Re: GMAT Diagnostic Test Question 30 [#permalink]  27 Aug 2010, 11:48
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I solved this one with the following equation:

5/30 + 4(1/20+1/30) + N (1/20+1/30) = 1

A few simplifications and N=6
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Re: GMAT Diagnostic Test Question 30 [#permalink]  09 Oct 2010, 07:04
Kronax wrote:
I solved this one with the following equation:

5/30 + 4(1/20+1/30) + N (1/20+1/30) = 1

A few simplifications and N=6

Nice one, it is best simplified to denominator 12
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Re: GMAT Diagnostic Test Question 30 [#permalink]  14 Nov 2010, 22:59
If this question took me less than one minute and the previous question made me take a cyanide capsule, what would that tell me, simply the application of a formula in an abstract situation in regards to work is a place where I need work, and if so what would be the specific name of that kind of question or should I have been pleased to have a 50% chance on guessing?
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Re: GMAT Diagnostic Test Question 30 [#permalink]  04 Jan 2011, 14:56
I got this in under two minutes...used Rao's method mentioned above. I visualized the whole thing using a line and calculated how much do they get done in a day (1/20+1/30)=1/12. then basically set up the eqn (using x as the number of days A and B initially worked together)

x(1/12) + 5(1/30)+4(1/12)=1

solved it for x =6 Hence C

Definitely not a 750, more like a 650 or a weak 700.
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Re: GMAT Diagnostic Test Question 30 [#permalink]  17 Jul 2011, 09:16
Hi,

I just had question regarding the solution.

Generally rates are added when two or more people work together, even that is done in Question 29 of the diagnostic test. Why, in this question, we have multiplied individual rates as 1/20*1.30 I feel it should be 1/20 +1/30

It will be useful to have somebody's guidance in this regard

navin
Re: GMAT Diagnostic Test Question 30   [#permalink] 17 Jul 2011, 09:16

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# GMAT Diagnostic Test Question 30

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