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

 It is currently 07 Jul 2015, 19:27

### 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

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

Author Message
TAGS:
Senior Manager
Joined: 11 Feb 2007
Posts: 356
Followers: 1

Kudos [?]: 47 [0], given: 0

If an integer n is to be chosen at random from the integers [#permalink]  20 Feb 2007, 06:28
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 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

Thinking naively, I thought the answer was B.

It took me more than 10 min to get to the correct answer. (The answers don't have explanations so I have to figure it out)

Would someone be able to solve this prob in 2~3 min??

I need help in number theory
Manager
Joined: 14 Apr 2003
Posts: 85
Followers: 1

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

Find out how can be n * n+1 * n +2 be divisble by 8.

I think it can be if n is divisble by 4.

With this I get the answer as A which is not OA.
Senior Manager
Joined: 19 Jul 2006
Posts: 361
Followers: 1

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

D

When n is even: n*(n+1)*(n+2) is always divisible by 8

number of even numbers = 96/2 = 48

When n is odd : n*(n+1)*(n+2) is divisible by 8,
only if (n+1) is div. by 8
96/8 = 12

Req. prob. = ( 48+12)/96 = 5/8
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5068
Location: Singapore
Followers: 23

Kudos [?]: 195 [0], given: 0

n is a multiple of 2 accounts for 48 numbers. We also need to consider cases where (n+1) is 8. So these results have n being odd of 7,15,23.....95. These gives (96-8)/8 + 1 = 12. So total 60 numbers.

Senior Manager
Joined: 11 Feb 2007
Posts: 356
Followers: 1

Kudos [?]: 47 [0], given: 0

Wow...

I hadn't thought of that. That when n is even, n(n+1)(n+2) is divisible by 8. That makes the prob so much easier!

Thanks!

Similar topics Replies Last post
Similar
Topics:
2 If an integer n is to be chosen at random from the integers 4 30 Sep 2013, 19:59
107 If an integer n is to be chosen at random from the integers 19 28 Jan 2012, 03:03
If an integer n is to be chosen at random from the integers 12 12 May 2006, 10:53
If an integer n is to be chosen at random from the integers 18 04 May 2006, 11:19
If an integer n is to be chosen at random from the integers 8 25 Apr 2006, 11:24
Display posts from previous: Sort by