Last visit was: 10 Jul 2025, 13:14 It is currently 10 Jul 2025, 13:14
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
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 10 July 2025
Posts: 102,624
Own Kudos:
Given Kudos: 98,170
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,624
Kudos: 740,167
 [10]
1
Kudos
Add Kudos
9
Bookmarks
Bookmark this Post
User avatar
LevanKhukhunashvili
Joined: 13 Feb 2018
Last visit: 23 Jan 2021
Posts: 374
Own Kudos:
428
 [3]
Given Kudos: 50
GMAT 1: 640 Q48 V28
GMAT 1: 640 Q48 V28
Posts: 374
Kudos: 428
 [3]
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
rajatchopra1994
Joined: 16 Feb 2015
Last visit: 22 Jun 2024
Posts: 1,059
Own Kudos:
1,205
 [3]
Given Kudos: 30
Location: United States
Posts: 1,059
Kudos: 1,205
 [3]
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
avatar
wishmasterdj
Joined: 04 May 2016
Last visit: 25 Oct 2021
Posts: 94
Own Kudos:
Given Kudos: 10
Location: India
Schools: ISB '18 (A)
GMAT 1: 700 Q48 V37
GPA: 3.2
Schools: ISB '18 (A)
GMAT 1: 700 Q48 V37
Posts: 94
Kudos: 34
Kudos
Add Kudos
Bookmarks
Bookmark this Post
LCM question. see cyclicity between the 3 cases

the days coincide every LCM, thus every 140 days from the start they coincide. 140*2 is the only max cases with 365 days.

Thus 2/365.
User avatar
shwetakoshija
Joined: 08 Jul 2017
Last visit: 07 Jul 2025
Posts: 63
Own Kudos:
Given Kudos: 13
Expert
Expert reply
Posts: 63
Kudos: 51
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Given:
  • Aaron exercises every 4th day
  • Ben exercises every 7th day
  • Cliff exercises every 10th day

To Find: The probability that all 3 exercise on the same day, on a randomly selected day in a non-leap year (365 days). In other words, Prob(randomly selected day is a common exercise day for all 3).

Solution:
Step 1: Find the LCM (Least Common Multiple) of their schedules
We find the LCM of 4, 7, and 10 to determine how often all three exercise on the same day.
Prime factorization:
  • 4 = \(2^2\)
  • 7 = 7
  • 10 = 2 × 5
LCM = \(2^2\) × 5 × 7 = 140
So, they all exercise together once every 140 days.

Step 2: Count how many such days are in a year
Days in a non-leap year = 365
Common exercise days = Quotient upon dividing 365 by 140 = 2 days

Step 3: Compute the probability
  • Probability = Favorable days/Total days
    • = 2/365


Answer: A


Shweta Koshija
GMAT, GRE, SAT Coach for 10+ years
Moderators:
Math Expert
102624 posts
PS Forum Moderator
685 posts