As per the question John will work on \(j^{th}\) days after today
and Deborah will work \(d^{th}\) day after today.
So, the next time they will work together, it will be the LCM of \(j \)& \(d\)
1) j is even, and d is odd
Clearly NOT Sufficient.
(2) None of the prime factors that divide j evenly divide d evenly.
It means j and d are coprime and hence the LCM will be \(dj\).
So , they will work together on \(dj\) days after today, but the session will be over in \(dj-7\) days
So, they will not be able to work on the same day after today.
SUFFICIENT.
Answer BBunuel
John and Deborah work together at their college library. If John works on a given day, he won’t work again until the \(j^{th}\) day after that. If Deborah works on a given day, she won’t work again until the \(d^{th}\) day after that. In \(dj-7\) days, the semester will end and John and Deborah will no longer work at the library. If they both work today, will they both work on the same day again before the semester ends?
(1) j is even, and d is odd
(2) None of the prime factors that divide j evenly divide d evenly.
Are You Up For the Challenge: 700 Level Questions