Each of G, H, I, J, M, N and O has an exam on a different day of a week…
2025
Each of G, H, I, J, M, N and O has an exam on a different day of a week starting from Monday and ending on Sunday of the same week.
Only three people have exam between H and I. I has exam on the last day of the week. Only one person has exam between G and J. N has exam immediately the day before O. M does not have exam on Friday. J has exam on some day before G. How many people have exam after M?
- A.
Three
- B.
One
- C.
Six
- D.
Four
Attempted by 1 students.
Show answer & explanation
Correct answer: C
Concept
In day-of-the-week arrangement puzzles, convert each day into a numeric position (Monday = 1, Tuesday = 2, ..., Sunday = 7).
Translate every relational clue ('between', 'immediately before', 'some day before') into a position equation or inequality, fix the day that is stated in absolute terms first, then narrow the remaining positions by testing the leftover clues against each candidate case until exactly one full arrangement survives.
Step-by-Step Solution
Assign positions Monday = 1 through Sunday = 7. Since I has exam on the last day of the week, I = 7.
Only three people have exam between H and I: exactly three positions lie strictly between H's day and day 7, so H = 7 minus 4 = 3.
J has exam on some day before G, and only one person has exam between G and J, so G = J + 2. Excluding the days already fixed for H (3) and I (7), the remaining days are 1, 2, 4, 5, 6; the only pairs fitting G = J + 2 are (J = 2, G = 4) or (J = 4, G = 6).
N has exam immediately the day before O, so O = N + 1, using whichever days remain for M, N and O once G and J are fixed.
Testing J = 4, G = 6: the three leftover days for M, N, O are 1, 2, 5. The only consecutive pair among these is (N = 1, O = 2), which forces M = 5 (Friday) -- but M does not have exam on Friday, so this case fails.
Testing J = 2, G = 4: the three leftover days for M, N, O are 1, 5, 6. The only consecutive pair among these is (N = 5, O = 6), which leaves M = 1 (Monday) -- this satisfies every clue.
The complete arrangement is: Monday = M, Tuesday = J, Wednesday = H, Thursday = G, Friday = N, Saturday = O, Sunday = I.
M's exam is on the very first day of the week (Monday), so all six of the other people (J, H, G, N, O, I) have their exam on a day after M.
Cross-Check
Day | Person |
|---|---|
Monday | M |
Tuesday | J |
Wednesday | H |
Thursday | G |
Friday | N |
Saturday | O |
Sunday | I |
Between H (Wednesday) and I (Sunday): the days Thursday, Friday, Saturday hold G, N, O -- exactly three people, matching the clue.
I sits on Sunday, the last day of the week, matching the clue.
Between G (Thursday) and J (Tuesday): only Wednesday (H) lies between them -- exactly one person, matching the clue.
N (Friday) is immediately followed by O (Saturday), matching the clue.
M's exam is on Monday, not Friday, matching the clue.
J (Tuesday) is before G (Thursday), matching the clue.
So the number of people with an exam after M is 6.