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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?

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:

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.

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.

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.

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:

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?

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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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