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# Joan has 100 candies to distribute among 10 children. If each child re

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Senior Manager
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Joan has 100 candies to distribute among 10 children. If each child re [#permalink]

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18 Oct 2010, 09:51
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5% (low)

Question Stats:

88% (00:51) correct 12% (00:48) wrong based on 43 sessions

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Joan has 100 candies to distribute among 10 children. If each child receives at least 1 candy and no two children receive the same number of candies, what is the maximum number of candies that a child can receive?

10
34
39
45
55
[Reveal] Spoiler: OA

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I'm the Dumbest of All !!

Kudos [?]: 592 [0], given: 193

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Re: Joan has 100 candies to distribute among 10 children. If each child re [#permalink]

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18 Oct 2010, 10:25
1
KUDOS
shrive555 wrote:
Joan has 100 candies to distribute among 10 children. If each child receives at least 1 candy and no two children receive the same number of candies, what is the maximum number of candies that a child can receive?

10
34
39
45
55

No its not a combination question.It is somewhat tricky.Here we have to distribute 100 candies in 10 children and no two children will receive the same number of candy .so for making the number of candies maximum for one child we have to make it minimum for the remaining children i.e 1,2,3,4,5,6,7,8,9 so total will be 45 for 9 children.
For the tenth child who is getting maximum, the number of candies will be ( 100-45)=55.Hence answer is E

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Re: Joan has 100 candies to distribute among 10 children. If each child re [#permalink]

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18 Oct 2010, 14:21
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shrive555 wrote:
Joan has 100 candies to distribute among 10 children. If each child receives at least 1 candy and no two children receive the same number of candies, what is the maximum number of candies that a child can receive?

10
34
39
45
55

To maximize the number of candies a child gets, we will need to minimize the number that the other 9 get.

Child 1 : We give him 1 because thats the minimum we can give
Child 2 : We can't give 1 (since number has to be unique). So we give 2
Child 3 : We can't give 1 or 2, so we give 3
....
Child 9 : We can't give 1,2,3,..,8. So we give 9

So total distributed so far = 1+2+3+...+9 = 9(10)/2 =45

The rest we give to child 10, which is the maximum possible, and is 100-45 or 55.

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Re: Joan has 100 candies to distribute among 10 children. If each child re [#permalink]

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01 Oct 2017, 03:45
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Re: Joan has 100 candies to distribute among 10 children. If each child re [#permalink]

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03 Oct 2017, 12:05
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Hello Moderators,

This is a Max/Min problem. Can you change the tag from "combinations" to "max/min" ?

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Re: Joan has 100 candies to distribute among 10 children. If each child re [#permalink]

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03 Oct 2017, 12:07
pikolo2510 wrote:
Hello Moderators,

This is a Max/Min problem. Can you change the tag from "combinations" to "max/min" ?

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Done. Thank you for noticing.
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Re: Joan has 100 candies to distribute among 10 children. If each child re [#permalink]

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16 Oct 2017, 00:35
shrive555 wrote:
Joan has 100 candies to distribute among 10 children. If each child receives at least 1 candy and no two children receive the same number of candies, what is the maximum number of candies that a child can receive?

10
34
39
45
55

hi

think easy
2 things to identify:

only integer values are in play
no child get 0 candy

now, as each child will get at least 1 candy, and as no two children will get the same number of candy
1+2+3+4+5+6+7+8+9 = 45

so the maximum number of candy a child can receive is (100 - 45) = 55

cheers
thanks

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Re: Joan has 100 candies to distribute among 10 children. If each child re   [#permalink] 16 Oct 2017, 00:35
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