Arghi wrote:
The ten children in a certain group contributed a total of 28 pieces of clothing to a charity. If the range of the numbers of pieces of clothing contributed by the ten children was 2, which of the following could be the number of children in the group who contributed 3 pieces of clothing each?
l. 0
ll. 5
lll. 9
A) l only
B) lll only
C) l and ll only
D) l and lll only
E) l, ll, and lll
Answer choice eliminationI. 0The 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. 5Let'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. 9Let'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