https://prepswift.gregmat.com/quizzes/quiz/prepswift-of-multiples-in-interval (Question 3)
Hello! Im new to this and didnt understand the solution. Can someone maybe explain it different? TIA!!
So, when you get the value of B as 219. We check what is the closest next number that is a multiple of 3 is, which is 222. However, we want to keep the number of multiples as 45 still and not 46 if we do it at 222. So the maximum is 221 since the closest multiple of 3 is still 219. Whether it is 219/220 or 221, the number of multiples remains the same. And the maximum here is 221.
What exactly is the point of this pattern recognition put in the solution for this question:
Notice that there is exactly one multiple between 87+2 (for reasons we’ve already explained above)
there are exactly two multiples between 87 and 87+3×1+2 (we’ve widened the range by 3 to include the additional multiple 90)
there are exactly three multiples between 87 and 87+3×2 +2 (we’ve widened the range by 3 again)
hence, there are exactly 45 multiples between 87 and 87+44×3+2. This is 87+132+2=221.
Testing with smaller, easy-to-verify values and generalising it to the original problem.
why isnt the answer 219 itself? it is divisble by 3 and keeps the multiples number as 45 as well. I still did not get it.
Answer these questions
- How many multiples of 3 are there between 85 and 219, inclusive?
- How many multiples of 3 are there between 85 and 221, inclusive?
- Between 219 and 221, which is greater?
It should become clear why 221 is the answer.
If you still don’t get it, lemme know.