Discussion

Explanation:

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).

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