CAT 2019 Slot 1 — DILR Question 14
Answer the following question based on the information given below.
âââââââA new game show on TV has 100 boxes numbered 1, 2, . . . , 100 in a row, each containing a mystery prize. The prizes are items of different types, a, b, c, . . . , in decreasing order of value. The most expensive item is of type a, a diamond ring, and there is exactly one of these. You are told that the number of items at least doubles as you move to the next type. For example, there would be at least twice as many items of type b as of type a, at least twice as many items of type c as of type b and so on. There is no particular order in which the prizes are placed in the boxes.
What is the maximum possible number of different types of prizes?
Answer & solution
Answer: 6
There is exactly one prize of type a.
As we need to find maximum possible different types of prizes, number of prizes of type b has to be minimum possible and hence must be 2, number of items of type c = 4 …and so on.
1(type a) + 2(type b) + 4(type c) + 8(type d) + 16(type e) + 32(type e) = 63
Suppose there is prize of type f then number of items has to be at least 64. But then there are more than 100 items, which is not true. So there cannot be prize of type f.
Answer: 6.