Last visit was: 25 Apr 2026, 11:32 It is currently 25 Apr 2026, 11:32
Home
Messages
Tests
Schools
Events
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
CounterSniper
User avatar
Joined: 20 Feb 2015
Last visit: 14 Apr 2023
Posts: 611
Own Kudos:
859
 [18]
Given Kudos: 74
Concentration: Strategy, General Management
Posts: 611
Kudos: 859
 [18]
On this year's Westchester basketball team, the players are all either Updated on: 03 Jul 2019, 04:41
Originally posted by CounterSniper on 05 Sep 2018, 09:43.
Last edited by Sajjad1994 on 03 Jul 2019, 04:41, edited 1 time in total.
Formatted Properly and added source.
2
Kudos
Add Kudos
16
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

45% (medium)

Question Stats:

71% (02:23) correct 29% (02:27) wrong based on 458 sessions

History

Date
Time
Result
Not Attempted Yet
On this year's Westchester basketball team, the players are all either 5,7,or 11 years of age. If the product of ages of the players on the team is 18,865 , then what is the probability that a randomly selected team member will not be 7


A \(\frac{3}{7}\)

B \(\frac{2}{5}\)

C \(\frac{16}{37}\)

D \(\frac{3}{5}\)

E \(\frac{49}{55}\)
ShowHide Answer
Official Answer
B
User avatar
jaysonbeatty12
User avatar
Joined: 14 Aug 2018
Last visit: 14 Dec 2023
Posts: 18
Own Kudos:
71
 [4]
Given Kudos: 3
Location: United States (WA)
Schools: Cambridge Judge (A)
GMAT 1: 670 Q43 V40
GMAT 2: 750 Q47 V47
GPA: 3.3
WE:Education (Education)
Schools: Cambridge Judge (A)
GMAT 2: 750 Q47 V47
Posts: 18
Kudos: 71
 [4]
On this year's Westchester basketball team, the players are all either Updated on: 06 Sep 2018, 08:42
Originally posted by jaysonbeatty12 on 05 Sep 2018, 10:18.
Last edited by jaysonbeatty12 on 06 Sep 2018, 08:42, edited 1 time in total.
4
Kudos
Add Kudos
Bookmarks
Bookmark this Post
This is a time consuming but not impossible question. Here is how I would solve this question.

Understand the Question - Behind this word problem lurks a pretty standard Number Properties / Primes and divisibility question. The core skill being tested is the ability to prime factor a number, in this case 18,865. The good news is that they tell you the three factors - 5, 7 and 11. One of these numbers, 5, is easy to factor out. One of these numbers, 11, has a little remembered rule. Lastly, one of these numbers, 7, has a super complicated algorithm that is better off ignored. So, a simple restatement of this question is "How many factors of 5, 7, and 11 are in 18,865?"

Understand the Answer Choices - The denominator of the whichever answer choice is correct will at maximum be equal to the total number of 5s, 7s, and 11s in 18,865 - the numerator will be the number of 5s and 11s. This is from the probability equation = (total number of desired outcomes)/(total number of outcomes). This makes answer choices C and E pretty unlikely as the denominators are way too high. Eliminate.

Plan - what's the fastest way to attack this question? Well, you know by the question that there is at least one 5, 7, and 11. So, dividing by these numbers is a reasonable way to start. I would divide by 5 or 11 first as these are faster. If you happen to be slow at division, guessing among A, B, and D is also reasonable.

Solve - 18865 / 5 = 3,773. No more factors of 5 (Do you know why?)(Does not end in 0 or 5)
3,773 / 11 = 343 No more factors of 11 (Do you know why?) (the outside numbers do not add to the inside number)
343 / 7 = 49
49 = 7 * 7

So the prime factorization of 18,865 is 5*7*7*7*11
Eliminate A as 7 will not be the denominator
Desired outcomes = 2 (one 5 and one 11)
Total Outcomes = 5
B is correct

Jayson Beatty
Indigo Prep
User avatar
CounterSniper
User avatar
Joined: 20 Feb 2015
Last visit: 14 Apr 2023
Posts: 611
Own Kudos:
859
 [1]
Given Kudos: 74
Concentration: Strategy, General Management
Posts: 611
Kudos: 859
 [1]
On this year's Westchester basketball team, the players are all either 06 Sep 2018, 00:09
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
jaysonbeatty12
This is a time consuming but not impossible question. Here is how I would solve this question.

Understand the Question - Behind this word problem lurks a pretty standard Number Properties / Primes and divisibility question. The core skill being tested is the ability to prime factor a number, in this case 18,865. The good news is that they tell you the three factors - 5, 7 and 11. One of these numbers, 5, is easy to factor out. One of these numbers, 11, has a little remembered rule. Lastly, one of these numbers, 7, has a super complicated algorithm that is better off ignored. So, a simple restatement of this question is "How many factors of 5, 7, and 11 are in 18,865?"

Understand the Answer Choices - The denominator of the whichever answer choice is correct will at maximum be equal to the total number of 5s, 7s, and 11s in 18,865 - the numerator will be the number of 5s and 11s. This is from the probability equation = (total number of desired outcomes)/(total number of outcomes). This makes answer choices C and E pretty unlikely as the denominators are way too high. Eliminate.

Plan - what's the fastest way to attack this question? Well, you know by the question that there is at least one 5, 7, and 11. So, dividing by these numbers is a reasonable way to start. I would divide by 5 or 7 first as these are faster. If you happen to be slow at division, guessing among A, B, and D is also reasonable.

Solve - 18865 / 5 = 3,773. No more factors of 5 (Do you know why?)(Does not end in 0 or 5)
3,773 / 11 = 343 No more factors of 11 (Do you know why?) (the outside numbers do not add to the inside number)
343 / 7 = 49
49 = 7 * 7

So the prime factorization of 18,865 is 5*7*7*7*11
Eliminate A as 7 will not be the denominator
Desired outcomes = 2 (one 5 and one 7)
Total Outcomes = 5
B is correct

Jayson Beatty
Indigo Prep
Show more


The solution is correct , there is however a small typo , it should be 11 instead of 7
User avatar
fskilnik
User avatar
Joined: 12 Oct 2010
Last visit: 03 Jan 2025
Posts: 883
Own Kudos:
1,887
 [3]
Given Kudos: 57
Status:GMATH founder
Expert
Expert reply
Posts: 883
Kudos: 1,887
 [3]
On this year's Westchester basketball team, the players are all either 06 Sep 2018, 09:57
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
CounterSniper
On this year's Westchester basketball team, the players are all either 5,7,or 11 years of age. If the product of ages of the players on the team is 18,865 , then what is the probability that a randomly selected team member will not be 7?

A \(\frac{3}{7}\)
B \(\frac{2}{5}\)
C \(\frac{16}{37}\)
D \(\frac{3}{5}\)
E \(\frac{49}{55}\)
Show more
\(? = P\left( {{\text{choose}}\,{\text{at}}\,{\text{random}}\,\,{\text{not}}\,{\text{a}}\,\,7{\text{y}}\,{\text{player}}} \right)\)

There are only 2 real "problems" here:

1. To factorize 18,865 quickly to get:
\(18865 = 5 \cdot {7^3} \cdot 11\)

2. To know how many players are in a basketball team: 5 (*) so that we may conclude that:
(*) https://www.google.com.br/search?q=numb ... e&ie=UTF-8

There are one 5y , three 7y and one 11y players.

Answer: 2/5.

To factorize 18,865 I suggest:

(a) Obviously divisible by 5, to get (in less than a minute):

\(\frac{{18865}}{5} = \frac{{18 \cdot 1000 + 500 + 300 + 50 + 15}}{5} = 18 \cdot 200 + 100 + 60 + 10 + 3\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,18865 = 5 \cdot 3773\)

(b) 3773 is OBVIOUSLY divisible by 11 (because 3-7+7-3 = 0) :: check this: https://www.math.hmc.edu/funfacts/ffiles/10013.5.shtml

Hence:

\(\frac{{3773}}{{11}} = \frac{{3300 + 33 + 44 \cdot 10}}{{11}} = 300 + 3 + 40 = 343\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,3773 = 11 \cdot 343\,\,\,\)

(c) Now the hard part (how would we imagine 343 is divisible by 7?)... but the examiner gave us the hint(only 5y, 11y... and 7y players!):

Hence:

\(\frac{{343}}{7} = \frac{{350 - 7}}{7} = 49\,\,\,\,\,\, \Rightarrow \,\,\,\,\,3773 = 7 \cdot 49 = {7^3}\,\,\)

Finally, let´s group all together:

\(18865 = 5 \cdot 11 \cdot {7^3}\)


This powerful breaking numbers technique is part of our method, by the way!


This solution follows the notations and rationale taught in the GMATH method.

Regards,
fskilnik.
avatar
shardul171
avatar
Joined: 01 Jan 2017
Last visit: 30 Jan 2023
Posts: 5
Given Kudos: 30
Posts: 5
Kudos: 0
On this year's Westchester basketball team, the players are all either 11 Sep 2018, 07:56
Kudos
Add Kudos
Bookmarks
Bookmark this Post
This is a time consuming but not impossible question. Here is how I would solve this question.

Understand the Question - Behind this word problem lurks a pretty standard Number Properties / Primes and divisibility question. The core skill being tested is the ability to prime factor a number, in this case 18,865. The good news is that they tell you the three factors - 5, 7 and 11. One of these numbers, 5, is easy to factor out. One of these numbers, 11, has a little remembered rule. Lastly, one of these numbers, 7, has a super complicated algorithm that is better off ignored. So, a simple restatement of this question is "How many factors of 5, 7, and 11 are in 18,865?"

Understand the Answer Choices - The denominator of the whichever answer choice is correct will at maximum be equal to the total number of 5s, 7s, and 11s in 18,865 - the numerator will be the number of 5s and 11s. This is from the probability equation = (total number of desired outcomes)/(total number of outcomes). This makes answer choices C and E pretty unlikely as the denominators are way too high. Eliminate.

Plan - what's the fastest way to attack this question? Well, you know by the question that there is at least one 5, 7, and 11. So, dividing by these numbers is a reasonable way to start. I would divide by 5 or 11 first as these are faster. If you happen to be slow at division, guessing among A, B, and D is also reasonable.

Solve - 18865 / 5 = 3,773. No more factors of 5 (Do you know why?)(Does not end in 0 or 5)
3,773 / 11 = 343 No more factors of 11 (Do you know why?) (the outside numbers do not add to the inside number)
343 / 7 = 49
49 = 7 * 7

So the prime factorization of 18,865 is 5*7*7*7*11
Eliminate A as 7 will not be the denominator
Desired outcomes = 2 (one 5 and one 11)
Total Outcomes = 5
B is correct

Jayson Beatty
Indigo Prep

I understood the factorization part. I did not understand the part about why a certain number can/cannot be in the numerator.
User avatar
CounterSniper
User avatar
Joined: 20 Feb 2015
Last visit: 14 Apr 2023
Posts: 611
Own Kudos:
859
Given Kudos: 74
Concentration: Strategy, General Management
Posts: 611
Kudos: 859
On this year's Westchester basketball team, the players are all either 11 Sep 2018, 10:06
Kudos
Add Kudos
Bookmarks
Bookmark this Post
shardul171
This is a time consuming but not impossible question. Here is how I would solve this question.

Understand the Question - Behind this word problem lurks a pretty standard Number Properties / Primes and divisibility question. The core skill being tested is the ability to prime factor a number, in this case 18,865. The good news is that they tell you the three factors - 5, 7 and 11. One of these numbers, 5, is easy to factor out. One of these numbers, 11, has a little remembered rule. Lastly, one of these numbers, 7, has a super complicated algorithm that is better off ignored. So, a simple restatement of this question is "How many factors of 5, 7, and 11 are in 18,865?"

Understand the Answer Choices - The denominator of the whichever answer choice is correct will at maximum be equal to the total number of 5s, 7s, and 11s in 18,865 - the numerator will be the number of 5s and 11s. This is from the probability equation = (total number of desired outcomes)/(total number of outcomes). This makes answer choices C and E pretty unlikely as the denominators are way too high. Eliminate.

Plan - what's the fastest way to attack this question? Well, you know by the question that there is at least one 5, 7, and 11. So, dividing by these numbers is a reasonable way to start. I would divide by 5 or 11 first as these are faster. If you happen to be slow at division, guessing among A, B, and D is also reasonable.

Solve - 18865 / 5 = 3,773. No more factors of 5 (Do you know why?)(Does not end in 0 or 5)
3,773 / 11 = 343 No more factors of 11 (Do you know why?) (the outside numbers do not add to the inside number)
343 / 7 = 49
49 = 7 * 7

So the prime factorization of 18,865 is 5*7*7*7*11
Eliminate A as 7 will not be the denominator
Desired outcomes = 2 (one 5 and one 11)
Total Outcomes = 5
B is correct

Jayson Beatty
Indigo Prep

I understood the factorization part. I did not understand the part about why a certain number can/cannot be in the numerator.
Show more


Once we are done with factorization
we are left with finding the probability

what do we need ?
probability that a randomly selected team member will not be 7

total possible outcomes = number of (prime factors of 18865=5*7*7*7*11) = 5
required outcome = total possible outcomes - number of 7's =2

p(not being 7) = 2/5
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 25 Apr 2026
Posts: 22,286
Own Kudos:
26,537
 [3]
Given Kudos: 302
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: 22,286
Kudos: 26,537
 [3]
On this year's Westchester basketball team, the players are all either 04 Mar 2020, 06:21
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
CounterSniper
On this year's Westchester basketball team, the players are all either 5,7,or 11 years of age. If the product of ages of the players on the team is 18,865 , then what is the probability that a randomly selected team member will not be 7


A \(\frac{3}{7}\)

B \(\frac{2}{5}\)

C \(\frac{16}{37}\)

D \(\frac{3}{5}\)

E \(\frac{49}{55}\)
Show more

Let’s prime factorize 18,865

18,865 = 5 x 3773 = 5 x 11 x 343 = 5 x 11 x 7 x 7 x 7

We see that there are a total of 5 players, and 3 of them are 7 years old, and 2 of them are not. So the probability that a randomly selected player will not be 7 is 2/5.

Answer: B
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,985
Own Kudos:
1,118
Posts: 38,985
Kudos: 1,118
On this year's Westchester basketball team, the players are all either 29 Oct 2025, 09:35
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109830 posts
Krunaal
Tuck School Moderator
852 posts