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A website currently has a bank of 770 questions with two new questions added every three days. A student has already completed 300 of the questions and plans on completing one question per day moving forward. In how many days will the student have completed all the questions available to her?

If they complete one everyday, and 2 new questions come up every three days, on the third day they have a net of one problem done, so they does two problems or so in a week, or 470 in 235 weeks.

Why is my reasoning wrong?

  • "...so she does two problems or so in a week, or 470 in 235 weeks" I think your problem is you are taking this estimation of yours too literally... more accurately she achieves +1 net problem every three days - meaning that in a week she advances by (1net/3days)*7days=2.333net problems. As a sanity check... it'll probably be easier to work the problem out in days and then divide by 7 at the end to get the correct number of weeks. – DotCounter Aug 16 '22 at 19:29
  • Often for these problems you need to find a span of time where everything repeats. Here it would be three days. You can then count those spans until you get close to the end, when you have to consider the sequence within the pattern. Here it seems that on one day two problems are added, but we are not given that the last addition was today, yesterday, or the day before. – Ross Millikan Aug 16 '22 at 20:57

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You should probably think about days and not weeks. Since in three weeks you have 14 new problems (21) days, and not 12 as it would be by your reasoning.

Marija
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