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

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

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

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.

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

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?

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

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

Re: Edward and Klara are both nurses who are good friends with e
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15 Jul 2019, 15:24

tricky

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

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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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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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