|
Author |
Message |
|
TAGS:
|
|
|
SVP
Joined: 04 May 2006
Posts: 1946
Schools: CBS, Kellogg
Followers: 10
Kudos [?]:
170
[0], given: 1
|
Are all of the numbers in a certain list of 15 numbers [#permalink]
 18 Jul 2009, 00:52
Question Stats:
54% (01:38) correct
45% (00:46) wrong based on 55 sessions
Are all of the numbers in a certain list of 15 numbers equal? (1) The sum of all the numbers in the list is 60 (2) The sum of any 3 numbers in the list is 12 OPEN DISCUSSION OF THIS QUESTION IS HERE: are-all-of-the-numbers-in-a-certain-list-of-15-numbers-equal-144144.html
_________________
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
|
|
|
SVP
Joined: 05 Jul 2006
Posts: 1564
Followers: 4
Kudos [?]:
65
[0], given: 37
|
Re: Equal number DS-find the shortcut [#permalink]
18 Jul 2009, 03:21
sondenso wrote: Are all of the numbers in a certain list of 15 numbers equal?
1. The sum of all the numbers in the list is 60
2. The sum of any 3 numbers in the list is 12 from one .....insuff from 2 the only possible way to be sure of that that they are all equall B
|
|
|
|
|
|
GMAT Instructor
Joined: 24 Jun 2008
Posts: 973
Location: Toronto
Followers: 174
Kudos [?]:
454
[0], given: 3
|
Re: Equal number DS-find the shortcut [#permalink]
18 Jul 2009, 14:34
sondenso wrote: Are all of the numbers in a certain list of 15 numbers equal?
1. The sum of all the numbers in the list is 60
2. The sum of any 3 numbers in the list is 12
Guys, can you tell me what is the logic disguided in the second stat.? Thanks! There are a few ways to look at this. One is to reverse the problem: say they aren't all equal. Write the set in increasing order: {a, b, c, ..., m, n, o}, and while some of these might be equal, we must have a < o. Well clearly then the sum of the three smallest numbers is less than the sum of the three largest, (a+b+c < m+n+o), so the sum of any three numbers in the list isn't always the same. So the only way S2 can be true is if all the numbers are equal.
_________________
Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.
Private GMAT Tutor based in Toronto
|
|
|
|
|
|
SVP
Joined: 04 May 2006
Posts: 1946
Schools: CBS, Kellogg
Followers: 10
Kudos [?]:
170
[0], given: 1
|
Re: Equal number DS-find the shortcut [#permalink]
18 Jul 2009, 18:29
IanStewart wrote: sondenso wrote: Are all of the numbers in a certain list of 15 numbers equal?
1. The sum of all the numbers in the list is 60
2. The sum of any 3 numbers in the list is 12
Guys, can you tell me what is the logic disguided in the second stat.? Thanks! There are a few ways to look at this. One is to reverse the problem: say they aren't all equal. Write the set in increasing order: {a, b, c, ..., m, n, o}, and while some of these might be equal, we must have a < o. Well clearly then the sum of the three smallest numbers is less than the sum of the three largest, (a+b+c < m+n+o), so the sum of any three numbers in the list isn't always the same. So the only way S2 can be true is if all the numbers are equal. Thanks IanStewart, I got it
_________________
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Manager
Status: Single
Joined: 05 Jun 2011
Posts: 136
Location: Shanghai China
Followers: 2
Kudos [?]:
1
[0], given: 0
|
Re: Equal number DS-find the shortcut [#permalink]
01 Aug 2011, 20:34
For B, any three number's sum is 12. So what if 2,5,5, the sum is 12 but they are not equal. Could you explain this ???? IanStewart wrote: sondenso wrote: Are all of the numbers in a certain list of 15 numbers equal?
1. The sum of all the numbers in the list is 60
2. The sum of any 3 numbers in the list is 12
Guys, can you tell me what is the logic disguided in the second stat.? Thanks! There are a few ways to look at this. One is to reverse the problem: say they aren't all equal. Write the set in increasing order: {a, b, c, ..., m, n, o}, and while some of these might be equal, we must have a < o. Well clearly then the sum of the three smallest numbers is less than the sum of the three largest, (a+b+c < m+n+o), so the sum of any three numbers in the list isn't always the same. So the only way S2 can be true is if all the numbers are equal. |
|
|
|
|
|
Intern
Joined: 04 Mar 2010
Posts: 2
Followers: 0
Kudos [?]:
0
[0], given: 0
|
Re: Equal number DS-find the shortcut [#permalink]
06 Aug 2011, 14:06
If the numbers are 2,5,5 then sum of any three numbers can't always be 12. For any three numbers to be 12 they have to be equal...hence B
|
|
|
|
|
|
Intern
Affiliations: CSCP APICS
Joined: 28 May 2011
Posts: 14
Location: Saudi Arabia
Followers: 0
Kudos [?]:
1
[0], given: 0
|
Re: Equal number DS-find the shortcut [#permalink]
07 Aug 2011, 01:00
i would say both statments together are correct.
because taking statment 1 and 2 will reveal that 60 divided by 15 is 4
so we know the set is containing the number 4
and statment 2 saying that 3 times 4 is 12
agree or disagree?
|
|
|
|
|
|
Manager
Joined: 06 Apr 2011
Posts: 77
Location: India
GMAT 1: Q V
Followers: 0
Kudos [?]:
9
[0], given: 22
|
Re: Equal number DS-find the shortcut [#permalink]
07 Aug 2011, 04:06
Quote: There are a few ways to look at this. One is to reverse the problem: say they aren't all equal. Write the set in increasing order: {a, b, c, ..., m, n, o}, and while some of these might be equal, we must have a < o. Well clearly then the sum of the three smallest numbers is less than the sum of the three largest, (a+b+c < m+n+o), so the sum of any three numbers in the list isn't always the same. So the only way S2 can be true is if all the numbers are equal. Thanks for this explanation, IanStewart.
_________________
Regards,
Asher
|
|
|
|
|
|
Intern
Joined: 05 Dec 2012
Posts: 14
GMAT 1: 680 Q44 V38
Followers: 0
Kudos [?]:
2
[0], given: 20
|
Re: Are all of the numbers in a certain list of 15 numbers [#permalink]
04 Mar 2013, 01:02
Hello !
Here is how I solved it. Please correct me if I'm wrong :
(1) : Since you don't have any contraints regarding the numbers : the fifteen numbers can all equal 4 or you can have fourteen 0 and one 60. Not sufficient.
(2) : There are several ways to reach 12 by adding 3 numbers together :
4 + 4 + 4 = 12
3 + 3 + 6 = 12
8 + 2 +2 = 12
etc...
Let's consider the ways where you have at least 2 different numbers. For examples : 3 + 3 + 6. Let's say your fifteen numbers are divided in 5 groups of numbers composed by 3, 3 and 6 :
Statements 2 tells us we can pick any 3 numbers and get 12 by adding them. If you pick one full group : 3+3+6, you get 12. But if you pick 3, 3 from one group and another 3 from another group, you get 3+3+3 = 9. It is therefore impossible to have different numbers, they all have to be the same. Sufficient.
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 12116
Followers: 1879
Kudos [?]:
10131
[0], given: 965
|
Re: Are all of the numbers in a certain list of 15 numbers [#permalink]
04 Mar 2013, 03:10
pancakeFR wrote: Hello !
Here is how I solved it. Please correct me if I'm wrong :
(1) : Since you don't have any contraints regarding the numbers : the fifteen numbers can all equal 4 or you can have fourteen 0 and one 60. Not sufficient.
(2) : There are several ways to reach 12 by adding 3 numbers together :
4 + 4 + 4 = 12
3 + 3 + 6 = 12
8 + 2 +2 = 12
etc...
Let's consider the ways where you have at least 2 different numbers. For examples : 3 + 3 + 6. Let's say your fifteen numbers are divided in 5 groups of numbers composed by 3, 3 and 6 :
Statements 2 tells us we can pick any 3 numbers and get 12 by adding them. If you pick one full group : 3+3+6, you get 12. But if you pick 3, 3 from one group and another 3 from another group, you get 3+3+3 = 9. It is therefore impossible to have different numbers, they all have to be the same. Sufficient. Are all of the numbers in a certain list of 15 numbers equal?(1) The sum of all the numbers in the list is 60. Clearly insufficient. (2) The sum of any 3 numbers in the list is 12. Since the sum of ANY 3 numbers is 12 then ALL numbers must equal to 12/3=4, because if not all the numbers equal to 4, then we could pick certain set of 3 numbers so that their sum is not 12. Sufficient. Answer: B. OPEN DISCUSSION OF THIS QUESTION IS HERE: are-all-of-the-numbers-in-a-certain-list-of-15-numbers-equal-144144.html
_________________
NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders
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. NEW!!! ,11 Mixed Questions NEW!!!, 12 Fresh Meat NEW!!!
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. NEW!!!, 11 New DS set. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
|
Re: Are all of the numbers in a certain list of 15 numbers
[#permalink]
04 Mar 2013, 03:10
|
|
|
|
|
|
|
|
|
|
|
close
