What we see: a Data Sufficiency rate question. Two machines work together at steady speeds. We need the exact clock time the order was finished.
Step 1. Know what would answer it.
What we see: we are asked for a time of day, not how long it took.
What it means: we need a fixed point in time (like "half done at 2 p.m.") plus how fast the work goes. Speed alone, or a starting point alone, is not enough.
What we do and why: we read each statement asking, "Does this give both a clock time and a speed?"
Step 2. Statement 1 alone.
What we see: both machines run at the same rate.
What it means: this tells us how the work is shared, but no speed and no clock time.
What we do and why: we cannot find any time from this, so statement 1 is not enough.
Step 3. Statement 2 alone.
What we see: \(\frac{1}{2}\) done by 2:00 p.m., \(\frac{5}{6}\) done by 2:20 p.m.
What it means: in those 20 minutes they did \(\frac{5}{6} - \frac{1}{2} = \frac{5}{6} - \frac{3}{6} = \frac{2}{6} = \frac{1}{3}\) of the order. So \(\frac{1}{3}\) takes 20 minutes, and the whole order takes 60 minutes at this speed.
What we do and why: what is left at 2:20 is \(1 - \frac{5}{6} = \frac{1}{6}\), which is half of \(\frac{1}{3}\), so it takes 10 minutes. The order was done at 2:30 p.m. Statement 2 gives one exact time, so it is enough.
The trap: C. People think they need to know each machine's own speed, so they add statement 1. But the question only cares about the two machines together, and statement 2 already gives their combined speed.
Faster way: in statement 2, the gap from \(\frac{1}{2}\) to \(\frac{5}{6}\) is \(\frac{2}{6}\) in 20 minutes, so each \(\frac{1}{6}\) is 10 minutes. One more \(\frac{1}{6}\) is left: 2:30.
Takeaway: with machines working together, you only need their combined progress over time. Two progress readings at two clock times always give the finish time.
Answer: B
