2026 · Q75
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 IThe sum of their areas is 130π cm².
Statement IIThe 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?
Elementary MathematicsCircles
- AThe Question can be answered by using one of the statements alone, but cannot be answered using the other statement alone
- BThe Question can be answered by using either Statement alone
- CThe Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
- DThe Question cannot be answered even by using both the Statements together
Explanation
External touch gives p+q=14 (statement II) and the areas give p²+q²=130 (statement I). Then 2pq=(p+q)²−(p²+q²)=66, so (p−q)²=130−66=64 and p−q=8 (p>q). Neither statement alone determines it, option C.