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# Each of the integers from 0 to 9, inclusive, is written on a

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Each of the integers from 0 to 9, inclusive, is written on a [#permalink]

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24 Jul 2011, 03:48
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Difficulty:

45% (medium)

Question Stats:

44% (01:25) correct 56% (00:40) wrong based on 16 sessions

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Each of the integers from 0 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into hat. If the slips are then drawn one at a time without replacement, how many must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 10?

A. 3
B. 4
C. 5
D. 6
E. 7
[Reveal] Spoiler: OA
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Re: A difficult math, pls help [#permalink]

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24 Jul 2011, 06:47
tracyyahoo wrote:
Each of the integers from 0 to 9, inclusive, is written on a seperate slip of blank paper and the ten slips are dropped into hat. If the slips are then drawn one at a time without replacement, how many must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 10?

a)3
b)4
c)5
d)6
e)7

pls explain simply to me

The numbers that will add up to 10 are
1,9
2,8
3,7
4,6

to be sure we need 5,0, 4 of the above numbers + at-least 1 more
because we can have 5,0,9,8,7,6 which will not guarantee a sum of 10 for any 2 numbers but one more digit can guarantee the sum to be 10. i.e. 5,0,9,8,7,6 and any of (1,2,3,4) hence we need at-lease 7 numbers.

E
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Re: A difficult math, pls help [#permalink]

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24 Jul 2011, 14:36
Answer is 7. In the worst case, you could end up drawing 0,1,2,3,4,5. 7th draw will result in either of 6,7,8,9 which would result in the numbers adding to 10.
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Re: A difficult math, pls help   [#permalink] 24 Jul 2011, 14:36
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# Each of the integers from 0 to 9, inclusive, is written on a

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