19Six people, A, B, C, D, E, and F, deliver their presentations on six…

Concept

In a data-sufficiency ordering puzzle, a statement is sufficient on its own only if its clues, used alone, force exactly one full day-by-day arrangement of all six people. If a statement's own clues are equally satisfied by two or more different arrangements that disagree on the day being asked about, that statement alone cannot answer the question — no matter how many facts it lists.

Testing Statement I

1. "D delivers the presentation immediately before A" and "C delivers the presentation immediately after A" force D, A and C into one fixed block of three consecutive days, always in that order.

2. "Exactly two people deliver presentations between C and E" means E's day is exactly three days away from C's day — either three days after C or three days before C.

3. Placing the D-A-C block on Monday-Tuesday-Wednesday forces E onto Saturday (three days after C); the remaining Thursday and Friday then go to F and B, and "F delivers after D but before B" fixes F on Thursday and B on Friday — a fully consistent arrangement with C presenting on Wednesday.

4. Placing the same D-A-C block one day later, on Tuesday-Wednesday-Thursday, instead forces E onto Monday (three days before C); the remaining Friday and Saturday then go to F and B, and "F delivers after D but before B" fixes F on Friday and B on Saturday — an equally consistent arrangement, but now A presents on Wednesday, not C.

5. Two different placements of the block, both allowed by every clue in Statement I, name two different people for Wednesday — so Statement I alone does not fix a single answer.

Testing Statement II

1. "More than two people deliver presentations after A" means at least three of the six days fall after A's day, so A can only be on the 1st, 2nd or 3rd day of the week; "D delivers the presentation before A" then rules out A being 1st, leaving A on the 2nd or 3rd day.

2. "An equal number of people deliver presentations before F and after A" ties F's day directly to A's day — the count of days before F must equal the count of days after A.

3. Taking A on the 2nd day: the equal-count clue then places F on the 5th day, and D (who is before A) takes the 1st day. Only the 3rd, 4th and 6th days remain for B, C and E; "E delivers the presentation two days before B" fits only one pairing among them, forcing E onto the 4th day and B onto the 6th day, which leaves C on the 3rd day — and "C delivers after D" holds true for this placement.

4. Taking A on the 3rd day instead: the equal-count clue places F on the 4th day, and D takes the 1st or 2nd day; but then no arrangement of the remaining days lets "E delivers two days before B" hold at all, so this branch yields no valid arrangement.

5. Only the branch with A on the 2nd day survives, and it survives as exactly one arrangement — so Statement II's own clues fix a single, complete day-by-day schedule.

Cross-check

• More than two people after A (Tuesday): Wednesday, Thursday, Friday and Saturday all fall after Tuesday — four people, more than two. Holds.

• E (Thursday) is exactly two days before B (Saturday). Holds.

• C (Wednesday) comes after D (Monday). Holds.

• People before F (Friday) = Monday to Thursday = four; people after A (Tuesday) = Wednesday to Saturday = four — equal. Holds.

• D (Monday) comes before A (Tuesday). Holds.

Every clue in Statement II is satisfied by exactly one arrangement, so Statement II alone is sufficient to answer the question — the presentation on Wednesday is delivered by C. Statement I alone is not sufficient, since its own clues fit two different arrangements that disagree on Wednesday's presenter.