Last visit was: 18 Jun 2024, 14:42 It is currently 18 Jun 2024, 14:42

Close

GRE Prep 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 GRE 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
Retired Moderator
Joined: 19 Nov 2020
Posts: 326
Own Kudos [?]: 358 [1]
Given Kudos: 64
GRE 1: Q160 V152
Send PM
Intern
Intern
Joined: 12 Jul 2021
Posts: 4
Own Kudos [?]: 0 [0]
Given Kudos: 2
Send PM
Retired Moderator
Joined: 19 Nov 2020
Posts: 326
Own Kudos [?]: 358 [0]
Given Kudos: 64
GRE 1: Q160 V152
Send PM
Verbal Expert
Joined: 18 Apr 2015
Posts: 28951
Own Kudos [?]: 33733 [0]
Given Kudos: 25368
Send PM
Re: What is the probability of selecting a number that has exactly ... [#permalink]
Expert Reply
The OA MUST be posted always.

At the very least, use the feature to reveal the OA after a while, postponing the OA itself
Verbal Expert
Joined: 18 Apr 2015
Posts: 28951
Own Kudos [?]: 33733 [0]
Given Kudos: 25368
Send PM
Re: What is the probability of selecting a number that has exactly ... [#permalink]
Expert Reply
The answer is C but in A we do have 1/3

Should be 1/9
Retired Moderator
Joined: 19 Nov 2020
Posts: 326
Own Kudos [?]: 358 [0]
Given Kudos: 64
GRE 1: Q160 V152
Send PM
Re: What is the probability of selecting a number that has exactly ... [#permalink]
Carcass wrote:
The answer is C but in A we do have 1/3

Should be 1/9
or 3/9 reduced to 1/3, otherwise the question becomes selves-made)

Your answer is accepted as the correct one.
avatar
Intern
Intern
Joined: 02 Jul 2021
Posts: 4
Own Kudos [?]: 7 [1]
Given Kudos: 2
Send PM
Re: What is the probability of selecting a number that has exactly ... [#permalink]
1
Finding the right answer to this question requires us to do 2 things :
1. Identify the numbers having exactly 3 factors
2. Finding the probability that if you pick any number randomly from the list, it belongs to the one in list #1

1. We all know that any integer is divisible by 1 and itself. That means 2 factors are bare minimum to any number. So, to identify the number with 3 factors, we just need to identify the numbers from the given list that have only one factor apart from 1 and itself.
Now, since all the numbers in the given list are perfect squares, the only integers that will have 1 extra factor in addition to 1 and itself would be the prime numbers. This is because composite numbers can be factorized into 2 or more integers, so we would never have 'only' 1 additional factor for composites.
For example,
for primes,
49 = 7^2 ; factors = {1,7,49}
25 = 5^2 ; factors = {1,5,25}

and for composites,
36 = 6^2 ; factors = {1,2,4,3,9,12,18,36}

2. since we have 4 numbers out of total 9 numbers as the squares of prime numbers ( 5^2 ,7^2 , 11^2 ,13^2 ) our probability would be 4/9.
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Own Kudos [?]: 2998 [1]
Given Kudos: 172
Location: India
WE:Education (Education)
Send PM
Re: What is the probability of selecting a number that has exactly ... [#permalink]
1
motion2020 wrote:
What is the probability of selecting a number that has exactly three factors from the following set of numbers?

{25, 36, 49, 64, 81, 100, 121, 144, 169}

(A) 1/3
(B) 2/9
(C) 4/9
(D) 5/9
(E) 7/9


A number with exactly three factors must be a perfect square of a prime number

All the numbers are perfect squares, but we need to look for squares of ONLY prime numbers
i.e. \(5^2, 7^2, 11^2\), and \(13^2\)

So, the required probability = \(\frac{4}{9}\)

Hence, option C
Verbal Expert
Joined: 18 Apr 2015
Posts: 28951
Own Kudos [?]: 33733 [0]
Given Kudos: 25368
Send PM
Re: What is the probability of selecting a number that has exactly ... [#permalink]
Expert Reply
the only positive integers with exactly three factors are the squares of primes. For instance, the factors of 9 are 1, 3, and 9, and the factors of 49 are 1, 7, and 49.
User avatar
GRE Prep Club Legend
GRE Prep Club Legend
Joined: 07 Jan 2021
Posts: 4603
Own Kudos [?]: 69 [0]
Given Kudos: 0
Send PM
Re: What is the probability of selecting a number that has exactly ... [#permalink]
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep 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.
Prep Club for GRE Bot
[#permalink]
Moderators:
Moderator
1088 posts
GRE Instructor
218 posts

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