The ten children in a certain group contributed a total of 28 pieces

Answer choice elimination

I. 0

The group consists of 10 children. Let's assume each child initially donates two clothes

G = {2, 2, 2, 2, 2, 2, 2, 2, 2, 2}

The number of clothes donated = 2*10 = 20

The remaining 8 clothes can be distributed as follows

G = {2, 2, 2, 2, 2, 2, 4, 4, 4, 4}

Hence, we can have a scenario in which no children donates 3 clothes.

II. 5

Let's assume that 5 children donate 3 clothes each.

Number of clothes donated = 5 * 13 = 15

Remaining = 28 - 15 = 13

There are two possible cases from here

Case 1 : 3 is the maximum number of clothes donated

G = {_, _, _, _, _, 3, 3, 3, 3, 3}

As the range is 2, the minimum number of clothes donated = 1

G = {1, _, _, _, _, 3, 3, 3, 3, 3}

The remaining 12 clothes are therefore donated by the remaining children. However, the maximum number of clothes that they can donate = is 4*2 = 8. Hence, this case is not possible.

Case 2 : 3 is not the maximum number of clothes donated

G = {.... 3, 3, 3, 3, 3 ...}

Let's assume 4 is the maximum number of clothes donated.

G = { _, _, _, _, 3, 3, 3, 3, 3, 4}

Remaining = 28 - 19 = 9. However the maximum number of clothes that the remaining students can donate = 4*2 = 8. Hence, this case is not possible.

Therefore II is not possible.

III. 9

Let's assume 9 students donate three pieces of clothes

G = { _, 3, 3, 3, 3, 3, 3, 3, 3, 3}

The remaining 1 cloth can be accommodated as follows

G = { 1, 3, 3, 3, 3, 3, 3, 3, 3, 3}

Hence, this is a possible case.

Option D