This is a question with a very subtle trap laid out for the unsuspecting. This is also a question where you can eliminate some answer options, just by looking at the statements given as part of the question.
The range of a given set of numbers is the difference between the greatest and the smallest numbers. So, essentially, it’s a positional value since it depends on the relative positions of the numbers involved.
At first look, although 29 appears to be the biggest number in the set, we cannot say anything till we know the exact values of p, q and r. Therefore, any statement/combination that gives us unique values/ranges for these variables will help us answer the question.
Statement I is insufficient since it does not provide any information about r. It also does not provide us with complete information about q.
Think about it! At least one of q and r can be greater than 29 and the range will be unknown since we do not the exact values of either q or r.
Answer options A and D can be eliminated. Possible answer options are B, C or E.
Statement II is insufficient because of similar reasons in that, it does not provide any information about q. Neither does it tell us anything about p.
p can be smaller than 5 and q can be greater than 29. p can be greater than 5 and q can be smaller than 29.
Answer option B can be eliminated. Possible answer options are C or E.
Combining statements I and II, the only thing we can say conclusively is that 5<p<15. We still do not know about the positions of q and r.
The combination of statements is also insufficient. Answer option C can be eliminated.
The correct answer option is E.
Hope this helps!
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