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:

In list L above, there are 3 positive integers, where each o [#permalink]

Show Tags

19 Jul 2011, 15:45

2

This post received KUDOS

5

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

75% (hard)

Question Stats:

45% (01:49) correct
55% (01:22) wrong based on 74 sessions

HideShow timer Statistics

List L: ABC, BCA, CAB

In list L above, there are 3 positive integers, where each of A, B, and C is a different nonzero digit. Which of the following is the sum of all the positive integers that MUST be factors of the sum of the integers in list L?

In list L above, there are 3 positive integers, where each of A, B, and C is a different nonzero digit. Which of the following is the sum of all the positive integers that MUST be factors of the sum of the integers in list L?

47 114 152 161 488

Let's try to sum the 3 given numbers taking their place values into account: (100A + 10B + C) + (100B + 10C + A) + (100C + 10A + B) = 100(A + B + C) + 10(A + B + C) + (A + B + C) = 111*(A + B + C)

We know 111 = 37 * 3 so the sum will certainly have 1, 3, 37 and 111 as factors. 1 + 3 + 37 + 111 = 152

Note: How do we know that (A + B + C) will not give us a factor that we get every time? Try and take a few cases where A, B and C have different characteristics e.g. case 1: they are all odd, case 2: they are all even with no multiple of 3 etc. We want to see if there are cases where (A+B+C) has no common factors with other cases. Let's say A, B and C are all odd. 1+3+5 = 9. Factors 3 and 3 A, B and C are all even. 2+4+8 = 14. Factors 2 and 7 Other factors will depend on values of A, B and C. Hence there is no other factor which we MUST get. _________________

In list L above, there are 3 positive integers, where each of A, B, and C is a different nonzero digit. Which of the following is the sum of all the positive integers that MUST be factors of the sum of the integers in list L?

47 114 152 161 488

Let's try to sum the 3 given numbers taking their place values into account: (100A + 10B + C) + (100B + 10C + A) + (100C + 10A + B) = 100(A + B + C) + 10(A + B + C) + (A + B + C) = 111*(A + B + C)

We know 111 = 37 * 3 so the sum will certainly have 1, 3, 37 and 111 as factors. 1 + 3 + 37 + 111 = 152

Note: How do we know that (A + B + C) will not give us a factor that we get every time? Try and take a few cases where A, B and C have different characteristics e.g. case 1: they are all odd, case 2: they are all even with no multiple of 3 etc. We want to see if there are cases where (A+B+C) has no common factors with other cases. Let's say A, B and C are all odd. 1+3+5 = 9. Factors 3 and 3 A, B and C are all even. 2+4+8 = 14. Factors 2 and 7 Other factors will depend on values of A, B and C. Hence there is no other factor which we MUST get.

Karishma - 2 questions 1) How will we find out all the possible values of (A+B+C) in 2mns ? 2) A, B and C are all even. 2+4+8 = 14. Factors 2 and 7 In this case : 111*(A + B + C) should be having the following factors 1, 3, 37 and 111 and 2,7 So sum of factors = 152+2+7=161 So are we not getting 2 ambiguous answers as per the question ? Please correct me if I am wrong. _________________

Labor cost for typing this post >= Labor cost for pushing the Kudos Button http://gmatclub.com/forum/kudos-what-are-they-and-why-we-have-them-94812.html

Karishma - 2 questions 1) How will we find out all the possible values of (A+B+C) in 2mns ?

Getting 111*(A + B + C) is less than a minute job. After this, we are looking for 2 cases such that (A+B+C) share no common factor. Why? Because the question specifically says 'MUST be factors'. If I can quickly find two cases where (A+B+C) do not have any common factors, I know there is no other factor which MUST be a factor of the sum of the list. Then I will know that only the factors of 111 MUST be factors of the sum of the list. To find the two cases, I will try and take the values of A, B and C as varied as possible in the two cases. Case 1: All odd to get odd A+B+C = 1+3+5 = 9 Now in the next case I don't want 3 to be a factor. I try to find some even values 2+4+6 = 12 NO. 2+4+8 = 14 Yes. 3 is not a factor here. So there is no other number that definitely needs to be a factor of the sum of the list.

krishp84 wrote:

2) A, B and C are all even. 2+4+8 = 14. Factors 2 and 7 In this case : 111*(A + B + C) should be having the following factors 1, 3, 37 and 111 and 2,7 So sum of factors = 152+2+7=161 So are we not getting 2 ambiguous answers as per the question ? Please correct me if I am wrong.

No, in this case, there will be many other factors. 6, 21 etc... Anyway, the question says "MUST be factors". It is not NECESSARY that 2 and 7 will be factors of A+B+C (as shown above in the case where A+B+C = 9). Hence, they will not be included. _________________

Excellent posts dLo saw your blog too..!! Man .. you have got some writing skills. And Just to make an argument = You had such an amazing resume ; i am glad...

So Much $$$ Business school costs a lot. This is obvious, whether you are a full-ride scholarship student or are paying fully out-of-pocket. Aside from the (constantly rising)...

I barely remember taking decent rest in the last 60 hours. It’s been relentless with submissions, birthday celebration, exams, vacating the flat, meeting people before leaving and of...

Rishabh from Gyan one services, India had a one to one interview with me where I shared my experience at IMD till now. http://www.gyanone.com/blog/life-at-imd-interview-with-imd-mba/ ...