If Katya works the second shift on Tuesday at the gallery, then which one of the following could be true?

Zia on August 13, 2020

Explanation

Why A is not the right answer?

Reply

Victoria on August 22, 2020

Hi @zia305,

Happy to help!

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.