Last visit was: 14 Jul 2024, 11:03 It is currently 14 Jul 2024, 11:03
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
SORT BY:
Date
Tags:
Show Tags
Hide Tags
GMAT Club Legend
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21835
Own Kudos [?]: 11778 [2]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Send PM
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11470
Own Kudos [?]: 34310 [3]
Given Kudos: 322
Send PM
CEO
CEO
Joined: 07 Mar 2019
Posts: 2617
Own Kudos [?]: 1865 [2]
Given Kudos: 763
Location: India
WE:Sales (Energy and Utilities)
Send PM
GMAT Club Legend
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21835
Own Kudos [?]: 11778 [0]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Send PM
Re: A standard set of billiard balls includes 16 balls: 15 numbered balls [#permalink]
Expert Reply
OFFICIAL EXPLANATION

Hi All,

We're told that a standard set of billiard balls includes 16 balls: 15 numbered balls – with each of the numbers 1 to 15, inclusive, appearing on one ball each – and 1 white ball which is not numbered. If an additional ball from another standard set of billiard balls is accidentally included with an existing standard set of 16 balls, then what is the probability that the extra ball is NOT numbered with a multiple of 2 or 3. While this question might be a bit 'wordy', the 'math' behind this Probability question isn't that difficult - and by simply 'mapping out' what is described, we can get to the correct answer without too much work.

We have 16 balls: fifteen are numbered 1-15, inclusive and one is un-numbered. To answer the question, we have to determine what fraction of those balls are NOT numbered with a multiple of 2 or a multiple of 3. Listing out the options is a fairly easy way to find what we're looking for.

Multiples of 2: 2, 4, 6, 8, 10, 12, 14
Multiples of 3: 3, 6, 9, 12, 15

Notice how the values 6 and 12 appear in BOTH lists; we should not count those numbers twice though (just once each). At this point, we can either calculate the fraction of balls in this combined list... and subtract that fraction from the number 1... or we can list out the balls that fit what we're looking for...

The list of balls that fits what we are looking for is: 1, 5, 7, 11, 13 and the un-numbered ball --> 6 total balls out of 16 total --> 6/16 = 3/8

Final Answer:

GMAT assassins aren't born, they're made,
Rich
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 33966
Own Kudos [?]: 851 [0]
Given Kudos: 0
Send PM
Re: A standard set of billiard balls includes 16 balls: 15 numbered balls [#permalink]
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.
GMAT Club Bot
Re: A standard set of billiard balls includes 16 balls: 15 numbered balls [#permalink]
Moderator:
Math Expert
94342 posts