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Edward and Klara are both nurses who are good friends with e

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Asif123
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Edward and Klara are both nurses who are good friends with e [#permalink] New post   Updated on: 11 Apr 2019, 15:47
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Edward and Klara are both nurses who are good friends with each other. Edward works at Brigade Hospital, where, in every 10 day cycle, he works the first 7 days and has three days off. Klara works at Cedar Mountain Hospital, where, in every 7 day cycle, she works the first 5 days, and has 2 days off. Assume that both start their respective cycles on Day 1 of Week 1.

In which weeks do they have the same two days off?

Indicate all weeks in which they have the same two days off.

a. Week 3
b. Week 4
c. Week 5
d. Week 6
e. Week 7
f. Week 8
g. Week 9
h. Week 10
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E,H

Originally posted by Asif123 on 09 Apr 2019, 08:28.
Last edited by Carcass on 11 Apr 2019, 15:47, edited 2 times in total.
Edited by Carcass
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Re: Edward and Klara are both nurses who are good friends with e [#permalink] New post   11 Apr 2019, 04:01
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Asif123 wrote:
Edward and Klara are both nurses who are good friends with each other. Edward works at Brigade Hospital, where, in every 10 day cycle, he works the first 7 days and has three days off. Klara works at Cedar Mountain Hospital, where, in every 7 day cycle, she works the first 5 days, and has 2 days off. Assume that both start their respective cycles on Day 1 of Week 1. In which weeks do they have the same two days off?

Indicate all weeks in which they have the same two days off.

a. Week 3
b. Week 4
c. Week 5
d. Week 6
e. Week 7
f. Week 8
g. Week 9
h. Week 10


As Klara works for 5 days and take 2 day off i.e. - - - - - o o
so in every week she will have last 2 days off, however things gonna change for Edward

Edward ( o = off, - = working)

Week 1 - - - - - - -

week 2 o o o - - - -

week 3 - - - o o o -

Week 4 - - - - - - o

Week 5 o o - - - - -

Week 6 - - o o o - -

Week 7 - - - - - o o

Week 8 o - - - - - -

Week 9 - o o o - - -

Week 10 - - - - o o o

For Week 7 and Week 10, they will have same days off.
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jelal123
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Re: Edward and Klara are both nurses who are good friends with e [#permalink] New post   18 Jun 2019, 08:39
pranab01 wrote:
Asif123 wrote:
Edward and Klara are both nurses who are good friends with each other. Edward works at Brigade Hospital, where, in every 10 day cycle, he works the first 7 days and has three days off. Klara works at Cedar Mountain Hospital, where, in every 7 day cycle, she works the first 5 days, and has 2 days off. Assume that both start their respective cycles on Day 1 of Week 1. In which weeks do they have the same two days off?

Indicate all weeks in which they have the same two days off.

a. Week 3
b. Week 4
c. Week 5
d. Week 6
e. Week 7
f. Week 8
g. Week 9
h. Week 10


As Klara works for 5 days and take 2 day off i.e. - - - - - o o
so in every week she will have last 2 days off, however things gonna change for Edward

Edward ( o = off, - = working)

Week 1 - - - - - - -

week 2 o o o - - - -

week 3 - - - o o o -

Week 4 - - - - - - o

Week 5 o o - - - - -

Week 6 - - o o o - -

Week 7 - - - - - o o

Week 8 o - - - - - -

Week 9 - o o o - - -

Week 10 - - - - o o o

For Week 7 and Week 10, they will have same days off.


Any time saving mechanism pls?
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DevB
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Re: Edward and Klara are both nurses who are good friends with e [#permalink] New post   02 Jul 2019, 02:07
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Edward has  3 days off after 7 days working in 10 days cycle

3 days before completion of cycle

so Edward off days are

10n-2, 10n-2 , 10n    where n ≥1

Klara has 2 days off after 5 days working in 7 days cycle

2 days before completion of cycle

so klara off days are

7m-1 , 7m  where m ≥1

As they started on same day

so 7m-1 should equal to 10n-2 , or 10n-1 to have same two days off

Case 1

7m-1 = 10n-2

=> 7m = 10n-1

This equation will hold true for m = 7  & n = 5

this mean 48th & 49th days are off for both (week 7)

Case 2

7m-1 = 10n-1

=> 7m = 10n

This will hold true for m = 10 & n = 7

this mean 69th & 70th days are off for both (week 10)

So in week 7 & week 10 they have same two days off
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Re: Edward and Klara are both nurses who are good friends with e [#permalink] New post   15 Jul 2019, 15:24
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Re: Edward and Klara are both nurses who are good friends with e [#permalink] New post   15 Jul 2024, 10:36
Hello from the GRE Prep Club BumpBot!

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Re: Edward and Klara are both nurses who are good friends with e [#permalink]
15 Jul 2024, 10:36
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