It is currently 24 Jun 2017, 19:33

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Are all of the numbers in a certain list of 15 numbers

Author Message
TAGS:

Hide Tags

SVP
Joined: 04 May 2006
Posts: 1892
Schools: CBS, Kellogg
Are all of the numbers in a certain list of 15 numbers [#permalink]

Show Tags

18 Jul 2009, 00:52
5
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

69% (01:29) correct 31% (00:43) wrong based on 250 sessions

HideShow timer Statistics

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
[Reveal] Spoiler: OA

_________________
SVP
Joined: 05 Jul 2006
Posts: 1747
Re: Equal number DS-find the shortcut [#permalink]

Show Tags

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 Tutor
Joined: 24 Jun 2008
Posts: 1179
Re: Equal number DS-find the shortcut [#permalink]

Show Tags

18 Jul 2009, 14:34
1
KUDOS
Expert's post
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.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

SVP
Joined: 04 May 2006
Posts: 1892
Schools: CBS, Kellogg
Re: Equal number DS-find the shortcut [#permalink]

Show Tags

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
_________________
Manager
Status: Single
Joined: 05 Jun 2011
Posts: 124
Location: Shanghai China
Re: Equal number DS-find the shortcut [#permalink]

Show Tags

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
Re: Equal number DS-find the shortcut [#permalink]

Show Tags

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
Re: Equal number DS-find the shortcut [#permalink]

Show Tags

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
Re: Equal number DS-find the shortcut [#permalink]

Show Tags

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: 13
GMAT 1: 680 Q44 V38
Re: Are all of the numbers in a certain list of 15 numbers [#permalink]

Show Tags

04 Mar 2013, 01:02
1
KUDOS
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.
Math Expert
Joined: 02 Sep 2009
Posts: 39662
Re: Are all of the numbers in a certain list of 15 numbers [#permalink]

Show Tags

04 Mar 2013, 03:10
3
KUDOS
Expert's post
1
This post was
BOOKMARKED
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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: are-all-of-the-numbers-in-a-certain-list-of-15-numbers-equal-144144.html
_________________
Re: Are all of the numbers in a certain list of 15 numbers   [#permalink] 04 Mar 2013, 03:10
Similar topics Replies Last post
Similar
Topics:
31 Are all of the numbers in a certain list of 15 numbers equal 18 19 Feb 2017, 22:27
Are all of the numbers in a certain list of 15 numbers 4 29 Jul 2011, 02:56
Are all of the numbers in a certain list of 15 numbers equal 2 15 Apr 2011, 21:29
Are all of the numbers in a certain list of 15 numbers 7 07 Aug 2010, 01:07
6 Are all of the numbers in a certain list of 15 numbers 14 21 Feb 2016, 22:14
Display posts from previous: Sort by