Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 05 May 2015, 07:12

### 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:
Manager
Joined: 09 Feb 2010
Posts: 71
Followers: 0

Kudos [?]: 33 [0], given: 4

Are all of the numbers in a certain list of 15 numbers [#permalink]  03 Aug 2010, 12:36
00:00

Difficulty:

45% (medium)

Question Stats:

80% (01:37) correct 20% (02:05) wrong based on 10 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.
[Reveal] Spoiler: OA
Manager
Joined: 09 Feb 2010
Posts: 71
Followers: 0

Kudos [?]: 33 [0], given: 4

Re: DS QUESTION-DIFFICULT [#permalink]  03 Aug 2010, 12:36
Can someone explain this.
GMAT Instructor
Joined: 24 Jun 2008
Posts: 978
Location: Toronto
Followers: 281

Kudos [?]: 799 [0], given: 3

Re: DS QUESTION-DIFFICULT [#permalink]  03 Aug 2010, 12:47
zest4mba 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.

I think I've posted different solutions to this question elsewhere, but one way to look at Statement 2:

let a, b, c and d be four random numbers from the list. From Statement 2, since the sum of *any* three numbers is 12, we know

a + b + c = 12
d + b + c = 12

and if you subtract the second equation from the first, you find that a - d = 0, so a = d. Since a and d are just randomly chosen numbers from the list, we could do the same thing for any of the numbers in our list, and so they all need to be equal. Since Statement 1 is not sufficient, the answer is B.
_________________

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

Manager
Joined: 06 Oct 2009
Posts: 98
Location: Mexico
Concentration: Entrepreneurship, Finance
GMAT 1: 610 Q42 V34
GPA: 3.85
WE: Sales (Commercial Banking)
Followers: 1

Kudos [?]: 51 [0], given: 3

Re: DS QUESTION-DIFFICULT [#permalink]  03 Aug 2010, 14:42
This was my approach

You have 15 numbers that add up to 60. Factoring 60 you get that the only combination of two factors that have 15 must have 4 on them. There is no other number than 4 that repeated 15 times add up to 60

1) You know that you need a 4 for the statement to be sufficient, but as it can be any other number or fraction is not sufficient.

2) Any combination of 3 numbers of the list add 12. You can see that 4 is your lucky number, therefore answer is B.

Hope Im right!
Senior Manager
Joined: 25 Feb 2010
Posts: 476
Followers: 4

Kudos [?]: 50 [0], given: 9

Re: DS QUESTION-DIFFICULT [#permalink]  04 Aug 2010, 19:09
IanStewart wrote:
zest4mba 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.

I think I've posted different solutions to this question elsewhere, but one way to look at Statement 2:

let a, b, c and d be four random numbers from the list. From Statement 2, since the sum of *any* three numbers is 12, we know

a + b + c = 12
d + b + c = 12

and if you subtract the second equation from the first, you find that a - d = 0, so a = d. Since a and d are just randomly chosen numbers from the list, we could do the same thing for any of the numbers in our list, and so they all need to be equal. Since Statement 1 is not sufficient, the answer is B.

I still didn't get you....

There are 15 different numbers, but we took only 4 for our example.

what if a + b+ c = 12
and d + e+ f = 12
_________________

GGG (Gym / GMAT / Girl) -- Be Serious

Its your duty to post OA afterwards; some one must be waiting for that...

GMAT Instructor
Joined: 24 Jun 2008
Posts: 978
Location: Toronto
Followers: 281

Kudos [?]: 799 [0], given: 3

Re: DS QUESTION-DIFFICULT [#permalink]  04 Aug 2010, 21:28
onedayill wrote:
IanStewart wrote:
zest4mba 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.

I think I've posted different solutions to this question elsewhere, but one way to look at Statement 2:

let a, b, c and d be four random numbers from the list. From Statement 2, since the sum of *any* three numbers is 12, we know

a + b + c = 12
d + b + c = 12

and if you subtract the second equation from the first, you find that a - d = 0, so a = d. Since a and d are just randomly chosen numbers from the list, we could do the same thing for any of the numbers in our list, and so they all need to be equal. Since Statement 1 is not sufficient, the answer is B.

I still didn't get you....

There are 15 different numbers, but we took only 4 for our example.

what if a + b+ c = 12
and d + e+ f = 12

Say our list is:

a, b, c, d, e, f, g, h, i, j, k, l, m, n, o

I just took the first four numbers and proved a=d. There's nothing special about the first four numbers in the list; I can use the same logic to prove that any two numbers are equal here. For example, if I want to prove that b=d, we have

b + c + a = 12
d + c + a = 12

Subtract the second equation from the first:

b - d = 0
b = d

So now we know that b = d. Since we saw that a=d as well, a, b and d are all equal. We can do this for all the letters in the list, so they all must be 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

Senior Manager
Status: Fighting on
Joined: 14 Mar 2010
Posts: 318
Schools: UCLA (R1 interview-WL), UNC(R2--interview-ding) Oxford(R2-Admit), Kelley (R2- Admit ), McCombs(R2)
WE 1: SE - 1
WE 2: Engineer - 3
Followers: 4

Kudos [?]: 22 [0], given: 3

Re: DS QUESTION-DIFFICULT [#permalink]  05 Aug 2010, 09:23
Question type : yes/no

Given to us that a list contains 15 numbers

statement 1) sum of all numbers is 15.

The statement does not answer the question whether the all numbers are the same as all numbers can be zero except
one which might be 60.

INSUFFICIENT

statement 2) The sum of any 3 numbers in the list is 12.

so this basically mean x1+x2+x10 = 12
x3+x4+x15 = 12 ... so on

so for the sum to be twelve for any numbers in the List, the numbers must be 4 each.
This answers our original question of if all the numbers are equal or not.
SUFFICIENT
Manager
Joined: 18 Feb 2010
Posts: 174
Schools: ISB
Followers: 7

Kudos [?]: 134 [0], given: 0

Re: DS QUESTION-DIFFICULT [#permalink]  07 Aug 2010, 00:07
zest4mba 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.

Choice A ...

0 0 0 0 0 0 0....60 (14 zeros)
4 4 4 4 4 4 4 (fifteen 4's)

Insufficient...

Choice B...

only posibility is fifteen 4s to add upto 12 on selecting 3 numbers

So choice B is the answer....
_________________

CONSIDER AWARDING KUDOS IF MY POST HELPS !!!

Re: DS QUESTION-DIFFICULT   [#permalink] 07 Aug 2010, 00:07
Similar topics Replies Last post
Similar
Topics:
1 Are all of the numbers in a certain list of 15 numbers 5 31 Jul 2011, 03:10
Are all of the numbers in a certain list of 15 numbers 3 22 Jul 2009, 11:19
Are all of the numbers in a certain list of 15 numbers 4 17 Feb 2008, 16:15
Are all of the numbers in a certain list of 15 numbers 5 09 Oct 2005, 04:25
Are all of the numbers in a certain list of 15 numbers 1 01 Jun 2005, 18:10
Display posts from previous: Sort by