Elevation Relationships Analysis

The question provides information about the relative elevations of five different places: Darjeeling, Gangtok, Kalimpong, Pelling, and Siliguri. To determine which statements can be inferred, we need to establish the relationships between their elevations based on the given facts.

Understanding the Given Elevation Facts

Let's list the facts provided in the paragraph using inequality symbols, where '>' means 'at a higher elevation than' and '<' means 'at a lower elevation than'.

• Kalimpong is at a lower elevation than Gangtok.
  • \(\text{Kalimpong} < \text{Gangtok}\)
• Pelling is at a lower elevation than Gangtok.
  • \(\text{Pelling} < \text{Gangtok}\)
• Pelling is at a higher elevation than Siliguri.
  • \(\text{Pelling} > \text{Siliguri}\)
• Darjeeling is at a higher elevation than Gangtok.
  • \(\text{Darjeeling} > \text{Gangtok}\)

Constructing the Overall Elevation Order

Now, let's combine these facts to create a more complete picture of the elevation relationships:

1. We know Darjeeling is higher than Gangtok: \(\text{Darjeeling} > \text{Gangtok}\).
2. We know Gangtok is higher than both Kalimpong and Pelling: \(\text{Gangtok} > \text{Kalimpong}\) and \(\text{Gangtok} > \text{Pelling}\).
3. We also know Pelling is higher than Siliguri: \(\text{Pelling} > \text{Siliguri}\).

Combining these, we can establish the following chain for some places:

\(\text{Darjeeling} > \text{Gangtok} > \text{Pelling} > \text{Siliguri}\)

However, the position of Kalimpong relative to Pelling and Siliguri is not directly given. We only know \(\text{Kalimpong} < \text{Gangtok}\).

Evaluating Each Statement for Inference

Statement i: Pelling is at a higher elevation than Kalimpong

• We know \(\text{Pelling} < \text{Gangtok}\) and \(\text{Kalimpong} < \text{Gangtok}\).
• Both Pelling and Kalimpong are at lower elevations than Gangtok.
• However, the information does not provide any direct comparison or implied comparison between Pelling and Kalimpong. We cannot determine if Pelling is higher or lower than Kalimpong.
  • For example, if Gangtok is at 1000m, Pelling could be at 800m and Kalimpong at 700m (so Pelling > Kalimpong).
  • But Pelling could also be at 700m and Kalimpong at 800m (so Kalimpong > Pelling).
• Therefore, this statement cannot be inferred.

Statement ii: Kalimpong is at a lower elevation than Darjeeling

• We know \(\text{Darjeeling} > \text{Gangtok}\) (Darjeeling is higher than Gangtok).
• We also know \(\text{Gangtok} > \text{Kalimpong}\) (Gangtok is higher than Kalimpong).
• Combining these, we get a clear chain: \(\text{Darjeeling} > \text{Gangtok} > \text{Kalimpong}\).
• This logically implies that Darjeeling is at a higher elevation than Kalimpong, or conversely, Kalimpong is at a lower elevation than Darjeeling.
• Therefore, this statement can be inferred.

Statement iii: Kalimpong is at a higher elevation than Siliguri

• We know \(\text{Kalimpong} < \text{Gangtok}\).
• We also know \(\text{Gangtok} > \text{Pelling} > \text{Siliguri}\). So, \(\text{Gangtok} > \text{Siliguri}\).
• We have Kalimpong is lower than Gangtok, and Siliguri is lower than Gangtok.
• However, there is no direct link or transitive property that allows us to compare Kalimpong and Siliguri.
  • For instance, if Gangtok is at 1000m, Pelling at 800m, and Siliguri at 600m. Kalimpong could be at 700m (Kalimpong > Siliguri).
  • But Kalimpong could also be at 500m (Kalimpong < Siliguri).
• Therefore, this statement cannot be inferred.

Statement iv: Siliguri is at a lower elevation than Gangtok

• We are given \(\text{Pelling} < \text{Gangtok}\) (Pelling is at a lower elevation than Gangtok).
• We are also given \(\text{Pelling} > \text{Siliguri}\) (Pelling is at a higher elevation than Siliguri).
• Combining these two, we get a clear chain: \(\text{Gangtok} > \text{Pelling} > \text{Siliguri}\).
• This directly implies that Gangtok is at a higher elevation than Siliguri, or conversely, Siliguri is at a lower elevation than Gangtok.
• Therefore, this statement can be inferred.

Conclusion

Based on our analysis, only statements ii and iv can be inferred from the given paragraph.

The inferable statements are:

• ii. Kalimpong is at a lower elevation than Darjeeling
• iv. Siliguri is at a lower elevation than Gangtok