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Following every 11 consecutive days of swimming practice, [#permalink]

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12 Sep 2008, 06:46

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Following every 11 consecutive days of swimming practice, Danny has 3 days off. On the 183rd day from today, will Danny practice swimming or have a day off ?

(1) Exactly 13 days ago Danny was on a day off (2) Tomorrow Danny will start his three days off

Following every 11 consecutive days of swimming practice, Danny has 3 days off. On the 183rd day from today, will Danny practice swimming or have a day off ?

(1) Exactly 13 days ago Danny was on a day off (2) Tomorrow Danny will start his three days off

B is enough to answer the question.

183rd day from today. If today was a practice day and tomorrow on you have the 3 off days starting so 183 - 4 = 179 . Divide 179/14 (11 consecutive + 3 off) you get a remainder of 11. which will be working days

(1) you dont know if its 1st or 2nd or 3rd day off. So, wouldnt know if he will have the day off or swim.

I think that's precisely the trick of this question.

I don't it matters what day off he was on 13 days ago. Either way, he'll be off because the result is the same. There are 13 cycles (11 days of practice + 3 days off) plus one day in 183 days (note that today + 13 days ago is one full cycle = 14 days).

Following every 11 consecutive days of swimming practice, Danny has 3 days off. On the 183rd day from today, will Danny practice swimming or have a day off ?

(1) Exactly 13 days ago Danny was on a day off (2) Tomorrow Danny will start his three days off

IMO B (1) does not help because since the day off can be any day out of 3 days we get diff answers ,if we say today is first day off or tomorro is first day off (2) this clearly answers since we know that starting from 3 days from tomo ,11days +3days holidays is the pattern
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Following every 11 consecutive days of swimming practice, Danny has 3 days off. On the 183rd day from today, will Danny practice swimming or have a day off ?

(1) Exactly 13 days ago Danny was on a day off (2) Tomorrow Danny will start his three days off

14day cycle; 183 days = 14 * 13 cycles + 1 day

B.

1) implies that today is Danny's 10th working day/11th working day/1st day of holiday. so 183th day can be either 11th working day or 1st holiday or 2nd holiday of the 13th cycle from today. so insuff

2)implies today is 11th working day. 183rd day will be 1st holiday.

There is a cycle of 14 days. 11 days of work + 3 days of rest. The same action Danny is doing today will also in 14 days from today, 28 days from today etc.

Using the first statement we know what he did 13 days ago, and therefore we can conclude about what he will do tomorrow, 15 days ahead, 29 days ahead etc. Meaning that in every day that has a remainder of 1 when divided by 14, he will do the same. 183 days from today, answers his criteria and therefore we can conclude that it will also be a day of rest.

Using the second statement we can know exactly when the cycle begins and therefore we can calculate what Danny will do in any day (past or future), and there it is sufficient.

There is a cycle of 14 days. 11 days of work + 3 days of rest. The same action Danny is doing today will also in 14 days from today, 28 days from today etc.

Using the first statement we know what he did 13 days ago, and therefore we can conclude about what he will do tomorrow, 15 days ahead, 29 days ahead etc. Meaning that in every day that has a remainder of 1 when divided by 14, he will do the same. 183 days from today, answers his criteria and therefore we can conclude that it will also be a day of rest.

I don't agree with this reasoning. can you elaborate further?