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

 It is currently 18 Dec 2014, 06:33

### 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:
Intern
Joined: 11 May 2004
Posts: 49
Location: USA
Followers: 0

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

If an integer n is to be chosen at random from the integers [#permalink]  23 Jun 2006, 14:39
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
VP
Joined: 02 Jun 2006
Posts: 1267
Followers: 2

Kudos [?]: 40 [0], given: 0

Messed up this ... deleting.

Last edited by haas_mba07 on 23 Jun 2006, 15:29, edited 2 times in total.
Intern
Joined: 11 May 2004
Posts: 49
Location: USA
Followers: 0

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

i dont get it, if one of the ways of an odd # is even why cant it be divisible by odd, i mean a number like 7 would be divisible by 8. N+1=8 hence thats at least one odd # tat can be divisible by 8, so i dont understand why its 48.....and cant be any odd #'s
VP
Joined: 02 Jun 2006
Posts: 1267
Followers: 2

Kudos [?]: 40 [0], given: 0

You are right..

If I pick 7 then 7 x 8 x 9 will also be divisible by 8....

GMATCUBS21 wrote:
i dont get it, if one of the ways of an odd # is even why cant it be divisible by odd, i mean a number like 7 would be divisible by 8. N+1=8 hence thats at least one odd # tat can be divisible by 8, so i dont understand why its 48.....and cant be any odd #'s
Intern
Joined: 11 May 2004
Posts: 49
Location: USA
Followers: 0

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

well u said n is even, and i just told u that n can also be odd, so how do u get 48, please explain......im not as good at math as u...so how do u do this one....its not that u do all even's because i just showed u 7 works....so how do u do it
VP
Joined: 02 Jun 2006
Posts: 1267
Followers: 2

Kudos [?]: 40 [0], given: 0

I think I finally got the right one.. although my first answer 1/2 still remains the same.

Between 1-10 : you have 5 numbers you can pick to get nx (n+1) x (n+2) divisible by 8 : {2, 4, 6, 7, 8}

Continuing this from 10-20 : 5 more and so on.

In total from 1-90 you have 9x5 = 45 numbers.

Between 91-96 you can pick 3 more to get the satisfying condition: 92, 94, 96

Therefore in total you can pick : 48
Probability = 48/96 = 1/2
Senior Manager
Joined: 22 May 2006
Posts: 375
Location: Rancho Palos Verdes
Followers: 1

Kudos [?]: 22 [0], given: 0

Is N(N+1)(N+2) multiple of 8?

1 2 3
2 3 4
3 4 5
.....
7 8 9

When N is even number, "N(N+1)(N+2)" is always multiple of 8.
Thus probability = 48/96 = 1/2

When N is odd number and N+1 is multiple of 8, N(N+1)(N+2) is multiple of 8
Thus, probability = 12/96 = 1/8

1/2+1/8 = 5/8
or
(48+12)/96 = 5/8

Ans is D.
_________________

The only thing that matters is what you believe.

Intern
Joined: 14 May 2006
Posts: 32
Followers: 0

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

I will go with answer b 3/8 [#permalink]  22 Jul 2006, 10:32
If I pick any no from the set 7, 8, 9, 14, 15, 16 ..............94,95,96. then I can satisfy the condition n(n+1)(n+2) divisibel by 8. Such 36 no I can pick so probability is 36/96 So the answer is 3/8.

Pravin
Intern
Joined: 14 May 2006
Posts: 32
Followers: 0

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

Sorry [#permalink]  22 Jul 2006, 10:35
The set should be 6,7,8, 14,15,16.....94,95,96. Ans is same. I commit typing mistake.

Pravin
Intern
Joined: 14 May 2006
Posts: 32
Followers: 0

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

I got in GMAT trap. [#permalink]  22 Jul 2006, 11:07
I think I am right now. One need to pick up even integer. If 'n' is even and not divisible by 4 then n+2 will be divisible by 4 so n*(n+2) will be divisible by 8. There are total 48 even integers and ans should 1/2. I think I am right now. I need to be careful about trap.

Pravin
Senior Manager
Joined: 22 May 2006
Posts: 375
Location: Rancho Palos Verdes
Followers: 1

Kudos [?]: 22 [0], given: 0

Re: I got in GMAT trap. [#permalink]  22 Jul 2006, 11:16
I think I am right now. One need to pick up even integer. If 'n' is even and not divisible by 4 then n+2 will be divisible by 4 so n*(n+2) will be divisible by 8. There are total 48 even integers and ans should 1/2. I think I am right now. I need to be careful about trap.

Pravin

When n is
n n+1
7 8
15 16
....
95 96.. total 12.

48+12 = 60 possible outcome. Thus 5/8 => D
_________________

The only thing that matters is what you believe.

Director
Joined: 28 Dec 2005
Posts: 758
Followers: 1

Kudos [?]: 8 [0], given: 0

Re: GMAT TEST #4 [#permalink]  22 Jul 2006, 16:09
GMATCUBS21 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

D IMO. If n>=2 then for any even n, n(n+1)(n+2) is divisible by 2 and 4, and therefore by 8.

Further, every 8th number will be divisible by 8
CEO
Joined: 20 Nov 2005
Posts: 2913
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
Followers: 17

Kudos [?]: 93 [0], given: 0

5/8

For all N = even N(N+1)(N+2) will be divisible by 8: Total = 48
For all N+1 = multiple of 8, N(N+1)(N+2) will be divisible by 8: Total = 12

Prob = 60/96 = 5/8
_________________

SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

SVP
Joined: 30 Mar 2006
Posts: 1739
Followers: 1

Kudos [?]: 37 [0], given: 0

For all even numbers N . n(n+1)(n+2) is divisible by 8. Even numbers = 48

For all odd numbers
From 1-10 - 1 odd number
2- 10 - 1 odd number

90-96 - 1

hence total odd numbers = 12

Total numbers = 60

Probabiltiy = 60/96 = 5/8
Similar topics Replies Last post
Similar
Topics:
If an integer n is to be chosen at random from the integers 7 11 Sep 2007, 12:18
2 If an integer n is to be chosen at random from the integer 1 5 02 Sep 2007, 00:08
If an integer n is to be chosen at random from the integers 9 21 Jun 2007, 19:47
If an integer n is to be chosen at random from the integers 1 13 Nov 2006, 07:20
1 If an integer n is to be chosen at random from the integers 4 05 Aug 2006, 07:06
Display posts from previous: Sort by