Directions: The questions below, consist of a question and three statements…
2023
Directions: The questions below, consist of a question and three statements numbered as I, II and III given below it. You have to decide whether the data given in the statements are sufficient to answer the question or not. Read all statements and choose the most appropriate option.
Q. Eight persons i.e., A, B, C, D, M, N, O and P attend a function in eight different months viz. January, March, April, May, July, August, November and December of the same year. Who will attend the function in May?
I. One person attends the function between M and N. P attends the function two persons after O but not after A. One person attends the function between A and C. N and P do not attend the function in the adjacent months.
II. O and N do not attend the function in the adjacent months. Two persons attend the function between N and D who does not attend the function just before O. C does not attend the function in the month having a minimum number of days.
III. A is neither the first person nor the last person to attend the function. D and M do not attend the function adjacent to each other. A does not attend the function just before M. B neither attend the function just after N nor just before O.
- A.
If data in statement I alone is sufficient
- B.
If data in statement II alone is sufficient
- C.
If data either in statement I alone or in statement III alone is sufficient
- D.
If data in all statements i.e., I, II and III even together is not sufficient
- E.
If data in all statements i.e., I, II and III together is sufficient
Show answer & explanation
Correct answer: E
Concept
In a data-sufficiency question you judge each statement (or combination) ONLY by whether it forces a single, unique answer to the asked question — here, exactly one named person fixed in May. A statement (or set) is 'sufficient' only if every arrangement satisfying it yields the SAME May-person; if two valid arrangements give different May-persons, that statement (or set) is insufficient. You test the statements as supplied and never carry a fact from one statement into another.
Application — each statement alone is insufficient
Statement I fixes only a relative block (one person between M and N; P two places after O with P before A; one person between A and C; N and P not in adjacent months). This block can slide across the eight months, so the May-person is not pinned — valid arrangements leave May as B, C, D, M, N, O or P depending on where the block sits. Not unique, so insufficient.
Statement II fixes only spacing (O and N not adjacent; two persons between N and D; D not just before O; C not in a 30-day month) and anchors no one to a specific month, so every person remains a possible May-person. Insufficient.
Statement III is almost entirely exclusion rules (A not first or last; D and M not adjacent; A not just before M; B not just after N nor just before O) and leaves thousands of arrangements. Insufficient.
Application — every pair is still insufficient
No pair pins May to one person either:
I together with II still allows May to be A, B, C, D or P (more than one), so it is insufficient.
I together with III leaves May as B, C, D, M, N or P.
II together with III leaves May open to every person.
Because each single statement and each pair admits more than one May-person, none of them resolves the question on its own.
Cross-check — all three together force one seating
Imposing I, II and III simultaneously, the exclusion rules of III remove every alternative left open by I and II, and the constraints intersect to exactly one arrangement:
Month | Person |
|---|---|
January | O |
March | D |
April | P |
May | A |
July | N |
August | C |
November | M |
December | B |
This arrangement is unique, so the May-person is determined (it is A) only when statements I, II and III are used together. Hence the data in all three statements together is sufficient, while no smaller combination is.