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

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

- 5
- 4
- 3
- 6

- Minimum possible number is when there is 1 of type a and 99 of type b which is in accordance to the condition.
- Maximum possible number is when 1 of a, 2 of b, 4 of c, 8 of d, 16 of e, 32 of f,

Now left boxes woud be 100 â€“ (1+2+â€¦32) = 37

Now if one more type is to be added then we need at least 64 which is not available thus maximum possible is 6. - Lets try to prove the given options possible using easy numbers.

op1:never possible

op2: 1,30,69 is possible

op3: 1,2,4,18.75 is possible

op4: 1,9,30,60 is possible. - There have to be then at least 31 + `1 + 43 = 75 gifts of same type,

Thus maximum possible number of boxes = 5 when all types are lest 1,2,4,18,75

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