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

It is currently 15 Nov 2019, 10:53

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

An integer n between 1 and 99, inclusive, is to be chosen at

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

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
B
Joined: 19 May 2018
Posts: 14
GPA: 3.7
Reviews Badge
Re: An integer n between 1 and 99, inclusive, is to be chosen at  [#permalink]

Show Tags

New post 24 Aug 2018, 23:01
DensetsuNo

Why doesn't your method for these types of questions work here?

#s in sequence: 3
#s we have: 2

1 - 2/3 = 3/3 - 2/3 = 1/3

Am I just missing something here?
Intern
Intern
avatar
Joined: 21 Sep 2018
Posts: 2
Re: An integer n between 1 and 99, inclusive, is to be chosen at  [#permalink]

Show Tags

New post 29 Oct 2018, 05:11
LalaB wrote:
the required number = (if n is even )+ (if n is divisible by 3) - (if n is even and divisible by 3)=
=(49+33-16)/99=66/99=2/3


Hi, could you explain how you derived the number "if n is even and divisible by 3"? I assume you did not simple count them, am I right?

LalaB
Intern
Intern
avatar
B
Joined: 03 Apr 2017
Posts: 14
Re: An integer n between 1 and 99, inclusive, is to be chosen at  [#permalink]

Show Tags

New post 15 May 2019, 07:39
An integer n between 1 and 99, inclusive, is to be chosen at random. What is the probability that n(n+1) will be divisible by 3 ?

A) 1/9
B) 1/3
C) 1/2
D) 2/3
E) 5/6

Can someone explain to me why this method does not work?

I caught the pattern of 6 possibilities that meet the question stems criteria from 1 - 10 {2,3,5,6,8,9}.
I multiplied 6 by 10 given the range described above happens 10 times 1 -10, 11 - 20, 21 - 30, 31 - 40, and etc...
This now gives me 60/100 which simplifies to 3/5.
It seems I am missing 6 cases.

Additionally, can someone explain how they got a denominator of 99 and not 100?
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15449
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: An integer n between 1 and 99, inclusive, is to be chosen at  [#permalink]

Show Tags

New post 15 May 2019, 20:39
Hi peterpark,

To start, we're told that N is an integer from 1 to 99, inclusive, so your fraction will be out of 99 (not 100).

Based on your work, you actually spotted a pattern, but you didn't interpret it correctly. Instead of focusing on the 'first 10 terms', try focusing on 'groups of 3'...

IF....
N = 1....(1)(2) = 2 is NOT divisible by 3.
N = 2....(2)(3) = 6 IS divisible by 3
N = 3....(3)(4) = 12 IS divisible by 3.

In these first 3 examples, notice how 2 of the 3 are divisible by 3....What happens when we look at the NEXT 3 numbers....

IF....
N = 4....(4)(5) = 20 is NOT divisible by 3.
N = 5....(5)(6) = 30 IS divisible by 3
N = 6....(6)(7) = 42 IS divisible by 3.

The pattern REPEATS! This means that for ever 3 consecutive values of N, 2 of the 3 will be divisible by 3. Since we're dealing with the numbers 1 to 99, inclusive, that means we'll have 33 "sets" of 3 numbers (as shown above). Thus, 2/3 of ALL the values WILL be divisible by 3...

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Senior Manager
Senior Manager
User avatar
P
Status: Gathering chakra
Joined: 05 Feb 2018
Posts: 440
Premium Member
Re: An integer n between 1 and 99, inclusive, is to be chosen at  [#permalink]

Show Tags

New post 24 May 2019, 12:28
Given: 1<int n<99
Question: does n or n+1 have a factor of 3?

Draw a chart and find a pattern:
n | +1| div by 3?
2 | 3 | Y
3 | 4 | Y
4 | 5 | N
5 | 6 | Y
6 | 7 | Y
7 | 8 | N
8 | 9 | Y
9 |10| Y
10|11| N
...
95|96| Y
96|97| Y
97|98|N

It's a good idea to check the end because the pattern might be cut off at a different point (if n was <97).
So, we can see that 2/3 will be divisible by 3. Thus, D.
Intern
Intern
avatar
B
Joined: 07 Jun 2019
Posts: 16
Re: An integer n between 1 and 99, inclusive, is to be chosen at  [#permalink]

Show Tags

New post 19 Jul 2019, 09:21
This problem is a perfect example where the concept of both number series and probability is mixed.
n * (n+1) can be a multiple of 3 if eaither of n or (n+1) is multiple of 3..
Thus there are two parallel series..
Series 1 - 2,5,8........98 ---> Total 33 numbers
Series 2 - 3,6,9........99 ---> Total 33 numbers

Thus we can select 33 + 33 total 66 numbers out of the 99 numbers.
Hence the probability is 66/99 --- > 2/3 Option D :)
GMAT Club Bot
Re: An integer n between 1 and 99, inclusive, is to be chosen at   [#permalink] 19 Jul 2019, 09:21

Go to page   Previous    1   2   [ 26 posts ] 

Display posts from previous: Sort by

An integer n between 1 and 99, inclusive, is to be chosen at

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





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