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

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Math Expert
Joined: 02 Sep 2009
Posts: 60539
John and Deborah work together at their college library. If John works  [#permalink]

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03 Dec 2019, 01:26
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Difficulty:

65% (hard)

Question Stats:

50% (02:08) correct 50% (02:48) wrong based on 30 sessions

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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.

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Re: John and Deborah work together at their college library. If John works  [#permalink]

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03 Dec 2019, 03:31
1
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.

Bunuel wrote:
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.

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Re: John and Deborah work together at their college library. If John works  [#permalink]

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09 Jan 2020, 05:31
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.

Re: John and Deborah work together at their college library. If John works   [#permalink] 09 Jan 2020, 05:31
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