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# GMAT Diagnostic Test Question 30

Author Message
Manager
Joined: 25 May 2011
Posts: 147

Kudos [?]: 75 [1], given: 71

Re: GMAT Diagnostic Test Question 30 [#permalink]

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16 Sep 2011, 23:51
1
KUDOS
T= number of days which A & B work together before A leaves B

Equ:

T(1/20+1/30) + 5(1/30) + 4(1/20+1/30)=1
T=6

Kudos [?]: 75 [1], given: 71

Intern
Joined: 06 Nov 2011
Posts: 36

Kudos [?]: 8 [0], given: 50

Location: Germany
Concentration: Entrepreneurship, General Management
GMAT Date: 03-10-2012
GPA: 3
Re: GMAT Diagnostic Test Question 30 [#permalink]

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20 Nov 2011, 03:20
Took me 7 min to solve

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.

Kudos [?]: 8 [0], given: 50

Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132612 [0], given: 12326

Re: GMAT Diagnostic Test Question 30 [#permalink]

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08 Apr 2012, 12:45
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.

_________________

Kudos [?]: 132612 [0], given: 12326

Intern
Joined: 02 Nov 2012
Posts: 35

Kudos [?]: 4 [0], given: 11

Re: GMAT Diagnostic Test Question 30 [#permalink]

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22 Nov 2012, 05:46
700 question it is.

Kudos [?]: 4 [0], given: 11

Current Student
Joined: 24 Apr 2012
Posts: 38

Kudos [?]: 18 [0], given: 35

GMAT 1: 660 Q48 V33
WE: Information Technology (Health Care)
Re: GMAT Diagnostic Test Question 30 [#permalink]

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28 Dec 2012, 14:31
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

Kudos [?]: 18 [0], given: 35

Intern
Status: Going the extra mile
Joined: 08 Feb 2014
Posts: 20

Kudos [?]: 19 [0], given: 57

Location: Netherlands
GMAT 1: 470 Q37 V18
GMAT 2: 570 Q36 V32
GMAT 3: 560 Q37 V30
GMAT 4: 610 Q41 V34
Re: GMAT Diagnostic Test Question 30 [#permalink]

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20 Apr 2014, 07:43
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

_________________

Structural persistence is the key to succes .
Party hard, study harder.

Still bashing, will continue to do so , although it's important to chill aswell ; )
STUDY+CHILL=VICTORY

Kudos [?]: 19 [0], given: 57

Re: GMAT Diagnostic Test Question 30   [#permalink] 20 Apr 2014, 07:43

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# GMAT Diagnostic Test Question 30

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