CAT · 2019 · Question 16 of 32

CAT 2019 LRDI Slot 1 Question 16 · LR - Mathematical Reasoning

Answer it first: the answer and the solution appear right after.

Questions on this set: Q13 Q14 Q15 Q16

Answer the following question based on the information given below.

​​​​​​​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.

Q16 LR - Mathematical Reasoning MULTIPLE CHOICE

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?

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