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

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Joined: 18 Feb 2012
Posts: 2
Each of the integers from 0 to 9, inclusive, is written on a  [#permalink]

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Updated on: 12 Sep 2013, 01:45
3
17
00:00

Difficulty:

65% (hard)

Question Stats:

54% (01:28) correct 46% (01:35) wrong based on 473 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

Originally posted by joynal2u on 11 Apr 2012, 09:26.
Last edited by Bunuel on 12 Sep 2013, 01:45, edited 3 times in total.
Edited the question and the OA
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Joined: 02 Sep 2009
Posts: 55266
Re: Each of the integers from 0 to 9, inclusive, is written on  [#permalink]

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11 Apr 2012, 09:45
4
3
joynal2u wrote:
Each of the integers from 0 to 9, inclusive, is written on separrate slip of blank paper and the ten slips are dropped into a 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

I am getting how to solve this problem.

You should consider the worst case scenario: if you pick numbers 0, 1, 2, 3, 4, and 5 then no two numbers out of these 6 add up to 10.

Now, the next, 7th number whatever it'll be (6, 7, 8, or 9) will guarantee that two number WILL add up to 10. So, 7 slips must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 10.

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

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25 Jun 2013, 08:58
Bunuel wrote:
joynal2u wrote:
Each of the integers from 0 to 9, inclusive, is written on separrate slip of blank paper and the ten slips are dropped into a 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

I am getting how to solve this problem.

You should consider the worst case scenario: if you pick numbers 0, 1, 2, 3, 4, and 5 then no two numbers out of these 6 add up to 10.

Now, the next, 7th number whatever it'll be (6, 7, 8, or 9) will guarantee that two number WILL add up to 10. So, 7 slips must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 10.

Hi Bunnel,
This solution means we are actually able to decide what we are going to pick. Right?
I some how got the idea we can not see which slip we are going to pick, so my answer was 9.
If we cannot decide which one to pick then will 9 be correct?
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Joined: 02 Sep 2009
Posts: 55266
Re: Each of the integers from 0 to 9, inclusive, is written on  [#permalink]

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25 Jun 2013, 10:28
1
2
cumulonimbus wrote:
Bunuel wrote:
joynal2u wrote:
Each of the integers from 0 to 9, inclusive, is written on separrate slip of blank paper and the ten slips are dropped into a 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

I am getting how to solve this problem.

You should consider the worst case scenario: if you pick numbers 0, 1, 2, 3, 4, and 5 then no two numbers out of these 6 add up to 10.

Now, the next, 7th number whatever it'll be (6, 7, 8, or 9) will guarantee that two number WILL add up to 10. So, 7 slips must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 10.

Hi Bunnel,
This solution means we are actually able to decide what we are going to pick. Right?
I some how got the idea we can not see which slip we are going to pick, so my answer was 9.
If we cannot decide which one to pick then will 9 be correct?

Nope. The question asks "how many must be drawn to ensure that..."

To ensure that the sum will be 10 we should consider the worst possible scenario.

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Hope it helps.
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Re: Each of the integers from 0 to 9, inclusive, is written on a  [#permalink]

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15 Jul 2014, 23:36
manish2014 wrote:
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 a 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

You can make a sum of 10 by pairing these numbers:
1, 9
2, 8
3, 7
4, 6

So if you pick only one number from each of these pairs and the leftover 2 numbers: 0 and 5, you would have picked 6 numbers without any two numbers adding up to 10. When you pick the next number (7th), there will be one of the 'sum 10' pairs. So picking 7 numbers will give you one of the required pairs for sure!

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

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15 Feb 2016, 19:50
oh damn..again missed the question because i misread the condition..
i thought the sum of ALL is equal to 10..what a crucial mistake
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Posts: 7684
Re: Each of the integers from 0 to 9, inclusive, is written on a  [#permalink]

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15 Feb 2016, 21:48
1
2
joynal2u wrote:
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

Hi,

If we can correlate the info of the Q with the properties of number, teh Q can turn into a sitter...

given

1) 0 to 9 numbers are written..
2) no number can be repeated..
3) min number that we MUST have some TWO numbers picked up totalling to 10..

Info

1) there are two digits which do not add up to 10 when combined with a DIFFERENT number :- 0,5
2) remaining 8 can be divided into 4 pair of digits that add up to 10 :- 1,9 : 2,8 : 3,7 : 4,6 ...

Method

We pick up the worst scenario, where none add up to 10..
1) we can straight way pick up 0 and 5..
2) thereafter we can pick up one each from the 4 pairs : 1 or 9 : 2 or 8 : 3 or 7 : 4 or 6..
3) Now, whatever we pick from remaining 4, it will make a pair with the 6 already picked to add up to 10..
so the answer is we require 2+4+1=7 to be sure that some slip will add up to 10....

ans 10.. E
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Re: Each of the integers from 0 to 9, inclusive, is written on a  [#permalink]

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29 Dec 2017, 10:23
joynal2u wrote:
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

Just a view :

Even after drawing 7 if we pair it with 0 we will not get a 10 , Drawing 7 does not ensure that sum of ANY of the drawn slips will be 10.
Yes, we can make a 10 but we can also NOT do so.
Isn't the question asking how many we must draw to ensure (100%) that sum of ANY of the 2 drawn slips must be 10?

Maybe I am over reading the word " ANY".

How many must be withdrawn so that we CAN make a pair with a sum 10 seems , more appropriate.
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Re: Each of the integers from 0 to 9, inclusive, is written on a  [#permalink]

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11 Mar 2018, 22:58
stne wrote:
joynal2u wrote:
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

Just a view :

Even after drawing 7 if we pair it with 0 we will not get a 10 , Drawing 7 does not ensure that sum of ANY of the drawn slips will be 10.
Yes, we can make a 10 but we can also NOT do so.
Isn't the question asking how many we must draw to ensure (100%) that sum of ANY of the 2 drawn slips must be 10?

Maybe I am over reading the word " ANY".

How many must be withdrawn so that we CAN make a pair with a sum 10 seems , more appropriate.

Hello

I think the question does NOT mention the word ANY. The question clearly states, "....how many must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 10". So if we pick 7 slips, we can be completely sure that we will be able to find two slips here which will add up to '10'. And in worst case scenario, 7 slips are what are required to be drawn.
Re: Each of the integers from 0 to 9, inclusive, is written on a   [#permalink] 11 Mar 2018, 22:58
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