Study the following information and answer the questions that follow: A…
2024
Study the following information and answer the questions that follow: A company is planning to organise 8 lectures — A, B, C, D, E, F, G and H — for 3 subjects: Quants, D.I. and English. The lectures are spread over three days. Quants is to be covered first in 3 lectures, followed by English, and then D.I. in the last 2 lectures. Lectures A, C and D have to be on different days. Lectures B and F have to be on the same day, but lecture B cannot be clubbed with A, G or D. Lectures G and H have to be on the same day. Lecture A is a lecture on Quants, and lecture C cannot be on the last day. It is also known that there are at least 3 lectures on day 1. Which of the following lectures were for D.I.?
- A.
D, F
- B.
B, C
- C.
G, H
- D.
Data inadequate
Show answer & explanation
Correct answer: D
Concept: in a scheduling/arrangement puzzle that asks you to pin down one specific fact, that fact is determinable only if every arrangement consistent with all the given constraints agrees on it. If two or more genuinely different, fully constraint-satisfying arrangements disagree on the queried fact, the correct response is that the data is inadequate to decide — even after you have correctly built one valid arrangement that answers it.
By the stated subject order, the first 3 lectures delivered are Quants, the next 3 are English, and the last 2 are D.I. — so "which lectures are D.I." really asks which two letters occupy the final two slots of the overall sequence.
Lecture A is given as a Quants lecture, so A must sit among the first three slots.
Because A, C and D must be on pairwise different days and there are only 3 days total, each day must hold exactly one of A, C, D. Day 1 must be A's day (Quants occupies the first 3 overall positions, and day 1 — needing at least 3 lectures itself — necessarily covers those first 3 positions). Since C cannot be on the last day, C must take the middle day, leaving D as the only one of the three left for the last day — so D is always on the last day, and since the last day's lectures are always among the final D.I. positions, D is always a D.I. lecture.
B cannot share a day with A (the first day) or D (the last day), so B must be on the middle day — and F, who must share B's day, is on the middle day too. G and H must share a day; testing the last day for them forces the first day down to only 2 lectures (below the required minimum of 3) or strands one of A, C, D without a valid day, so G and H are always on the first day, alongside A. Only lecture E's day is left open by the clues, and only the WITHIN-A-DAY order is also left open by them.
Two independently valid, fully constraint-satisfying schedules already disagree on D's D.I. partner. Schedule 1: day 1 = A, G, H (3, exactly the Quants block); day 2 = B, C, F (3, exactly the English block); day 3 = D, E (2, exactly the D.I. block) -> D.I. = D, E. Schedule 2: day 1 = A, G, H (3); day 2 = B, C, E, F (4, stretching one position into the D.I. block) with F scheduled last within that day; day 3 = D (1) -> D.I. = D, F. Both schedules satisfy every stated clue exactly.
Cross-check: in Schedule 2, A, C, D still fall on different days; B and F still share a day and B is clubbed only with C, E and F, never A, G or D; G and H still share a day; C is still not on the last day; day 1 still has 3 lectures (at least 3). So Schedule 2 is just as valid as Schedule 1, yet the two disagree on D's partner (E vs F) -- proving the second D.I. lecture is never fixed by the given clues. This same reasoning also rules out B,C and G,H outright: D is unconditionally a D.I. lecture in every valid schedule (as shown above), so any pair that omits D, like B,C, can never be it; and G,H are unconditionally on the first day in every valid schedule, so they can never be the D.I. pair either. With D's partner undetermined and the only other two options impossible outright, the pair of D.I. lectures cannot be pinned down from the given information -- "Data inadequate" is the only option that can be defended with certainty.