Last visit was: 10 Jul 2025, 20:36 It is currently 10 Jul 2025, 20:36
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
User avatar
siddharthsinha123
Joined: 10 Jul 2016
Last visit: 01 Apr 2019
Posts: 32
Own Kudos:
218
 [23]
Given Kudos: 85
Products:
Posts: 32
Kudos: 218
 [23]
2
Kudos
Add Kudos
21
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 10 Jul 2025
Posts: 11,294
Own Kudos:
41,667
 [8]
Given Kudos: 333
Status:Math and DI Expert
Products:
Expert
Expert reply
Posts: 11,294
Kudos: 41,667
 [8]
3
Kudos
Add Kudos
5
Bookmarks
Bookmark this Post
User avatar
BillyZ
User avatar
Current Student
Joined: 14 Nov 2016
Last visit: 03 May 2025
Posts: 1,147
Own Kudos:
21,909
 [7]
Given Kudos: 926
Location: Malaysia
Concentration: General Management, Strategy
GMAT 1: 750 Q51 V40 (Online)
GPA: 3.53
Products:
4
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
General Discussion
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 10 Jul 2025
Posts: 102,631
Own Kudos:
740,220
 [4]
Given Kudos: 98,170
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,631
Kudos: 740,220
 [4]
1
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 10 Jul 2025
Posts: 21,070
Own Kudos:
26,130
 [1]
Given Kudos: 296
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 21,070
Kudos: 26,130
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
siddharthsinha123
n is an integer from 1 to 50, what is the probability that n(n+1) is not divisible by 4?

A. 12/25
B. 13/25
C. 14/25
D. 15/25
E. 16/25

We can use the following equation:

1 = P(n(n+1) is divisible by 4) + P(n(n+1) is NOT divisible by 4)

Thus:

P(n(n+1) is NOT divisible by 4) = 1 - P(n(n+1) is divisible by 4)

Let’s determine the probability that n(n+1) is divisible by 4. If n(n+1) is divisible by 4, then either n is divisible by 4 or n +1 is divisible by 4. Calculating the number of values of n divisible by 4 is the same as calculating the number of multiples of 4 between 1 and 50 inclusive. To calculate this, we can use this formula:

(largest multiple of 4 - smallest multiple of 4)/4 + 1

(48 - 4)/4 + 1

44/4 + 1 = 11 + 1 = 12

Thus, there are 12 multiples of 4 between 1 and 50 inclusive. That is, n can be any one of these 12 multiples of 4 so that n(n + 1) will be divisible by 4.

Similarly, if (n + 1) is a multiple of 4, n(n + 1) also will be divisible by 4. Since we know that there are 12 values of n that are multiples of 4, there must be another 12 values of n such that (n + 1) is a multiple of 4. Let’s expand on this idea:

When n = 3, n + 1 = 4, and thus n(n+1) is a multiple of 4.

When n = 23, n + 1 = 24, and thus n(n+1) is a multiple of 4.

When n = 47, n + 1 = 48, and thus n(n+1) is a multiple of 4.

We can see that there are 12 values of n that are multiples of 4, and 12 more values of n for (n + 1) to be a multiple of 4. Since there are 50 total integers from 1 to 50, inclusive, the probability of selecting a value of n so that n(n+1) is a multiple of 4 is:

24/50 = 12/25

Thus, the probability that n(n+1) IS NOT a multiple of 4 is 1 - 12/25 = 13/25.

Answer: B
User avatar
Fdambro294
Joined: 10 Jul 2019
Last visit: 06 Apr 2025
Posts: 1,353
Own Kudos:
Given Kudos: 1,658
Posts: 1,353
Kudos: 705
Kudos
Add Kudos
Bookmarks
Bookmark this Post
(N) (N + 1) will be divisible by 4 if the integer N that is picked is either of the form:


N = 4k

or

N = 4k - 1


Find how many multiples of 4 there are from 1 to 50

Then double that amount because for each corresponding multiple there will be one value that is (-1) below that multiple

Ex: (3 and 4) ——- (7 and 8) ........ (47 and 48)


Count = (48 - 4)/4 + (1)

Count = 12

12 * 2 = 24 integers N such that (N) (N + 1) will be divisible by 4

Thus:

50 integers - (24 multiples of 4) =

26 Numbers that will NOT make (N) (N + 1) divisible by 4

Probability = 26/50 = 13/25

13/25

Posted from my mobile device
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 37,380
Own Kudos:
Posts: 37,380
Kudos: 1,010
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Moderators:
Math Expert
102631 posts
PS Forum Moderator
686 posts