NIMCET 2023
A junior school is offering five after-school activities: Karate, Handwork, Music, Dance and Gymnastics. Each of the five students Leena, Megan, Neha, Omar and Pixie has subscribed to at least one activity. As per the school rules, anyone who subscribes to Gymnastics must also subscribe to Dance; Karate and Handwork must always be subscribed together; Music and Dance cannot be subscribed together.The following information is available about the students' subscriptions:(i) Megan subscribed to four activities.(ii) Leena subscribed to Gymnastics but not Karate.(iii) Pixie subscribed to only one activity and is the only one who subscribed to that activity.(iv) Omar subscribed to three activities.(v) Neha subscribed to only one activity.How many activities are subscribed to by exactly two people each?
Answer (Detailed Solution Below)View answer ▾Hide ▴
Answer: Option A — 3
Detailed Solution
Four activities without Music is the only allowed set of four (Music excludes Dance, and Gymnastics needs Dance), so Megan has Karate, Handwork, Dance and Gymnastics.
Leena has Gymnastics, so Dance; she has no Karate, so no Handwork; Dance rules out Music. Leena: Dance and Gymnastics.
A single activity can only be Music or Dance (Karate needs Handwork, Gymnastics needs Dance). Dance is already taken, so Pixie has Music and nobody else does. Then Omar's three activities are Karate, Handwork and Dance, and Neha has Dance.
Counts: Karate 2, Handwork 2, Music 1, Dance 4, Gymnastics 2. Exactly two people: Karate, Handwork and Gymnastics, i.e. 3 activities.
✓ Check
In the table every student follows all three rules, and each clue (i) to (v) holds.⚠ Common trap
(C) 2 forgets Gymnastics, which Megan and Leena both take.Quick tip
Fix Megan (4 activities cannot include Music), then Leena, then Pixie (Music), then Omar and Neha
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Analytical Reasoning — Preparation
This question tests your understanding of Analytical Reasoning, a key topic in the Logical Reasoning section. The detailed solution above uses a step-by-step approach to show the reasoning, and where available, a shortcut that helps you solve similar questions in under 90 seconds during the actual exam.
Analytical reasoning questions give a set of conditions about people, objects or events and ask you to deduce facts from them. They include puzzles on scheduling (who does what on which day), distribution (who owns which item), floor-based puzzles, comparisons, and grouping or selection problems where certain people must or cannot be chosen together. The key is organising the information. Draw a table or grid with the categories as rows and columns, and fill in the definite clues first. Then use the conditional clues to eliminate possibilities, marking crosses for what is impossible and ticks for what is certain. When a clue leaves two possibilities, write both cases and test each against the remaining clues. Usually one case leads to a contradiction. Most puzzles have four or five questions, so time spent setting up a clear grid pays off. Practise the analytical reasoning puzzles below. Each solution shows the grid built step by step.