Yesterday, Manhattan GMAT posted a GMAT question on our blog. Today, they have followed up with the answer:
Call the rate for a Type 1 machine x; call the rate for a Type 2 machine y. The Rate-Time-Work equations become the following:
Equation #1: “It takes n Type 1 machines six times as long to produce 120 bolts…”
nx(6t) = 120
Equation #2: “… as it takes 2n Type 2 machines…”
2nyt = 120
Notice that t is simply the time for 2n Type 2 machines to make 120 bolts. It shows up in both equations.
Equation #3: “Together, one Type 1 machine and one Type 2 machine can make 24/n bolts in 4 hours.”
(x + y)4 = 24/n
Equation #4 (the question): “How many hours will it take for 5n Type 1 machines to produce 60 bolts?”
T = ? in 5nxT = 60
Now solve. Equation #3 can be rearranged and simplified quickly:
nx + ny = 6
Isolate nx in Equation #1 and ny in Equation #2:
nx = 20/t and ny = 60/t
nx + ny = 20/t + 60/t = 80/t = 6, so t = 40/3. This means that nx = 20/t = 20/(40/3) = 3/2.
Finally, if 5nxT = 60, we can sub in for nx with 3/2, leaving 5(3/2)T = 60. T = 8.
You might notice that n is a dummy variable – the answer cannot depend on the value of n. So you could simply pick n = 1 and solve.
The correct answer is D.