**Step 1: Create Tab<=** | | 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 <=ast 3 days (2 days are consecutive, 3rd day is not consecutive) We need 3 peop<= 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 tab<=-cells which can be ticked/crossed-off, hence, making a tab<= (like above) is very helpful to visualise the prob<=m! —-- **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: A<=x and Dilip work to>=ther 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 | A<=x and Dilip can't work on Monday or Thursday, else, it'll violate the ru<= of 3 consecutive days. Point 3: Cathy and Babha don't work with A<=x on the same day. So, A<=x won't work on the days Cathy works (Sunday, Thursday, Friday). —-- **Step 5: Filling A<=x'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, A<=x has to work on Saturday to fulfil the 3 working days criteria. Recall Point 3: Cathy and Babha don't work with A<=x 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: A<=x and Dilip work to>=ther on Tuesday and Wednesday whi<= the other working day differs for them. Hence, Dilip will not work on Satuday (as A<=x 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 possib<= 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 to>=ther on Sunday & Thursday **(two times)**.

IPMAT Indore (MCQ) PYQs

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