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 touching externally have radii p, q (p > q) cm, where p, q are positive integers and each is greater than 1. What is the value of (p − q)?
Statement-I: Sum of areas of these circles is 130π cm².
Statement-II: Distance between centres of these two circles is 14 cm.
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
Statement I: p² + q² = 130. Possible integer pairs (p,q) with p > q > 1: (11,3), (9,7). So I alone is not sufficient. Statement II: For external tangency, p + q = 14. Possible pairs: (12,2),(11,3),(10,4),(9,5),(8,6). Not unique. Together: p + q = 14 and p² + q² = 130. Then 2pq = 196 − 130 = 66, pq = 33. So p, q are roots of t² − 14t + 33 = 0, giving t = 11 or 3. Hence p = 11, q = 3, and p − q = 8. Both statements needed together.
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