GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 17 Nov 2018, 18:23

Close

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
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.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • FREE Quant Workshop by e-GMAT!

     November 18, 2018

     November 18, 2018

     07:00 AM PST

     09:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score. November 18th, 7 AM PST
  • How to QUICKLY Solve GMAT Questions - GMAT Club Chat

     November 20, 2018

     November 20, 2018

     09:00 AM PST

     10:00 AM PST

    The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.

What is the probability of n(n+1)(n+2) being evenly divisible by 8? 1

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Intern
Intern
avatar
B
Joined: 30 Jan 2018
Posts: 17
Re: What is the probability of n(n+1)(n+2) being evenly divisible by 8? 1  [#permalink]

Show Tags

New post 10 Sep 2018, 02:48
GmatDaddy wrote:

To define a probability you need a sample space or the number of all possible outcomes.
Statemetn 2 does not define if n is integer or not, hence we can not count the total no of possible cases.

Thank you.
But I still doubt option A because sample space is not clear in option A too.
for eg. If I take first 8 positive intgers as my sample space then probability will be = 3/8
And if I take first 9 positive intgers as my sample space then probability will be = 3/9=1/3

Thanks in advance
Anurag Jain
[/quote][/quote]
GMATH Teacher
User avatar
G
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 477
Re: What is the probability of n(n+1)(n+2) being evenly divisible by 8? 1  [#permalink]

Show Tags

New post 10 Sep 2018, 10:33
jainanurag470 wrote:
But I still doubt option A because sample space is not clear in option A too.
for eg. If I take first 8 positive intgers as my sample space then probability will be = 3/8
And if I take first 9 positive intgers as my sample space then probability will be = 3/9=1/3

Thanks in advance
Anurag Jain


Hi, Anurag!

In the question stem pre-statements combined with statement (1), the sample space is the whole Z, in other words, the set of integers.

We are dealing with the product of ANY three consecutive integers, including negative ones, by the way!

As I mentioned, the proper way of calculating the probability asked is NOT in GMAT´s scope, but the "informal argument"
(interesting and PERFECT when (1+2) is considered) was presented in my solution.

Regards,
fskilnik.
_________________

Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or GMATH.com.br (Portuguese version)
Course release PROMO : finish our test drive till 30/Nov with (at least) 50 correct answers out of 92 (12-questions Mock included) to gain a 50% discount!

Intern
Intern
avatar
B
Joined: 30 Jan 2018
Posts: 17
Re: What is the probability of n(n+1)(n+2) being evenly divisible by 8? 1  [#permalink]

Show Tags

New post 11 Sep 2018, 22:22
fskilnik wrote:
jainanurag470 wrote:

Thanks in advance
Anurag Jain


Hi, Anurag!

In the question stem pre-statements combined with statement (1), the sample space is the whole Z, in other words, the set of integers.

We are dealing with the product of ANY three consecutive integers, including negative ones, by the way!

As I mentioned, the proper way of calculating the probability asked is NOT in GMAT´s scope, but the "informal argument"
(interesting and PERFECT when (1+2) is considered) was presented in my solution.

Regards,
fskilnik.



Hi fskilink,

First of all thank you for the solution.
I am convinced that solution is C but OA is A.
And with your provided solution I am not convinced that solution is A.

Thanks in advance
Anurag Jain
GMATH Teacher
User avatar
G
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 477
Re: What is the probability of n(n+1)(n+2) being evenly divisible by 8? 1  [#permalink]

Show Tags

New post 12 Sep 2018, 05:14
1
jainanurag470 wrote:
Hi fskilink,

First of all thank you for the solution.
I am convinced that solution is C but OA is A.
And with your provided solution I am not convinced that solution is A.

Thanks in advance
Anurag Jain


Dear Anurag,

Thank you for your contact and your strong desire to understand. That´s exactly what makes us stronger/wiser!

First of all, I believe I understand the reason you believe the answer is (C). You think something like this:

(1) If 1 <= N <= 2 , we have one answer (1/2) , but if 1 <= N <= 3 we have another answer (1/3), correct?

The rationale IS correct, but we must understand the statement (1) without being "contaminated" by the idea presented in (2)...

More explicitly: we look for the cases in which the expression n(n+1)(n+2) is divisible by 8, and using statement (1) only, we just know that n is an integer. Hence our question turns out to be:

Is n(n+1)(n+2) divisible by 8, when n is an integer? (Only considering the question stem pre-statements and statement (1) , both combined.)

Now I guess you understand that the expression n(n+1)(n+2) "runs" over infinite possibilities, because we must analyse ALL cases involved, some of them are the following:

when n = -200, we have to evaluate -200*(-199)*(-198)
when n = 0, we have to evaluate 0*1*2
when n = 1029 we have to evaluate 1029*1030*1031

In other words, we must ask ourselves the following: for EACH integer n, putting the value of the product n(n+1)(n+2) written in a small paper inside a box, (three small papers are with the numbers shown in red above) , do you understand we have infinite small papers inside the box?
(I didn´t say all numbers are different, because (-2)(-1)(0) equals (-1)(0)(1) for instance!)

If you understand that, great, because now you understand the question in blue: what is the probability that randomly choosing one small paper, you will get a number divisible by 8?

The answer IS possible to obtain, and it will be 5/8. The problem is to justify that using formal math. But, as I mentioned, this is out-of-our-scope!

I hope now things are clear!

Regards,
fskilnik.

P.S.: try my test-drive, please! Reason: students who want to understand things deeply and "as sub-product" to perform in REALLY higher-level are EXACTLY GMATH method profile...
_________________

Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or GMATH.com.br (Portuguese version)
Course release PROMO : finish our test drive till 30/Nov with (at least) 50 correct answers out of 92 (12-questions Mock included) to gain a 50% discount!

GMAT Club Bot
Re: What is the probability of n(n+1)(n+2) being evenly divisible by 8? 1 &nbs [#permalink] 12 Sep 2018, 05:14

Go to page   Previous    1   2   [ 24 posts ] 

Display posts from previous: Sort by

What is the probability of n(n+1)(n+2) being evenly divisible by 8? 1

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.