Each of C, D, E, F, X, Y and Z has an exam on a different day of a week starting from Monday and ending on Sunday of the same week.
X has exam on Friday. Only two people have exams between Y and X. Only four people have exams between C and Y. D has exam immediately after F. Z doesn’t have exam on Monday.

How many people have exam(s) between Z and E?3864

The correct option is Four.

Let's determine the schedule step-by-step for the seven people: C, D, E, F, X, Y, and Z, from Monday to Sunday.

Step 1: Place X
We are given that X has an exam on Friday.
Monday:
Tuesday:
Wednesday:
Thursday:
Friday: X
Saturday:
Sunday:

Step 2: Place Y
Only two people have exams between Y and X. This gives two possibilities for Y:
Case A: Y is on Tuesday (with Wednesday and Thursday in between).
Case B: Y is on Monday or after Sunday, which is not possible since the week ends on Sunday. So Y must be on Tuesday.
Monday:
Tuesday: Y
Wednesday:
Thursday:
Friday: X
Saturday:
Sunday:

Step 3: Place C
Only four people have exams between C and Y.
Since Y is on Tuesday, we count four days after Y (Wednesday, Thursday, Friday, Saturday), which means C must have an exam on Sunday.
Monday:
Tuesday: Y
Wednesday:
Thursday:
Friday: X
Saturday:
Sunday: C

Step 4: Place D and F
D has an exam immediately after F. This means F and D must be on consecutive days (F followed by D).
The available consecutive empty slots are Monday-Tuesday (no, Y is on Tuesday), Tuesday-Wednesday (no), Wednesday-Thursday (yes, both are free), Thursday-Friday (no, X is on Friday), Friday-Saturday (no), Saturday-Sunday (no, C is on Sunday).
Therefore, F must be on Wednesday, and D must be on Thursday.
Monday:
Tuesday: Y
Wednesday: F
Thursday: D
Friday: X
Saturday:
Sunday: C

Step 5: Place Z and E
The remaining empty days are Monday and Saturday.
We are told that Z does not have an exam on Monday. Therefore, Z must have an exam on Saturday, which leaves Monday for E.
Monday: E
Tuesday: Y
Wednesday: F
Thursday: D
Friday: X
Saturday: Z
Sunday: C

Step 6: Count the people between Z and E
E has an exam on Monday, and Z has an exam on Saturday.
The people between them are Y (Tuesday), F (Wednesday), D (Thursday), and X (Friday).
This makes a total of 4 people (Y, F, D, and X) who have exams between Z and E.