gmattesttaker2 wrote:Does Statement 1 mean that Machine Y's speed is 3/4(20) = 15 widgets per hour?

The answer is... it doesn't matter! Because this is a DS question, you don't actually have to do the math here.

First, figure out what your target question really is:

Given: If Machine X can produce 80 widgets in 4 hours, how long would it take machine X and Y working together, to produce 500 widgets?

Infer: If we know X's time and output, then we know X's rate: 80/4. If we want to know the time it would take X and Y working together, then we need Y's rate.

1.Machine Y works at 3/4 the speed of machine X
Don't waste time doing the math here! We know X's rate, so we can use this to get a value for Y's rate. Then we would be able to add X's and Y's together and solve for the time - but we don't need to actually do that!

2.If Machine Y's speed doubled, it would produce 120 widgets in 4 hours
If we are given information about twice Y's rate, then we can solve for Y's rate. Once again, don't actually do that math!

The answer is D.