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# Ten boys donated 28 clothes to an organization. If the

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Ten boys donated 28 clothes to an organization. If the [#permalink]

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07 Jan 2006, 23:07
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Ten boys donated 28 clothes to an organization. If the range of numbers of the clothes each boy donated is 2, how many boys donated exactly three clothes?

I: 0
II: 5
III: 9
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08 Jan 2006, 08:56
III. 9.

i. 0x3=0
10x2.8=28. not possible cux 2.8 cloths are not possible.
range = 2.8

ii. 5 x 3 = 15
5 x 2.6 = 13
total clothes = 28
total people = 10
range = 3-2.6= 1.6

iii. 9x3=27
1x1=1
total clothes = 28
total people = 10
range = 3-1=2
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08 Jan 2006, 13:38
I: 0
II: 9

Range = 2
There are several sets wirh range 2 and min max number pairs as: (1,3) (2,4), (3,5).....

Set1: (2,4) i.e, Set with min = 2 and max = 4 can have, 0 students contributing 3.
x=number of contributing 2
y= number of people contributing 4
2x+4y = 28
x+y = 10
=> x = 6 & y = 4

So there can be 0 boys contributing 3. (I: 0 is POSSIBLE)

Set2: (1,3)
x = number of contributing 1
y = number of people contributing 3

x + 3y = 28
x + y = 10
=> x = 1, y=9

Therefor 9 boys can be contributing 3 (III: 9 is POSSIBLE)

Others don't satisfy all the three conditions.

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08 Jan 2006, 14:38
great explanation giddi, the oa is I & III
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08 Jan 2006, 14:47
joemama142000 wrote:
great explanation giddi, the oa is I & III

No problemo!
Man this was a tough one. I would definitely screw up such questions on my exam.
BTW what's the source?
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"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."

- Bernard Edmonds

08 Jan 2006, 14:47
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