The Quick Way Through GMAT Work Problems

by on August 20th, 2015

GMAT-blog-workproblemsA category of question that appears regularly on the GMAT is that of work problems. A typical question involves one machine working at a particular rate, and another machine working at a different rate. The question may ask you to work out how long a job will take if both machines work on it together.

Here’s a popular strategy that you can use (stay tuned for our tutors’ favorite strategy next week):

1. Stick with this formula for simpler problems:

1/x + 1/y = 1/t

x is the completion time for one machine, y is the completion time for the other, and t is the completion time when both machines work together. For example: Machine A takes 6 hours to do a job. Machine B takes 18 hours to do the same job. How long would it take to do the job if both machines worked together?

2. Applying the formula:

1/x + 1/y = 1/t

implies 1/6 + 1/18 = 1/t

implies 3/18 + 1/18 = 1/t

implies 4/18 = 1/t

implies t = 18/4 = 4.5

3. When things get trickier!

Take an example from Economist GMAT Tutor’s bank of questions:

Working alone, Manuel finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone. Manuel alone cleans the entire house in 6 hours. How many hours will it take Nick and Manuel to clean the entire house if they work together?

Solution: First, work out how long Nick takes to clean the house alone, using the various pieces of information given:

  • Manuel cleans the entire house in 6 hours.
  • Therefore, he cleans half the house in 6/2 = 3 hours.
  • This is one-third of the time it takes Nick to clean the whole house.
  • Therefore, Nick takes 3 * 3 = 9 hours to clean the house.

Second, apply the formula. We need the time they take together to clean one house (notice that ‘the house’ means one house):

1/6 + 1/9 = 1/t

3/18 + 2/18 = 1/t

5/18 = 1/t

t = 18/5 = 3.6

These problems may sound complicated, but as long as you use the one formula required, you can solve them within the two-minute target time for each question.

This post appeared first on the Economist GMAT Tutor blog.

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