Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 18 Feb 2012
Posts: 2

Each of the integers from 0 to 9, inclusive, is written on a [#permalink]
Show Tags
Updated on: 12 Sep 2013, 01:45
2
This post received KUDOS
16
This post was BOOKMARKED
Question Stats:
51% (01:06) correct 49% (01:01) wrong based on 368 sessions
HideShow timer Statistics
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
Official Answer and Stats are available only to registered users. Register/ Login.
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



Math Expert
Joined: 02 Sep 2009
Posts: 44655

Re: Each of the integers from 0 to 9, inclusive, is written on [#permalink]
Show Tags
11 Apr 2012, 09:45
3
This post received KUDOS
Expert's post
2
This post was BOOKMARKED
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.
Thanks in advance for your attempt 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. Answer: E.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 14 Nov 2011
Posts: 133
Location: United States
Concentration: General Management, Entrepreneurship
GPA: 3.61
WE: Consulting (Manufacturing)

Re: Each of the integers from 0 to 9, inclusive, is written on [#permalink]
Show Tags
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.
Thanks in advance for your attempt 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. Answer: E. 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?



Math Expert
Joined: 02 Sep 2009
Posts: 44655

Re: Each of the integers from 0 to 9, inclusive, is written on [#permalink]
Show Tags
25 Jun 2013, 10:28
1
This post received KUDOS
Expert's post
2
This post was BOOKMARKED
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.
Thanks in advance for your attempt 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. Answer: E. 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. Similar questions to practice: 12easypiecesornot126366.html#p1033935inhispocketaboyhas3redmarbles4bluemarblesand85216.htmlofthesciencebooksinacertainsupplyroom50areon131100.htmlinadeckof52cardseachcardisoneof4differentcolor83183.htmlaboxcontains10redpills5bluepills12yellow56779.htmleachoftheintegersfrom0to9inclusiveiswrittenon130562.htmlastudentisaskedtopickmarblesfromabagthatcontains72390.htmlofthesciencebooksinacertainsupplyroom50areon131100.htmlifalibrarianrandomlyremovessciencebooksfromalibrary93861.htmlm10q24ps69233.html#p1237169Hope it helps.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8025
Location: Pune, India

Re: Each of the integers from 0 to 9, inclusive, is written on a [#permalink]
Show Tags
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! Answer (E)
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Board of Directors
Joined: 17 Jul 2014
Posts: 2743
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

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



Math Expert
Joined: 02 Aug 2009
Posts: 5777

Re: Each of the integers from 0 to 9, inclusive, is written on a [#permalink]
Show Tags
15 Feb 2016, 21:48
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
_________________
Absolute modulus :http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
GMAT online Tutor



Senior Manager
Joined: 27 May 2012
Posts: 468

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



DS Forum Moderator
Joined: 22 Aug 2013
Posts: 1033
Location: India

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






