Statement I: Amit went to Rahul’s office on Wednesday and Friday. Statement…

Concept: in a "which day did X surely meet Y" data-sufficiency puzzle, the fact that a meeting took place is built into the question itself — it asks WHICH day the meeting certainly happened, not whether it happened — so a candidate schedule under which the meeting could never have happened on either given visit day is not a live possibility consistent with the question as posed, and is set aside before checking whether one single day is guaranteed across whatever remains. A statement combination is sufficient only when, among the schedules still live, one single day is guaranteed; if more than one day stays possible, or a statement in the combination could be dropped without losing that guarantee, the combination is not the minimal sufficient one.

Application:

1. Statement II fixes that Rahul was absent on exactly three days out of Monday–Saturday (never on Sunday).

2. Statement III rules out any two of those absent days falling on back-to-back calendar dates.

3. Listing every 3-day subset of the six weekdays with no two days adjacent gives exactly four possible absence patterns, shown below.

4. Statement I fixes Amit's two office visits as Wednesday and Friday. Checking the four patterns against these two days shows one pattern — Monday, Wednesday, Friday — has Rahul absent on both visit days, so under it no meeting could have happened at all on either visit; that is not a live possibility given the question's own premise that a meeting occurred, so this pattern is set aside.

5. Of the three remaining live patterns, Rahul is present in the office on Friday in every one — only the discarded pattern had him absent that day — while Wednesday is still an absence day in one of the three. So Friday is the one day Amit is guaranteed to have met Rahul, whichever of the three remaining patterns actually held.

Cross-check: drop any one statement and the certainty disappears. Statements I and II alone (without the non-consecutive rule) leave far more absence combinations open — even after applying the same "a meeting occurred" convention, Rahul could still be absent on Wednesday in some remaining patterns, on Friday in others, so no single day is guaranteed. Statements II and III alone (without Statement I) fix an absence pattern but give nothing to check it against, since Amit's visit days are unknown. Statements I and III alone (without the fixed count of three absences) leave the number and placement of absence days almost unconstrained. Only using all three together narrows things down to a single guaranteed day.

Result: all three statements are required — Friday is the day on which Amit surely met Rahul, so the correct option is "All are required."