Q) 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 ?
My Answer - 1406
My Approach - Since a student completes one question in 1 day, So in 3 days she solves 3 questions. But after every 3 days 2 more questions are added to the bank.
So in a span of 3 days, she reduces the number of questions to be solved by 1.
So initially she has 470 questions to solve, so after 1404 (468*3) days she will have left with 2 questions to solve. And by day 1406 she would have solved all the questions.
So the answer should be 1406 (rather than 1410 mentioned in the Video Solution)
@gregmat
@Leaderboard , I think sanket is correct here
I agree. We’ll need to fix this.
There are two questions left to solve after 1404 days. And he solves those in two days. But doesn’t the website add 1.33 questions in those two days? Then she is remaining with 1.33 questions after 1406 days. I think 1410 is the right answer.
The questions are added on day 1407.
I don’t understand how the answer will be 1406. I understand that after 468 questions are complete at the end of 1404 days, there are 2 more questions left (470 - 2). But those 2 questions can only be solved in 6 days (since 2 more questions are added every 3 days, therefore the last 2 questions can each be solved in 3 days) making the total to 1410 days. Can someone help me understand where I am going wrong?
which the student solves in day 1406. And then they have no more questions to do until day 1407, when the website adds three more days. That however is irrelevant in the context of the question, because we are looking for the first time when the student has done all the questions currently available in the site.
How does the student solve the last 2 questions in day 1405 and 1406? Every question from the bank needs 3 days to answer (since 2 more questions are added every three days). Day 1404 is when 468 questions are done. Day 1407 is when 469th question is done (considering there are also 2 other questions added from 1405-1407). And Day 1410 is when 470th question is made (Considering there are another 2 questions added from 1408-1410). Please explain where I am going wrong.
No? The student does one question every day…
I understand that. What I meant was one question from the bank takes 3 days (because 2 other extra questions are also added in the three days). So, one question from the bank in 3 days (plus 2 other extra questions)
Got my answer though. The 2 extra questions aren’t added till day 1407, which is why the answer is 1406. Thank you
So how to algebraically solve this problem?
