Additive Series

[Kmott42]

Hi guys,

I'm not actually a student, this is a problem I need to figure out for work. We're starting a study and we want to get 100 subjects as quickly as possible. Given constraints on our lab facilities, the fastest we can enroll people is two people one week, two people the next week, and then three people for one week. So the pattern would go 2, 2, 3, 2, 2, 3, 2, 2, 3.... etc. What I need to figure out is how many weeks it would then take us to reach 100 subjects if we enrolled at this rate. I'm terrible with this kind of basic logical/mathematical problem! The GRE math section was not fun for me. Can anyone tell me how to solve this problem? Thank you so much!

 

[daon2]

Hi guys,

I'm not actually a student, this is a problem I need to figure out for work. We're starting a study and we want to get 100 subjects as quickly as possible. Given constraints on our lab facilities, the fastest we can enroll people is two people one week, two people the next week, and then three people for one week. So the pattern would go 2, 2, 3, 2, 2, 3, 2, 2, 3.... etc. What I need to figure out is how many weeks it would then take us to reach 100 subjects if we enrolled at this rate. I'm terrible with this kind of basic logical/mathematical problem! The GRE math section was not fun for me. Can anyone tell me how to solve this problem? Thank you so much!

On a practical level: Every three weeks you're enrolling 7 people. 100/7 ~ 14.3, so 15 repetitions of 2,2,3 will be more than enough, or 45 weeks. But notice this is admitting 15*7=105 people, and removing the latter two from the back-end of 2,2,3, you can finish 2 weeks earlier, or 42 weeks exactly. <--edit: subtraction fail (should be 43)

 

[Deleted member 4993]

You will admit 98 pupil in 42 weeks

You will admit 2 more (to make 100) on the 43 rd. week