We know that there are five students working 10 shifts over 5 days. Each day has a first and second shift which do not overlap.
_ _ _ _ _ _ _ _ _ _ M T W R F
The question stem tells us that K works the second shift on Tuesday and answer choice (A) tells us that G works the first shift on Monday.
G _ _ _ _ _ K _ _ _ M T W R F
We know that G and L never work on the same day as each other. This means that L can work the second shift on Wednesday and Thursday or Thursday and Friday, with G working the first shift on the remaining free day. G cannot work the first shift on Tuesday because they work two non-consecutive days and they cannot work the second shift Monday because no student works both shifts of any day.
Therefore, we have two options.
Option 1
G _ G _ K _ K _ L L M T W R F
Option 2
G _ _ _ G _ K L L K M T W R F
We run into an issue with Rule 5 here. Rule 5 tells us that H and J must work the same day as each other at least once. However, there are no days left with two open shifts. Therefore, it cannot be true that G works the first shift on Monday.
Answer choice (B) is correct because there is at least one schedule which could be true.
H G H J G J K L L K M T W R F
Notice that this meets all of our rules:
- No student works both shifts on any day. - L works the second shift on two consecutive days (Wednesday and Thursday) - G works the first shift on two non-consecutive days (Tuesday and Friday) - K works the second shift on Tuesday and Friday - H and J work on the same day at least once (Monday) - G and L never work the same day as each other
Hope this helps! Please let us know if you have any further questions.
