Correct Option (4)
Data is inadequate
The given information can be translated into the following inequalities:
- Randhir > Kunal + Debu (R > K + D)
- Kunal + Shankar > Randhir (K + S > R)
- Sonal > Shankar (So > Sh)
- Neha > Randhir (N > R)
From the first two statements (R > K + D and K + S > R), it can be inferred that Shankar > Debu (Sh > D).
We have established that Neha has more marks than Randhir (N > R) and Sonal has more marks than Shankar (So > Sh).
However, there is no direct or indirect relationship provided to compare Neha's marks with Sonal's marks. For instance, while N > R, we cannot ascertain if N > So or So > N. Similarly, while So > Sh, we cannot ascertain if So > N or N > So.
Without a definitive comparison between Neha and Sonal, the individual with the highest marks cannot be determined conclusively. Therefore, the data provided is inadequate.
Incorrect Options
Randhir (1): This option is incorrect because the statement "Neha obtained more marks than Randhir" (N > R) explicitly indicates that Randhir is not the highest scorer.
Neha (2): While Neha has more marks than Randhir (N > R), there is insufficient information to compare Neha's marks with Sonal's marks. Sonal is stated to have more marks than Shankar (So > Sh), but the relationship between Neha and Sonal remains undefined, preventing a conclusive determination of Neha as the highest scorer.
Sonal (3): This option is incorrect because, similar to Neha, there is no information to compare Sonal's marks with Neha's marks. Sonal has more marks than Shankar (So > Sh), but the absence of a clear comparison between Sonal and Neha means Sonal cannot be definitively declared the highest scorer.