Author 
Message 
Director
Status: 1,750 Q's attempted and counting
Affiliations: University of Florida
Joined: 09 Jul 2013
Posts: 510
Location: United States (FL)
GMAT 1: 600 Q45 V29 GMAT 2: 590 Q35 V35 GMAT 3: 570 Q42 V28 GMAT 4: 610 Q44 V30
GPA: 3.45
WE: Accounting (Accounting)

A bag contains six tokens, each labeled with one of the inte [#permalink]
Show Tags
27 Nov 2013, 22:15
8
This post was BOOKMARKED
Question Stats:
21% (01:47) correct 79% (01:36) wrong based on 203 sessions
HideShow timer Statistics
A bag contains six tokens, each labeled with one of the integers from 1 to 6, inclusive. Each integer appears on one token. When three tokens are removed at random, without replacement, what is the probability that the sum of numbers on those three tokens is equal to the positive integer N? (1) There is only one combination of three tokens in the bag that sums to N (2) N is a multiple of 7 Attachment:
632444379.png [ 23.68 KiB  Viewed 2914 times ]
No explanation provided  Need help in solving. == Message from GMAT Club Team == This is not a quality discussion. It has been retired. If you would like to discuss this question please repost it in the respective forum. Thank you! To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative  Verbal Please note  we may remove posts that do not follow our posting guidelines. Thank you.
Official Answer and Stats are available only to registered users. Register/ Login.



VP
Joined: 02 Jul 2012
Posts: 1195
Location: India
Concentration: Strategy
GPA: 3.8
WE: Engineering (Energy and Utilities)

Re: A bag contains 6 tokens. [#permalink]
Show Tags
27 Nov 2013, 23:12
Actually, I think A is a better answer than D. Reasons: Statement 1) Whatever N is, there is only one combination to give it. N cannot be all 6,7,14 and 15. So probability has to be 1/20. Sufficient. Statement 2) What if N = 7000. In that case answer is 0. Insufficient. Edit: Tough one.. I thought the answer was an easyD A...
_________________
Did you find this post helpful?... Please let me know through the Kudos button.
Thanks To The Almighty  My GMAT Debrief
GMAT Reading Comprehension: 7 Most Common Passage Types



Intern
Joined: 19 Sep 2012
Posts: 26

Re: A bag contains 6 tokens. [#permalink]
Show Tags
27 Nov 2013, 23:24
Probability of getting sum of N from 3 tokens= no. of combinations from 3 tokens which leads to N/ total sum of combination from 3 token 1)> only 1 combnination of exists which leads to N... Hence, total outcomes =20.. using 6C3... 1/20.. 2) N is a multiple of 7.. Two such combinations exist.. 1,2,4 = 7 and 3,6,5 = 14... Probabilty = 2/20
Both the statements seem to contradict each other
What is OA ???
Dont know what am I missing here



Director
Status: 1,750 Q's attempted and counting
Affiliations: University of Florida
Joined: 09 Jul 2013
Posts: 510
Location: United States (FL)
GMAT 1: 600 Q45 V29 GMAT 2: 590 Q35 V35 GMAT 3: 570 Q42 V28 GMAT 4: 610 Q44 V30
GPA: 3.45
WE: Accounting (Accounting)

Re: A bag contains 6 tokens. [#permalink]
Show Tags
27 Nov 2013, 23:38
1
This post was BOOKMARKED
perseverance84 wrote: Probability of getting sum of N from 3 tokens= no. of combinations from 3 tokens which leads to N/ total sum of combination from 3 token 1)> only 1 combnination of exists which leads to N... Hence, total outcomes =20.. using 6C3... 1/20.. 2) N is a multiple of 7.. Two such combinations exist.. 1,2,4 = 7 and 3,6,5 = 14... Probabilty = 2/20
Both the statements seem to contradict each other
What is OA ???
Dont know what am I missing here The OA is B. I just did an excel workpaper to solve this problem and it appears there are four combinations that result in one number. It is 1,2,3 (sum=6), 1, 2, 4 (sum=7), 3,5,6 (sum= 14) and 4,5,6 (sum= 15). Here is the whole chart of the 20 combinations. 1 2 3 6 One combination 1 2 4 7 One combination 1 2 5 8 1 2 6 9 1 3 4 8 1 3 5 9 1 3 6 10 1 4 5 10 1 4 6 11 1 5 6 12 2 3 4 9 2 3 5 10 2 3 6 11 2 4 5 11 2 4 6 12 2 5 6 13 3 4 5 12 3 4 6 13 3 5 6 14 One combination 4 5 6 15 One combination



VP
Joined: 02 Jul 2012
Posts: 1195
Location: India
Concentration: Strategy
GPA: 3.8
WE: Engineering (Energy and Utilities)

Re: A bag contains 6 tokens. [#permalink]
Show Tags
27 Nov 2013, 23:50
Edited my previous answer. I go with A. Still don't agree with the OA though..
_________________
Did you find this post helpful?... Please let me know through the Kudos button.
Thanks To The Almighty  My GMAT Debrief
GMAT Reading Comprehension: 7 Most Common Passage Types



Senior Manager
Status: Countdown Begins...
Joined: 03 Jul 2016
Posts: 305
Location: India
Concentration: Technology, Strategy
GPA: 3.7
WE: Information Technology (Consulting)

Re: A bag contains six tokens, each labeled with one of the inte [#permalink]
Show Tags
28 Aug 2017, 23:44
Bunuel, please help in this question. I am unable to get the question stem. Does it not mean we just have 6 tokens with 16 written on it without duplicates?
_________________
Need Kudos to unlock GMAT Club tests



Math Expert
Joined: 02 Sep 2009
Posts: 45429

Re: A bag contains six tokens, each labeled with one of the inte [#permalink]
Show Tags
29 Aug 2017, 00:20
RMD007 wrote: Bunuel, please help in this question. I am unable to get the question stem. Does it not mean we just have 6 tokens with 16 written on it without duplicates? Yes, it means that there are 6 tokens numbered from 1 to 6, inclusive: [1]; [2]; [3]; [4]; [5]; [6]. A bag contains six tokens, each labeled with one of the integers from 1 to 6, inclusive. Each integer appears on one token. When three tokens are removed at random, without replacement, what is the probability that the sum of numbers on those three tokens is equal to the positive integer N?Notice several things: 1. We are picking without replacement, so if we pick [1] there won't be any more [1]'s left in the bag. 2. The least possible sum (N) is 1 + 2 + 3 = 6 and the greatest possible sum is 6 + 5 + 4 = 15. 3. The sums from 6 to 15 has different ways (combinations) to occur. For example, we can get 6 only in one way: 1 + 2 + 3 = 6 but we can get 8 in 2 ways: 1 + 2 + 5 = 1 + 3 + 4 = 8. 4.We can get the number of combinations for each sum, thus we can get the total number of combinations for all sums. (1) There is only one combination of three tokens in the bag that sums to N. There are many value of N possible for example, if N = 1, then the probability is 0 (you cannot get the sum of 1 by adding three positive integers). But if say N = 6 (we can get 6 in one way: 6 = 1 + 2 + 3 only), then the probability is not 0 (it does not matter what it's actually is). Not sufficient. (2) N is a multiple of 7. The greatest sum is 6 + 5 + 4 = 15, so for N to be a multiple of 7 it must be 7 or 14. Both of these numbers can be broken into the sum of three distinct positive integers only in one way: 7 = 1 + 2 + 4 and 14 = 6 + 5 + 3. Sufficient. Answer: B. Hope 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



Manager
Joined: 07 Jun 2017
Posts: 103

Re: A bag contains six tokens, each labeled with one of the inte [#permalink]
Show Tags
29 Aug 2017, 00:55
the answer should not be B because there is more than 1 combination has a multiple of 7. waiting someone to explain on this, thank you so much



Math Expert
Joined: 02 Sep 2009
Posts: 45429

Re: A bag contains six tokens, each labeled with one of the inte [#permalink]
Show Tags
29 Aug 2017, 01:44



Manager
Joined: 14 Mar 2011
Posts: 147

Re: A bag contains six tokens, each labeled with one of the inte [#permalink]
Show Tags
29 Aug 2017, 03:38
Hello Bunuel, Can you please explain more on this, Bunuel wrote: (1) There is only one combination of three tokens in the bag that sums to N. There are many value of N possible for example, if N = 1, then the probability is 0 (you cannot get the sum of 1 by adding three positive integers). But if say N = 6 (we can get 6 in one way: 6 = 1 + 2 + 3 only), then the probability is not 0 (it does not matter what it's actually is). Not sufficient.
A mentions that "there is only one combination of three tokens in the bag that sums to N", so how N=1 become one possibility. Please help !!
_________________
If you find my posts/replies helpful, please take a moment to click on the "kudos" icon.



Math Expert
Joined: 02 Sep 2009
Posts: 45429

Re: A bag contains six tokens, each labeled with one of the inte [#permalink]
Show Tags
29 Aug 2017, 04:04
1
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
godot53 wrote: Hello Bunuel, Can you please explain more on this, Bunuel wrote: (1) There is only one combination of three tokens in the bag that sums to N. There are many value of N possible for example, if N = 1, then the probability is 0 (you cannot get the sum of 1 by adding three positive integers). But if say N = 6 (we can get 6 in one way: 6 = 1 + 2 + 3 only), then the probability is not 0 (it does not matter what it's actually is). Not sufficient.
A mentions that "there is only one combination of three tokens in the bag that sums to N", so how N=1 become one possibility. Please help !! Yes, you can get N = 1 in only one way (in 0 ways) but the probability of getting the sum of 1 is 0, while you can get N = 6 also in only one way (in 1 way) but the probability of getting the sum of 6 is NOT 0.
_________________
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



Intern
Joined: 05 Feb 2014
Posts: 3

Re: A bag contains six tokens, each labeled with one of the inte [#permalink]
Show Tags
13 Oct 2017, 00:50
I am a little lost here. "what is the probability that the sum of numbers on those tokens is equal to the positive integer N" " the positive integer N". i might be mistake but "the number" should be one specific number. the probability of getting 7= the probability of getting 14. i am perfectly fine here. but probability of getting either 7 or 14 is twice as much. let us imagine this is not a DS question and it is a problem solving assignment where we have the general statement + the 2th (B) statement, "what is the probability that the sum of numbers on those tokens is equal to the positive integer N" == Message from GMAT Club Team == This is not a quality discussion. It has been retired. If you would like to discuss this question please repost it in the respective forum. Thank you! To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative  Verbal Please note  we may remove posts that do not follow our posting guidelines. Thank you.




Re: A bag contains six tokens, each labeled with one of the inte
[#permalink]
13 Oct 2017, 00:50






