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

It is currently 23 May 2015, 00:52

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If an integer n is to be chosen at random from the integers

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Intern
Intern
avatar
Joined: 07 Aug 2007
Posts: 16
Followers: 0

Kudos [?]: 4 [1] , given: 0

If an integer n is to be chosen at random from the integers [#permalink] New post 11 Nov 2007, 20:09
1
This post received
KUDOS
6
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

37% (02:35) correct 63% (01:56) wrong based on 174 sessions
If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8?

A. 1/4
B. 3/8
C. 1/2
D. 5/8
E. 3/4

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-an-integer-n-is-to-be-chosen-at-random-from-the-integers-126654.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 26 Jul 2014, 08:24, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
Kaplan Promo CodeKnewton GMAT Discount CodesManhattan GMAT Discount Codes
Manager
Manager
User avatar
Joined: 04 Sep 2007
Posts: 215
Followers: 1

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

Re: If an integer n is to be chosen at random from the integers [#permalink] New post 11 Nov 2007, 20:22
2
This post was
BOOKMARKED
plaza202 wrote:
If an integer n is to be chosen at randon from the integers 1 to 96 inclusive, what is the probability that n(n+1)(n+2) will be divisible by 8?

a) 1/4
b) 3/8
c) 1/2
d) 5/8
e) 3/4.

please help .................


I will go with D 5/8

If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8?

total nos of ways in which we can choose n = 96

n(n + 1)(n + 2) will be divisible by 8?

case 1: n = odd then n+2 =odd & n+1 will be even i.e this needs get divided by 8, hence is a multiple of 8 so we have 8..96 = 12 multiples to fill the n+1 pos hence 12 ways

case 2: n is even then n+2 will be even & the product will be divisible by 24 & thus 8

so nos of values that can be used for n= 2....96 (all even nos) i.e 48 nos

total = 48+12 =60 ways

so reqd P =60/96 =5/8
Director
Director
User avatar
Joined: 26 Jul 2007
Posts: 541
Schools: Stern, McCombs, Marshall, Wharton
Followers: 5

Kudos [?]: 119 [0], given: 0

Re: If an integer n is to be chosen at random from the integers [#permalink] New post 12 Nov 2007, 09:57
The question is asking if you select n what is the probability that the the product of n and the next two consecutive numbers is divisible by 8. For that to happen n would have to be an even number because if n is even then the third number would have to be an even number greater than 2.

ex. 2,3,4

The prime roots of 2 are of course 2 and the prime roots of 4 are 2 and 2. So any 3 consecutive numbers starting with an even number will be divisible by 8(2*2*2).

There are 48 even numbers and 96 possibilites. So 48/96 = 1/2.

Ans C
Senior Manager
Senior Manager
avatar
Joined: 19 Feb 2007
Posts: 327
Followers: 1

Kudos [?]: 14 [0], given: 0

Re: If an integer n is to be chosen at random from the integers [#permalink] New post 12 Nov 2007, 10:01
gixxer1000 wrote:
The question is asking if you select n what is the probability that the the product of n and the next two consecutive numbers is divisible by 8. For that to happen n would have to be an even number because if n is even then the third number would have to be an even number greater than 2.

ex. 2,3,4

The prime roots of 2 are of course 2 and the prime roots of 4 are 2 and 2. So any 3 consecutive numbers starting with an even number will be divisible by 8(2*2*2).

There are 48 even numbers and 96 possibilites. So 48/96 = 1/2.

Ans C


What abt 7,8,9

starts with an odd integer but is still divisible by 8
Director
Director
User avatar
Joined: 25 Oct 2006
Posts: 652
Followers: 9

Kudos [?]: 240 [0], given: 6

Re: If an integer n is to be chosen at random from the integers [#permalink] New post 12 Nov 2007, 12:00
Manager
Manager
avatar
Joined: 22 Jul 2008
Posts: 154
Followers: 1

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

Re: If an integer n is to be chosen at random from the integers [#permalink] New post 26 Aug 2008, 13:27
5/8 should be the answer.
48 numbers are even for n
12 triplets have multiples of 8 in them --- this implies that those odd numbers that are in those triplets are all game, e.g., 7-8-9 ,15-16-17, 23-24-25 etc. Therefore, 7, 15, 23 would also be counted as possible n. There are 12 such nos. Therefore, the total should be 48 +12 = 60. Hence, prob. = 60/96 = 5/8
Manager
Manager
avatar
Joined: 27 Oct 2008
Posts: 185
Followers: 1

Kudos [?]: 104 [0], given: 3

Re: If an integer n is to be chosen at random from the integers [#permalink] New post 28 Sep 2009, 04:06
2
This post was
BOOKMARKED
If an integer n is to be chosen at random from the integers 1 to 96 inclusive, what is the probability that n(n+1)(n+2) will be divisible by 8?

a) 1/4
b) 3/8
c) 1/2
d) 5/8
e) 3/4.

Soln:

n(n+1)(n+2) will be divisible by 8 when n is a multiple of 2 or when (n+1) is a multiple of 8.

Thus when n is even, this whole expression will be divisible by 8.
from 1 to 96, there are 48 even integers.

Now when (n+1) is multiple by 8, we have 12 such values for (n+1)

probability that n(n+1)(n+2) will be divisible by 8
= (48 + 12)/96
= 60/96
= 5/8

Ans is D
VP
VP
avatar
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1359
Followers: 13

Kudos [?]: 163 [0], given: 10

Re: If an integer n is to be chosen at random from the integers [#permalink] New post 02 May 2011, 22:13
choosing the first 8 numbers as sample period
(1,2,3),(2,3,4),(3,4,5),(4,5,6),(5,6,7),(6,7,8),(7,8,9),(8,9,10) for n= 1 to 8 respectively.

5 of the sets are divisible by 8
hence 5/8.
_________________

Visit -- http://www.sustainable-sphere.com/
Promote Green Business,Sustainable Living and Green Earth !!

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 4922
Followers: 298

Kudos [?]: 54 [0], given: 0

Premium Member
Re: If an integer n is to be chosen at random from the integers [#permalink] New post 26 Jul 2014, 05:02
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 27465
Followers: 4308

Kudos [?]: 42132 [0], given: 5957

If an integer n is to be chosen at random from the integers [#permalink] New post 26 Jul 2014, 08:25
Expert's post
4
This post was
BOOKMARKED
plaza202 wrote:
If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8?

A. 1/4
B. 3/8
C. 1/2
D. 5/8
E. 3/4

\(n(n + 1)(n + 2)\) is divisible by 8 in two cases:

A. \(n=even\), in this case \(n+2=even\) too and as \(n\) and \(n+2\) are consecutive even integers one of them is also divisible by 4, so their product is divisible by 2*4=8;
B. \(n+1\) is itself divisible by 8;

(Notice that these two sets have no overlaps, as when \(n\) and \(n+2\) are even then \(n+1\) is odd and when \(n+1\) is divisible by 8 (so even) then \(n\) and \(n+2\) are odd.)

Now, in EACH following groups of 8 numbers: {1-8}, {9-16}, {17-24}, ..., {89-96} there are EXACTLY 5 numbers satisfying the above two condition for n, for example in {1, 2, 3, 4, 5, 6, 7, 8} n can be: 2, 4, 6, 8 (n=even), or 7 (n+1 is divisible by 8). So, the overall probability is 5/8.

Answer: D.

Similar questions to practice:
if-integer-c-is-randomly-selected-from-20-to-99-inclusive-121561.html
an-integer-n-between-1-and-99-inclusive-is-to-be-chosen-at-160998.html

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-an-integer-n-is-to-be-chosen-at-random-from-the-integers-126654.html
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

If an integer n is to be chosen at random from the integers   [#permalink] 26 Jul 2014, 08:25
    Similar topics Author Replies Last post
Similar
Topics:
2 Experts publish their posts in the topic If an integer n is to be chosen at random from the integers ankurjohar 4 30 Sep 2013, 19:59
If an integer n is to be chosen at random from the integers topkool 1 13 Nov 2006, 07:20
2 Experts publish their posts in the topic If an integer n is to be chosen at random from the integers 1 to 96, GMATCUBS21 15 23 Jun 2006, 14:39
If an integer n is to be chosen at random from the integers TOUGH GUY 12 12 May 2006, 10:53
If an integer n is to be chosen at random from the integers M8 8 25 Apr 2006, 11:24
Display posts from previous: Sort by

If an integer n is to be chosen at random from the integers

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.