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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.

Which of the following is not possible?

Solution

✅ Correct Option: 3
Slide 1/2

Understanding the set :-

This is a minima maxima + quantitative set :

Here you have 100 boxes and a mystery prices in every box, named as a, b, c...

Also, it is given that, there is price of item a is highest , then prices b, then price c, and so on...

Price a - a diamond ring is only in one of the box,

and other prices are atleast double in quantity of previous item i.e.,

we know item a is only 1 , then item b will be atleast two and item c will again be atleast double of item b.

Now, lets try to solve the set with the given information -

Option A: There are exactly 75 items of type e.

a=1,b=2,c=4,d=8, e=85.

Here the maximum value of e= 85.

Hence it can take the value 75.

An example of such case is a=1,b=2,c=4,d=18, e=75.

Option B: There are exactly 30 items of type b.

a=1 b=30 and c=69.

Hence this case is also possible.

Option C: There are exactly 45 items of type c.

Since the value of d should be at least 90, it means that d is not present because 45+90 will be more than 100(maximum number of items). Only a,b and c are present.

The maximum value of b = 22 and a =1, but 45+22+1=68, which is less than 100.

So this case is not possible.

Option D: There are exactly 60 items of type d.

d=60, c=30, b=9 and a=1. a+b+c+d=100.

Hence this case is possible.

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