GRE Work Problems
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Problems involving work and rates can be a problem for many test-takers, but with a clear method to set them up and a little clever plugging in, you can learn to knock them out efficiently and accurately.
Typical GRE work problems look like this:
Working alone at her constant rate, Alicia can paint a room in 5 hours. Working alone at his constant rate, Bill can paint the same room in 6 hours. How many hours will it take the two of them, working together at their respective constant rates, to paint a room?
GRE Work Problems Step 1: Set Up a Rate * Time = Work Chart for GRE Work Problems
Whenever I’m faced with GRE work problems, I set up a chart: R * T = W across the top, my players down the side. I then fill in the information I’ve been given (5 hours and 6 hours are times, so put them in the time column).
GRE Work Problems Step 2: No Job? One Job? x Jobs? Plug in Some Pieces…
If I put 1 in the work column, I’m going to be forced to play with ugly fractions to solve this problem. Instead of wasting time on that, break up the job to something nice and big, easily divisible by 5 and 6. 5 x 6 = 30, so imagine the room is 30 feet long and plug THAT number into the chart.
GRE Work Problems Step 3: Find the Rates and Contemplate the Rate Column
Now I know that if the room is 30 feet long, Alicia is painting 30 feet in 5 hours, or 6 feet per hour, and Bill is painting 5 feet per hour.
What about together? Think about what happens every hour. Alicia is painting 6 feet, Bill is painting 5, so when they’re working together, they paint 11 feet every hour. Put that under the rate in the “together” row.
GRE Work Problems Step 4: Solve It!
Look at that final row. You now know 11 * t = 30, so t = 30/11 or 2 and 8/11 hours.
Let’s Do Another Problem
Imagine the following setup (questions to follow):
Machine X, working alone at a constant rate, produces w widgets in 15 minutes. Machine Y, working alone at a constant rate, takes twice as much time to produce w widgets. How long, working simultaneously at their respective rates, would it take both machines working together to complete 4w widgets?
Go ahead and set up your chart, then find a job to plug in (some multiple of 15 and 30. Let’s say w = 60) and find each machine’s rate. Working together, you know they make 6 widgets every minute, so making 240 widgets would take them 40 minutes.
(Be careful here! The work is no longer 60, it’s 4*60, or 240.)
You’re now ready to answer any other question the test might throw your way with the same scenario.
If the two machines work together to complete w widgets…
How many widgets did X make?
How many widgets did Y make?
First, go back and fill in that “together” row with the job of w = 60 widgets. Then figure out how much time it would take for them to finish the job. (6t=60, so t=10)
Then, see how many X could make in 10 minutes. (It could make 40)
And how many Y could make in 10 minutes. (It could make 20)
Multiple Identical Machines
Before we begin, you have to check a particular cognitive bias at the door.
If it takes 5 robots 5 hours to make a total of 5 toys, how long would it take 10 robots to make 10 toys?
It’s 10 hours, right? NOPE!!! (Don’t think too hard about this, but each robot is taking the whole five hours to make one toy, so each of those 10 robots is each taking 5 hours to make one toy so…confused yet?)
The best way to cope with complex GRE work problems involving a bunch of things all working at the same rate is to modify your work formula. Your new formula is R * T * N = W (Rate for each * time * number of workers = total work done).
If it takes 5 robots 5 hours to make a total of 5 toys, how long would it take 10 robots to make 10 toys at the same rate?
Set up your chart and find out one robot’s rate. n = 5 robots, t = 5 hours, and w = 5 toys:
Use that same rate in the next row and now slot in n = 10 robots and w = 10 toys.
Now solve for t!
You can find similar GRE work problems all throughout our 5-lb Book and the GRE Official Guide. Try a few for yourself (and if there’s no specified job, plug in your own)! ?
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When not onstage telling jokes, Neil Thornton loves teaching you to beat the GRE and GMAT. Since 1991, he’s coached thousands of students through the GRE, GMAT, LSAT, MCAT, and SAT and trained instructors all over the United States. He scored 780 on the GMAT, a perfect 170Q/170V on the GRE, and a 99th-percentile score on the LSAT. Check out Neil’s upcoming GRE course offerings here or join him for a free online study session twice monthly in Mondays with Neil.