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GMAT Diagnostic Test Question 30

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Re: GMAT Diagnostic Test Question 30 [#permalink] New post 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

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Re: GMAT Diagnostic Test Question 30 [#permalink] New post 20 Nov 2011, 02:20
Took me 7 min to solve :cry:

First: For A to finish this job, it takes him 20 days
Therefor: on one day he can finish \frac{1}{20} of the job
Second: For B to finish this job, it takes him 30 days.
Therefor: on one day he can finish \frac{1}{30} of the job

Together they can finish the job in \frac{1}{20} + \frac{1}{30}= \frac{1}{12} --> 12 Days.

(1): We know B worked for 5 days alone. Question: How much work he has done in 5 days out of the 12 Days?
--> \frac{1}{30} * 5 = \frac{5}{30}=\frac{1}{6}=\frac{2}{12} (easier to calculate later)

(2): We also know how long A worked with B together. Same question: How much work have they done in 4 days out of 12 days?
--> \frac{1}{12}*4 = \frac{4}{12}

--> 1 - \frac{4}{12} - \frac{2}{12} = \frac{6}{12}

After 6 Days A left the work.
Maybe not the best approach. And Q29 is harder than this one.
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Re: GMAT Diagnostic Test Question 30 [#permalink] New post 08 Apr 2012, 11:45
Expert's post
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



The rate of A is \frac{1}{20} job/day;
The rate of B is \frac{1}{30} job/day;
The combined rate of A and B is \frac{1}{20}+\frac{1}{30}=\frac{1}{12} job/day.

In 5 days that B worked alone (2nd stage) 5*\frac{1}{30}=\frac{2}{12} of the job was done;
In 4 day that A and B worked together (3rd stage) 4*\frac{1}{12}=\frac{4}{12} of the job was done;

So, in the 1st stage of the work 1-\frac{2}{12}-\frac{4}{12}=\frac{6}{12} part of the job was done by A and B together, which at the rate of \frac{1}{12} job/day took them 6 days.

Answer: C.
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Re: GMAT Diagnostic Test Question 30 [#permalink] New post 22 Nov 2012, 04:46
700 question it is.
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Re: GMAT Diagnostic Test Question 30 [#permalink] New post 28 Dec 2012, 13:31
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


I completed this in less than 1 min

Let x be the amount of days forthey worked together

so work done by A+ work done by B = 1
(x+4)*20 + (x+9)*30 = 1

and x =6 :)
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Re: GMAT Diagnostic Test Question 30 [#permalink] New post 20 Apr 2014, 06:43
I solved it slightly different.

Rate A: 1/20
Rate B: 1/30
Rate together: 5/60

They worked together for an unkown amount of days 5/60x
B worked alone for 5 days: 2/60 * 5 = 10/60
A en B completed the work in 4 days : 5/60 * 4 = 20/60

Line them up: 5/60x + 10/60 + 20/60 = 1
5/60x + 30/60 = 1
x = 6

Answer C
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Re: GMAT Diagnostic Test Question 30   [#permalink] 20 Apr 2014, 06:43
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