CAT 2019 Slot 1 — DILR Question 15
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.
Which of the following is not possible?
Answer & solution
- A
There are exactly 30 items of type b.
- B
There are exactly 75 items of type e.
- C
There are exactly 60 items of type d.
There are exactly 45 items of type c.
There is exactly one prize of type a.
[1]. If there are 30 items of type b, then items of type c = 100 – 30 −1 = 69. So this case is possible.
[2]. There are 75 items of type e, then items of type b, c and d = 100 – 75 −1 = 24.
Some of the values of (b, c, d) are (2, 4, 18) or (2, 5, 17) or (3, 6, 15). So this case is possible.
[3]. If there are 60 items of type d, then items of type b and c = 100 – 60 −1 = 39. So this case is possible as we can find many combinations for (b, c).
[4]. If there are 45 items of type c, then items of type a, b and c in all cannot be more than 1 + 22 + 45 = 68. Now items of type d has to be more than 90. But then total number of items exceed 100. So this case is not possible.
Hence, option (d).