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03 Dec 2019, 01:26
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B
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Difficulty:
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Question Stats:
44% (02:15) correct
56%
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wrong
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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.
Are You Up For the Challenge: 700 Level Questions
(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
03 Dec 2019, 03:31
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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
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
Bunuel
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
(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
General Discussion
ShankSouljaBoi
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09 Jan 2020, 05:31
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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.
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.
