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?
Coming back a bit late to this question, but although I understand the reasoning behind the 1406, and that is a correct answer, 1410 also is, and in fact, also 1408. It all depends on when +2 questions are added first: on day 1, 2 or 3. So I guess unless the prompt is more specific, all three answers must be considered.
Here is a small python code block that solves this questions.
for start_day in range(1, 4):
days = start_day
bank = 470
while(bank > 0):
days += 1
bank = bank - 1
if days % 3 == 0:
bank += 2
print(f"Days: {days-start_day}, Bank: {bank}")
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No, and this is because once the student has zero questions remaining, the process is terminated.
Reawakening the question!
The discrepancy comes from the fact that the problem doesn’t say when in the 3-day cycle the +2 questions are added, and whether the person solves first, or the questions are added first on the +2 day.
-
After 1404 days, the backlog is down to 2.
-
Addition on day 1407 (Last addition on day 1404)
If the next +2 comes after those two are solved, the student finishes on day 1406.
Explanation:
eod 1405 backlog = 1, eod 1406 backlog = 0
-
Addition on day 1406 (Last addition on day 1403)
If the +2 lands in the middle, it pushes the finish to 1406 again
Explanation:
eod 1405 backlog = 1, day 1406 backlog = 0 (before adding questions)
(assuming the questions are solved first, and later the 2 questions are added by the website on day 1406)
-
Addition on day 1405 (Last addition on day 1402)
If it lands even earlier, it pushes it to 1408
Explanation:
eod 1405 backlog = 1+2 = 3, eod 1406 backlog = 2, eod 1407 backlog = 1, day 1408 backlog = 0 (before adding questions)
(assuming the questions are solved first, and later the 2 questions are added by the website on day 1406)
So 1406/1408 are all possible depending on the phase. The question is underspecified unless it tells us exactly when the additions happen.
PS: This assumes the student solves first and then the +2 are added on a +2 day; reversing that order would change the possible answers to 1406/1408/1410.
So technically, considering all assumptions, 1406, 1408, and 1410 are all possible answers.
(I spent more time getting to the bottom of this than I’d like to admit 
)
2 Likes
Try now - I’ve made some adjustments to the problem.
Where is this problem in a quiz? I encountered it in The I’m Overwhelmed Study Plan: Module 5, Part 1, Words to Algebra III, and this forum was linked under that video.
I doubt it’s part of a quiz - it’s in the problem-solving section of the site.
Unable to spot it; would be really helpful if you could link it here 
Can’t link it. But you should be to filter for Algebra Hard Numeric Entry quant problems. It’s the last problem.
