Q1:ipmat indore 2022LRDI › ArrangementsEasyMCQ · MCQ
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. Ever … read passage
Number of days Bhabha and Cathy work together in a week is
- A0
- B1
- C3
- D2
Pick an option to attempt
The Setup: This is a logical arrangement puzzle requiring us to map five employees onto a 7-day schedule. We deduce one Master Matrix satisfying every daily capacity and every shift rule; that single grid then answers all five questions in this set.
Step 1: Check the shift arithmetic and fix the reading of 'consecutive'.
Total shifts required .
Five employees working exactly days each also supply shifts, so the grid is exactly saturated: every slot is filled and nobody has spare capacity.
A caselet like this is far easier to see than to hold in your head, so draw the grid first and fill cells in as they are forced. The margins carry the capacities, and they are what drive every deduction:
Each employee's three days therefore consist of exactly one consecutive pair plus a third day adjacent to neither.
The week is read as a cycle, so Saturday and Sunday count as consecutive. This is not a cosmetic detail: it means a run of Saturday, Sunday, Monday is a three-consecutive-day block and is barred. Read the week as a straight line instead and the puzzle admits three different grids, two of which contradict the stated answers to the later questions in this set, so the cyclic reading is the intended one.
Step 2: Fix Cathy, then Alex.
Alex works Tuesday and Wednesday. Neither Bhabha nor Cathy ever shares a day with Alex, so neither of them works Tuesday or Wednesday.
Cathy is additionally barred from Saturday and Monday. That removes Monday, Tuesday, Wednesday and Saturday, leaving exactly three days:
Cathy: Sunday, Thursday, Friday. (Thursday-Friday consecutive, Sunday isolated. Valid.)
Alex cannot share a day with Cathy, so Alex is barred from Sunday, Thursday and Friday. His third day could not have been Monday or Thursday in any case, since either would extend Tuesday-Wednesday into a three-day run. Only one day survives:
Alex: Tuesday, Wednesday, Saturday.
Step 3: Force Monday, and with it Ethan.
Tuesday and Wednesday are already full (Alex and Dilip), so no one else can work them.
Now look at Monday. Alex works only Tuesday, Wednesday and Saturday; Cathy is barred from Monday; Dilip's third day cannot be Monday, as that would extend Tuesday-Wednesday to three in a row. That leaves only Bhabha and Ethan available, and Monday needs exactly two people. So Bhabha and Ethan both work Monday.
Saturday needs one more person alongside Alex. Cathy is barred, Bhabha can never share a day with Alex, and Dilip's third day must differ from Alex's. So Ethan works Saturday.
Ethan now holds Monday and Saturday, and his third day cannot be Tuesday or Wednesday. Test what remains:
* Sunday would give Saturday, Sunday, Monday, three consecutive days on the cyclic week. Barred.
* Thursday would give Monday, Thursday, Saturday, which contains no consecutive pair at all. Barred.
* Friday gives Monday, Friday, Saturday, exactly one pair (Friday-Saturday). Valid.
Ethan: Monday, Friday, Saturday.
Step 4: Close out Dilip and Bhabha.
Friday now holds Cathy and Ethan, so it is full and Dilip's third day cannot be Friday. It also cannot be Monday or Thursday (three-in-a-row), nor Saturday (his third day must differ from Alex's). One option remains:
Dilip: Sunday, Tuesday, Wednesday.
Sunday needs three people and currently holds Cathy and Dilip, so Bhabha takes the last Sunday slot. Thursday needs two and holds only Cathy, so Bhabha works Thursday as well. Together with the Monday shift forced in Step 3:
Bhabha: Sunday, Monday, Thursday. (Sunday-Monday consecutive, Thursday isolated. Valid.)
Master Matrix:
Reading the grid down the columns: Alex takes Tuesday, Wednesday and Saturday; Bhabha Sunday, Monday and Thursday; Cathy Sunday, Thursday and Friday; Dilip Sunday, Tuesday and Wednesday; Ethan Monday, Friday and Saturday.
Every day carries exactly two workers except Sunday, which carries three, and every employee has exactly one consecutive pair plus one isolated day. No other grid satisfies all the constraints.
Step 5: Answer this question.
Bhabha works Sunday, Monday and Thursday. Cathy works Sunday, Thursday and Friday.
They overlap on exactly two days: Sunday and Thursday.
Final Answer: 2
| Day | Alex | Bhabha | Cathy | Dilip | Ethan | Needed |
|---|---|---|---|---|---|---|
| Sunday | 3 | |||||
| Monday | 2 | |||||
| Tuesday | 2 | |||||
| Wednesday | 2 | |||||
| Thursday | 2 | |||||
| Friday | 2 | |||||
| Saturday | 2 | |||||
| Works | 3 | 3 | 3 | 3 | 3 | 15 |
| Day | Alex | Bhabha | Cathy | Dilip | Ethan | Needed |
|---|---|---|---|---|---|---|
| Sunday | ✓ | ✓ | ✓ | 3 | ||
| Monday | ✓ | ✓ | 2 | |||
| Tuesday | ✓ | ✓ | 2 | |||
| Wednesday | ✓ | ✓ | 2 | |||
| Thursday | ✓ | ✓ | 2 | |||
| Friday | ✓ | ✓ | 2 | |||
| Saturday | ✓ | ✓ | 2 | |||
| Works | 3 | 3 | 3 | 3 | 3 | 15 |