CAT 2003 Slot 1 — QA Question 7
Answer the following question based on the information given below.
New Age Consultants have three consultants Gyani, Medha and Buddhi. The sum of the number of projects handled by Gyani and Buddhi individually is equal to the number of projects in which Medha is involved. All three consultants are involved together in 6 projects. Gyani works with Medha in 14 projects. Buddhi has 2 projects with Medha but without Gyani and 3 projects with Gyani but without Medha. The total number of projects for New Age Consultants is one less than twice the number of projects in which more than one consultant is involved.
Let A and B be two solid spheres such that the surface area of B is 300% higher than the surface area of A. The volume of A is found to be k% lower than the volume of B. The value of k must be
Answer & solution
- A
85.5
- B
92.5
- C
90.5
87.5
Ratio of areas of two spheres = s1 : s2 = 4 : 1
∴ Ratio of their radii = r1 : r2 = 2 : 1
∴ Ratio of their volumes = v1 : v2 = 8 : 1
Volume of A is 12.5% (1/8th) of the volume of B.
But, volume of A is k% less than B.
∴ k = (100 − 12.5) = 87.5%
Hence, option (d).