CAT 1998 — QA Question 42
Direction: Each question is followed by two statements, I and II. Answer the questions based on the statements and mark the answer as
1. if the question can be answered with the help of any one statement alone but not by the other statement.
2. if the question can be answered with the help of either of the statements taken individually.
3. if the question can be answered with the help of both statements together.
4. if the question cannot be answered even with the help of both statements together.
There are two concentric circles C1 and C2 with radii r1 and r2. The circles are such that C1 fully encloses C2. Then what is the radius of C1?
I. The difference of their circumference is k cm.
II. The difference of their areas is m sq. cm.
Answer & solution
Correct answer: 3
Answer: 3
The information given in the question implies that r1 > r2.
Statement I suggests that (r1 – r2) = . Hence, this statement alone does not give the value of r1.
Statement II implies that (r12 – r22) = .
Hence, again this statement alone is not sufficient to answer the question. But in the second equation, we simplify (r12 – r22) as (r1 + r2)(r1 – r2) and then substitute the value of (r1 – r2) from the first equation, we will get the value of (r1 + r2). Now we have two equations in r1 and r2, which can be solved simultaneously to get the value of r1. Hence, both the statements when together taken can answer the question.