CDS 2026 · PYQ · Data Sufficiency / Circles · medium
A Question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option.
Question: Two circles with radii p, q (p > q) in cm touch externally, where p, q are natural numbers and each greater than 1. What is the value of (p - q)?
Statement-I: The sum of their areas is 130π cm²
Statement-II: The distance between the centres of the two circles is 14 cm
Which one of the following is correct in respect of the above Question and the Statements?
A.The Question can be answered by using one of the statements alone, but cannot be answered using the other statement alone
B.The Question can be answered by using either Statement alone
C.The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone✓ Correct
D.The Question cannot be answered even by using both the Statements together
Explanation
Since the circles touch externally, the distance between centres equals p + q. From Statement-II alone, p + q = 14, but we cannot find p - q. From Statement-I alone, π(p² + q²) = 130π, so p² + q² = 130, which has multiple natural number solutions (e.g., p=11, q=3 or p=9, q=7), so p - q is not uniquely determined. Using both together: p + q = 14 and p² + q² = 130, so 2pq = 196 - 130 = 66, pq = 33. Then (p - q)² = 130 - 66 = 64, so p - q = 8. Both statements together uniquely determine p - q, but neither alone is sufficient.
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