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 Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Are all of the numbers in a certain list of 15 numbers [#permalink]

Show Tags

03 Aug 2010, 13:36

00:00

A

B

C

D

E

Difficulty:

35% (medium)

Question Stats:

82% (01:36) correct
18% (02:05) wrong based on 11 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.

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. _________________

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

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.

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...

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. _________________

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

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

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.

This is the kickoff for my 2016-2017 application season. After a summer of introspect and debate I have decided to relaunch my b-school application journey. Why would anyone want...

Check out this awesome article about Anderson on Poets Quants, http://poetsandquants.com/2015/01/02/uclas-anderson-school-morphs-into-a-friendly-tech-hub/ . Anderson is a great place! Sorry for the lack of updates recently. I...

“Oh! Looks like your passport expires soon” – these were the first words at the airport in London I remember last Friday. Shocked that I might not be...