A map shows the elevations of Darjeeling, Gangtok, Kalimpong, Pelling, and Siliguri. Kalimpong is at a lower elevation than Gangtok. Pelling is at a higher elevation than Gangtok. Pelling is at a higher elevation than Kalimpong. Siliguri is at a lower elevation than Darjeeling. Darjeeling is at a lower elevation than Gangtok. Siliguri is at a lower elevation than Kalimpong. Which of the following statements can be inferred from the paragraph above? i. Pelling is at a higher elevation than Siliguri. ii. Kalimpong is at a lower elevation than Darjeeling. iii. Darjeeling is at a lower elevation than Kalimpong. iv. Siliguri is at a lower elevation than Gangtok. A. Only i. B. Only ii and iii. C. Only i and iv. D. Only ii and iv.

GATE 2017 · General Aptitude · Passage Reading · medium

Answer: C. Only i and iv. — Pelling is higher than Siliguri (i) and Siliguri is lower than Gangtok (iv) are both provable by transitive chaining of the given elevation relationships.

1. List all given inequalities: 1. Kalimpong < Gangtok 2. Pelling > Gangtok (i.e., Gangtok < Pelling) 3. Pelling > Kalimpong (i.e., Kalimpong < Pelling) 4. Siliguri < Darjeeling 5. Darjeeling < Gangtok 6. Siliguri < Kalimpong
2. Build transitive chains: Chain A: Siliguri < Darjeeling (4), Darjeeling < Gangtok (5), Gangtok < Pelling (2) => Siliguri < Darjeeling < Gangtok < Pelling Chain B: Siliguri < Kalimpong (6), Kalimpong < Gangtok (1), Gangtok < Pelling (2) => Siliguri < Kalimpong < Gangtok < Pelling Note: No chain connects Darjeeling and Kalimpong directly or transitively.
3. Check each statement: Statement i: Pelling > Siliguri — From Chain A or B: Siliguri < ... < Pelling. TRUE (can be inferred). Statement ii: Kalimpong < Darjeeling — No chain establishes this. CANNOT be inferred. Statement iii: Darjeeling < Kalimpong — No chain establishes this either. CANNOT be inferred. Statement iv: Siliguri < Gangtok — From Chain A: Siliguri < Darjeeling < Gangtok. TRUE (can be inferred).
4. Select the correct option: Only i and iv are valid inferences. This corresponds to option C.