GMAT Practice Question Source:
Difficulty: Sub-600 Level
GMAT Study Guide Module:
GMAT Timing Tips:
Even though this is a relatively easy question, it gives us the opportunity to practice a number of my GMAT timing tips (the links below include growing lists of questions that you can use to practice each tip):
Rate problems: Use D = R x T and W = R x T
Like most work rate problems, we can start with the equation W = R x T and then plug in the work, rate, and time for each scenario that we are considering.
Set the amount of work equal to 1 for a single job
Because we’re talking about a single printing job, we just set W = 1 for each scenario.
Add rates when they are simultaneous
Let’s define variables for the rates for printing presses R, S, and T as Rr, Rs, and Rt. Remember that we can add rates when they are simultaneous, so, when all 3 presses are working together, the rate is Rr + Rs + Rt. When just S and R are working together, the rate is Rs + Rt.
Rate and time are reciprocals of each other for a single job
Since we are given the amounts of time for each scenario, we can set the rate equal to the reciprocal of the time for each scenario. This means that Rr + Rs + Rt = 1/4 and Rs + Rt = 1/5. In addition, we are solving for the time it takes printing press R to do the job working alone; if we call this time Tr, then Tr = 1/Rr, and we can solve for Tr if we know Rr.
Eliminate combinations of variables using substitution
While we can’t solve for Rs and Rt separately, we don’t have to. Since we know their sum Rs + Rt = 1/5, we can just plug this value in for (Rs + Rt) in the equation Rr + Rs + Rt = 1/4. This is enough to allow us to solve for Rr, which then allows us to solve for Tr, which is the final answer to this question.
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