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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?

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:

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.

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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