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Ten boys donated 28 clothes to an organization. If the

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New post 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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New post 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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New post 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.

What's the source joemama. I had to scratch my head several times and still I am not sure about the answer :shock:
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New post 08 Jan 2006, 14:38
great explanation giddi, the oa is I & III
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New post 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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  [#permalink] 08 Jan 2006, 14:47
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