A showroom is open on all seven days of the week throughout the year. There are five employees Alex, Bhabha, Cathy, Dilip and Ethan who work in the showroom. Every day except Sunday, two employees are required while on Sunday three employees need to work. Every employee works for three days in a week. Some additional information is also provided: - Every employee works on two consecutive days while the third day is not consecutive. - Alex and Dilip work together on Tuesday and Wednesday while the other working day differs for them. - Neither Bhabha nor Cathy works with Alex on any day. - Cathy does not work either on Saturday or on Monday. Number of days Bhabha and Cathy work together in a week is Option 1: 0 Option 2: 1 Option 3: 3 Option 4: 2

Answer: 2. Solution: Step 1: Create Table, A, B, C, D, E, Required, -, -, -, -, -, Sun, 3, Mon, 2, Tue, 2, Wed, 2, Thur, 2, Fri, 2, Sat, 2, Required, 3, 3, 3, 3, 3, Let the 5 employees be A, B, C, D and E. Each employee works at least 3 days (2 days are consecutive, 3rd day is not consecutive) We need 3 people working on Sunday, 2 on other days. There is no one correct method to solve it. The order of solving can be different. Focus on finding the table-cells which can be ticked/crossed-off, hence, making a table (like above) is very helpful to visualise the problem! —-- Step 2: Populate information from Clue-2, A, B, C, D, E, Required, -, -, -, -, -, Sun, 3, Mon, 2, Tue, ☑, ., ., ☑, ., 2, Wed, ☑, ., ., ☑, ., 2, Thur, 2, Fri, 2, Sat, 2, Required, 3, 3, 3, 3, 3, Point 2: Alex and Dilip work together on Tuesday and Wednesday. Ergo, no one else can work on those days. —-- Step 3: Populate information from Clue-4, A, B, C, D, E, Required, -, -, -, -, -, Sun, ☑, 3, Mon, ., 2, Tue, ☑, ., ., ☑, ., 2, Wed, ☑, ., ., ☑, ., 2, Thur, ☑, 2, Fri, ☑, 2, Sat, ., 2, Required, 3, 3, 3, 3, 3, Point 4: Cathy does not work either on Saturday or on Monday. Hence, she can work only on Sunday, Thursday and Friday. —-- Step 4: Can't work for 3 consecutive days, A, B, C, D, E, Required, -, -, -, -, -, Sun, ., ☑, 3, Mon, ., ., ., 2, Tue, ☑, ., ., ☑, ., 2, Wed, ☑, ., ., ☑, ., 2, Thur, ., ☑, ., 2, Fri, ., ☑, 2, Sat, ., 2, Required, 3, 3, 3, 3, 3, Alex and Dilip can't work on Monday or Thursday, else, it'll violate the rule of 3 consecutive days. Point 3: Cathy and Babha don't work with Alex on the same day. So, Alex won't work on the days Cathy works (Sunday, Thursday, Friday). —-- Step 5: Filling Alex's working days, A, B, C, D, E, Required, -, -, -, -, -, Sun, ., ☑, 3, Mon, ., ., ., 2, Tue, ☑, ., ., ☑, ., 2, Wed, ☑, ., ., ☑, ., 2, Thur, ., ☑, ., 2, Fri, ., ☑, 2, Sat, ☑, ., ., 2, Required, 3, 3, 3, 3, 3, Hence, Alex has to work on Saturday to fulfil the 3 working days criteria. Recall Point 3: Cathy and Babha don't work with Alex on the same day. So, Bhabha won't work on Satuday. —-- Step 6: Filling Monday, A, B, C, D, E, Required, -, -, -, -, -, Sun, ., ☑, 3, Mon, ., ☑, ., ., ☑, 2, Tue, ☑, ., ., ☑, ., 2, Wed, ☑, ., ., ☑, ., 2, Thur, ., ☑, ., 2, Fri, ., ☑, 2, Sat, ☑, ., ., 2, Required, 3, 3, 3, 3, 3, We see that only Bhabha and Ethan are free on Monday (which requires 2 employees). —-- Step 7: Filling Saturday, A, B, C, D, E, Required, -, -, -, -, -, Sun, ., ☑, 3, Mon, ., ☑, ., ., ☑, 2, Tue, ☑, ., ., ☑, ., 2, Wed, ☑, ., ., ☑, ., 2, Thur, ., ☑, ., 2, Fri, ., ☑, 2, Sat, ☑, ., ., ., ☑, 2, Required, 3, 3, 3, 3, 3, Point 2: Alex and Dilip work together on Tuesday and Wednesday while the other working day differs for them. Hence, Dilip will not work on Satuday (as Alex is working). Thus, only Ethan can work on Satuday to fulfil Saturday's requirement. —-- Step 8: Filling Sunday, A, B, C, D, E, Required, -, -, -, -, -, Sun, ., ☑, ☑, ☑, ., 3, Mon, ., ☑, ., ., ☑, 2, Tue, ☑, ., ., ☑, ., 2, Wed, ☑, ., ., ☑, ., 2, Thur, ., ☑, ., 2, Fri, ., ☑, ., 2, Sat, ☑, ., ., ., ☑, 2, Required, 3, 3, 3, 3, 3, Ethan can't work on Sunday, else it'll become 3 consecutive days. Hence, to fulfil the 3 employee requirement on Sunday, only Bhabha and Dilip can join Cathy. —-- Step 9: Filling Ethan, A, B, C, D, E, Required, -, -, -, -, -, Sun, ., ☑, ☑, ☑, ., 3, Mon, ., ☑, ., ., ☑, 2, Tue, ☑, ., ., ☑, ., 2, Wed, ☑, ., ., ☑, ., 2, Thur, ., ☑, ., ., 2, Fri, ., ., ☑, ., ☑, 2, Sat, ☑, ., ., ., ☑, 2, Required, 3, 3, 3, 3, 3, We need to have 2 consecutive days for Ethan -- only possible if he works on Friday. Thus, fulfilling his requirment and Friday's requirement. —-- Step 10: Filling Thursday, A, B, C, D, E, Required, -, -, -, -, -, Sun, ., ☑, ☑, ☑, ., 3, Mon, ., ☑, ., ., ☑, 2, Tue, ☑, ., ., ☑, ., 2, Wed, ☑, ., ., ☑, ., 2, Thur, ., ☑, ☑, ., ., 2, Fri, ., ., ☑, ., ☑, 2, Sat, ☑, ., ., ., ☑, 2, Required, 3, 3, 3, 3, 3, Finally, only Bhabha can work on Thursday and fulfil the remaining requirement. Bhabha and Cathy work together on Sunday & Thursday (two times).

Logical Reasoning

Arrangements

Easy

A showroom is open on all seven days of the week throughout the year. There are five employees Alex, Bhabha, Cathy, Dilip and Ethan who work in the showroom. Every day except Sunday, two employees are required while on Sunday three employees need to work. Every employee works for three days in a week. Some additional information is also provided:

Every employee works on two consecutive days while the third day is not consecutive.
Alex and Dilip work together on Tuesday and Wednesday while the other working day differs for them.
Neither Bhabha nor Cathy works with Alex on any day.
Cathy does not work either on Saturday or on Monday.

Number of days Bhabha and Cathy work together in a week is

✅ Correct Option: 4

Slide 1/10

Step 1: Create Table

	A	B	C	D	E	Required
Sun						3
Mon						2
Tue						2
Wed						2
Thur						2
Fri						2
Sat						2
Required	3	3	3	3	3

Let the 5 employees be A, B, C, D and E.

Each employee works at least 3 days (2 days are consecutive, 3rd day is not consecutive)

We need 3 people working on Sunday, 2 on other days.

There is no one correct method to solve it. The order of solving can be different. Focus on finding the table-cells which can be ticked/crossed-off, hence, making a table (like above) is very helpful to visualise the problem!

Step 2: Populate information from Clue-2

	A	B	C	D	E	Required
Sun						3
Mon						2
Tue	☑	.	.	☑	.	2
Wed	☑	.	.	☑	.	2
Thur						2
Fri						2
Sat						2
Required	3	3	3	3	3

Point 2: Alex and Dilip work together on Tuesday and Wednesday. Ergo, no one else can work on those days.

Step 3: Populate information from Clue-4

	A	B	C	D	E	Required
Sun			☑			3
Mon			.			2
Tue	☑	.	.	☑	.	2
Wed	☑	.	.	☑	.	2
Thur			☑			2
Fri			☑			2
Sat			.			2
Required	3	3	3	3	3

Point 4: Cathy does not work either on Saturday or on Monday. Hence, she can work only on Sunday, Thursday and Friday.

Step 4: Can't work for 3 consecutive days

	A	B	C	D	E	Required
Sun	.		☑			3
Mon	.		.	.		2
Tue	☑	.	.	☑	.	2
Wed	☑	.	.	☑	.	2
Thur	.		☑	.		2
Fri	.		☑			2
Sat			.			2
Required	3	3	3	3	3

Alex and Dilip can't work on Monday or Thursday, else, it'll violate the rule of 3 consecutive days.

Point 3: Cathy and Babha don't work with Alex on the same day. So, Alex won't work on the days Cathy works (Sunday, Thursday, Friday).

Step 5: Filling Alex's working days

	A	B	C	D	E	Required
Sun	.		☑			3
Mon	.		.	.		2
Tue	☑	.	.	☑	.	2
Wed	☑	.	.	☑	.	2
Thur	.		☑	.		2
Fri	.		☑			2
Sat	☑	.	.			2
Required	3	3	3	3	3

Hence, Alex has to work on Saturday to fulfil the 3 working days criteria.

Recall Point 3: Cathy and Babha don't work with Alex on the same day. So, Bhabha won't work on Satuday.

Step 6: Filling Monday

	A	B	C	D	E	Required
Sun	.		☑			3
Mon	.	☑	.	.	☑	2
Tue	☑	.	.	☑	.	2
Wed	☑	.	.	☑	.	2
Thur	.		☑	.		2
Fri	.		☑			2
Sat	☑	.	.			2
Required	3	3	3	3	3

We see that only Bhabha and Ethan are free on Monday (which requires 2 employees).

Step 7: Filling Saturday

	A	B	C	D	E	Required
Sun	.		☑			3
Mon	.	☑	.	.	☑	2
Tue	☑	.	.	☑	.	2
Wed	☑	.	.	☑	.	2
Thur	.		☑	.		2
Fri	.		☑			2
Sat	☑	.	.	.	☑	2
Required	3	3	3	3	3

Point 2: Alex and Dilip work together on Tuesday and Wednesday while the other working day differs for them.

Hence, Dilip will not work on Satuday (as Alex is working).

Thus, only Ethan can work on Satuday to fulfil Saturday's requirement.

Step 8: Filling Sunday

	A	B	C	D	E	Required
Sun	.	☑	☑	☑	.	3
Mon	.	☑	.	.	☑	2
Tue	☑	.	.	☑	.	2
Wed	☑	.	.	☑	.	2
Thur	.		☑	.		2
Fri	.		☑	.		2
Sat	☑	.	.	.	☑	2
Required	3	3	3	3	3

Ethan can't work on Sunday, else it'll become 3 consecutive days.

Hence, to fulfil the 3 employee requirement on Sunday, only Bhabha and Dilip can join Cathy.

Step 9: Filling Ethan

	A	B	C	D	E	Required
Sun	.	☑	☑	☑	.	3
Mon	.	☑	.	.	☑	2
Tue	☑	.	.	☑	.	2
Wed	☑	.	.	☑	.	2
Thur	.		☑	.	.	2
Fri	.	.	☑	.	☑	2
Sat	☑	.	.	.	☑	2
Required	3	3	3	3	3

We need to have 2 consecutive days for Ethan -- only possible if he works on Friday. Thus, fulfilling his requirment and Friday's requirement.

Step 10: Filling Thursday

	A	B	C	D	E	Required
Sun	.	☑	☑	☑	.	3
Mon	.	☑	.	.	☑	2
Tue	☑	.	.	☑	.	2
Wed	☑	.	.	☑	.	2
Thur	.	☑	☑	.	.	2
Fri	.	.	☑	.	☑	2
Sat	☑	.	.	.	☑	2
Required	3	3	3	3	3

Finally, only Bhabha can work on Thursday and fulfil the remaining requirement.

Bhabha and Cathy work together on Sunday & Thursday (two times).

Question 27

Which among the following employees do not work together on any of the days?

Question 28

One of the days Alex works on is

Question 29

The consecutive days on which Ethan works are

Question 30

Employees who work on Sunday are

Number of days Bhabha and Cathy work together in a week is

Solution

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