A 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.

**Question 1: **

What is the minimum possible number of different types of prizes?

**Show Answer**

**2**

**Question 2: **

What is the maximum possible number of different types of prizes?

**Show Answer**

**6**

**Question 3: **

Which of the following is not possible?

- There are exactly 30 items of type b.
- There are exactly 45 items of type c.
- There are exactly 75 items of type e.
- There are exactly 60 items of type d.

**Show Answer**

**2**

**Question 4: **

You ask for the type of item in box 45. Instead of being given a direct answer, you are told that there are 31 items of the same type as box 45 in boxes 1 to 44 and 43 items of the same type as box 45 in boxes 46 to 100.

What is the maximum possible number of different types of items?

- 6
- 3
- 5
- 4

**Show Answer**

**3**

### CAT 2019 LRDI sets

CAT 2019 LRDI set 1CAT 2019 LRDI set 2

CAT 2019 LRDI set 3

CAT 2019 LRDI set 4

CAT 2019 LRDI set 5

CAT 2019 LRDI set 6

CAT 2019 LRDI set 7 [Current page]

CAT 2019 LRDI set 8

CAT 2019 LRDI set 9

CAT 2019 LRDI set 10

CAT 2019 LRDI set 11

CAT 2019 LRDI set 12

CAT 2019 LRDI set 13

CAT 2019 LRDI set 14

CAT 2019 LRDI set 15

CAT 2019 LRDI set 16