John and Deborah work together at their college library. If John works

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 B


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For working on the same day LCM will be calculated. This LCM should be less than the number of days left in the semester ie. LCM < dj-7.

Column name ----> j d dj-7
4 3 5 --------> LCM of 4,3 = 12 < dj- 7 = 5 . NO they cant work on same day
8 4 25 --------> LCM of 8,4 = 8 < dj- 7 = 25 . Yes they can work on same day
A is out

B---> j and d are co primes or dont share a comon factor.
IF thats the case LCm of d,j = dj and dj is always > dj - 7 . Hence, we can sufficiently conclude that they cant work on the same day.


B is the correct answer.
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Hi ShankSouljaBoi

Doesn't the prompt require that D be odd? So the second illustration for Statement 1 below may not work, unless I am missing out on something. I am trying to test values to get a yes.

Statement B is obviously sufficient on its own.

example :
Statement 1 - Insufficient

d = 9, j = 8
semester will end in 65 days. Notice that since 8 and 9 are Co-primes, LCM (8,9) = 8x9 = 72. However, in 72 days the semester will be over. So, No

d= 15, j = 10
semester will end in 143 days. LCM (10,15) = 30. So they will work together after 30 days. So, Yes

Statement 2 - Sufficient

As given d and j are Co primes. Hence LCM (d,j) = dxJ. However, by then the semester will be over. So, No always.

B it is.