When ticket sales began, Pat was the nth customer in line for a ticket, and customers purchased their tickets at the rate of x customers per minute. Of the following, which best approximates the time, in minutes, that Pat had to wait in line from the moment ticket sales began?
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The wording tripped me up at first — I kept thinking n customers in line means n people ahead of Pat. Once I realized Pat IS the nth customer, the (n-1) made sense.
Same here, the 'nth customer in line' phrasing is doing a lot of work in this one.
Yeah I initially went straight for n/x and had to back up.
Decent rate problem, not too bad once you set it up. Took me about 90 seconds.
Agreed, pretty straightforward ratio reasoning if you don't overthink it.
Can someone explain why we divide by x instead of multiplying? I got stuck between C and D.
Think about units — you want minutes, and x is customers per minute, so you need customers divided by (customers/minute).
Ask yourself what happens if x gets bigger: waiting time should shrink. That kills the multiply options fast.
Nice one. I like that it tests whether you actually read 'nth customer' carefully rather than just plugging n/x.
What it tests
Your ability to combine individual work rates, usually by working with the fraction of a job completed per unit of time.
Common trap
Adding the times instead of the rates, or forgetting to take the reciprocal when combining rates.