GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 17 Jan 2019, 07:12

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
Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
  • The winning strategy for a high GRE score

     January 17, 2019

     January 17, 2019

     08:00 AM PST

     09:00 AM PST

    Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL.
  • Free GMAT Strategy Webinar

     January 19, 2019

     January 19, 2019

     07:00 AM PST

     09:00 AM PST

    Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

Distinct Factors

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

 
Manager
Manager
avatar
S
Joined: 17 Jul 2017
Posts: 94
CAT Tests
Distinct Factors  [#permalink]

Show Tags

New post 28 Oct 2018, 01:43
Can anyone help me understand the difference between factors and distinct factors?

https://gmatclub.com/forum/if-k-is-a-po ... 58398.html

in this question,
i proceeded like:

20k=2^2*5*k
since k is prime it will always have 2 factors
so answer must be
(2+1)(1+1)(1+1)
last 1+1 is for 2 factors of k
Where is my reasoning wrong?

What is the differnece between factors of a number and distinct factors ?

12 has 2*2*3=2^2*3
i.e (2+1)*(1+1)=6 factors
Are these distinct ?
1,2,3,4,6,12 are all distinct only.So what are non distinct factors?
Director
Director
User avatar
P
Joined: 18 Jul 2018
Posts: 565
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Premium Member Reviews Badge CAT Tests
Re: Distinct Factors  [#permalink]

Show Tags

New post 28 Oct 2018, 02:10
vanam52923 wrote:
Can anyone help me understand the difference between factors and distinct factors?

https://gmatclub.com/forum/if-k-is-a-po ... 58398.html

in this question,
i proceeded like:

20k=2^2*5*k
since k is prime it will always have 2 factors
so answer must be
(2+1)(1+1)(1+1)
last 1+1 is for 2 factors of k
Where is my reasoning wrong?

What is the differnece between factors of a number and distinct factors ?

12 has 2*2*3=2^2*3
i.e (2+1)*(1+1)=6 factors
Are these distinct ?
1,2,3,4,6,12 are all distinct only.So what are non distinct factors?


Hi,

For the first question. k is a prime. 20 = \(2^2\)\(5^1\). If k = 2 then 20K = \(2^3\)\(5^1\) = 4*2 = 8. or k be 5 then no. of factors would be 8. for other primes it'll be 3*2*2 = 12.

For distinct factors. consider a number 12. factors are (2,2,3) only 2 and 3 are distinct here.

Hope it helps
_________________

If you are not badly hurt, you don't learn. If you don't learn, you don't grow. If you don't grow, you don't live. If you don't live, you don't know your worth. If you don't know your worth, then what's the point?

Veritas Prep GMAT Instructor
User avatar
D
Joined: 16 Oct 2010
Posts: 8787
Location: Pune, India
Re: Distinct Factors  [#permalink]

Show Tags

New post 29 Oct 2018, 01:06
vanam52923 wrote:
Can anyone help me understand the difference between factors and distinct factors?

https://gmatclub.com/forum/if-k-is-a-po ... 58398.html

in this question,
i proceeded like:

20k=2^2*5*k
since k is prime it will always have 2 factors
so answer must be
(2+1)(1+1)(1+1)
last 1+1 is for 2 factors of k
Where is my reasoning wrong?

What is the differnece between factors of a number and distinct factors ?

12 has 2*2*3=2^2*3
i.e (2+1)*(1+1)=6 factors
Are these distinct ?
1,2,3,4,6,12 are all distinct only.So what are non distinct factors?


I have explained the problem with the first question on the link. k must be a prime number so it could be 2 or 5 too. In that case, the number of factors is different.

Total number of factors of the number are the distinct factors as you showed here:
12 has 2*2*3=2^2*3
i.e (2+1)*(1+1)=6 factors
Are these distinct ?
1,2,3,4,6,12 are all distinct only.

The concept of distinct/non distinct rarely comes into play and if it does, it does only when we are talking about prime factors.
12 = 2^2 * 3
Some may say that 12 has 3 prime factors: 2, 2 and 3
But usually when the question asks for number of prime factors, it means the number of distinct prime factors. Just for clarity, the question may mention "what are the number of distinct prime factors of 12?" There are two: 2 and 5
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

Intern
Intern
avatar
Joined: 10 May 2018
Posts: 34
Re: Distinct Factors  [#permalink]

Show Tags

New post 30 Oct 2018, 12:33
vanam52923 wrote:
Can anyone help me understand the difference between factors and distinct factors?

https://gmatclub.com/forum/if-k-is-a-po ... 58398.html

in this question,
i proceeded like:

20k=2^2*5*k
since k is prime it will always have 2 factors
so answer must be
(2+1)(1+1)(1+1)
last 1+1 is for 2 factors of k
Where is my reasoning wrong?

What is the differnece between factors of a number and distinct factors ?

12 has 2*2*3=2^2*3
i.e (2+1)*(1+1)=6 factors
Are these distinct ?
1,2,3,4,6,12 are all distinct only.So what are non distinct factors?


Regarding your query of factors versus distinct factors, as far as I know, it is totally fine to assume, every factor as distinct factor whenever a question asks you the number of factors. Of course, repeating the factors will lead to awkward, non unique answers.

So whether the question says find number of factors of 20 or number of unique factors of 20, answer shall remain 6.
Manhattan Prep Instructor
User avatar
G
Joined: 04 Dec 2015
Posts: 669
GMAT 1: 790 Q51 V49
GRE 1: Q170 V170
Re: Distinct Factors  [#permalink]

Show Tags

New post 05 Nov 2018, 12:51
vanam52923 wrote:
Can anyone help me understand the difference between factors and distinct factors?

https://gmatclub.com/forum/if-k-is-a-po ... 58398.html

in this question,
i proceeded like:

20k=2^2*5*k
since k is prime it will always have 2 factors
so answer must be
(2+1)(1+1)(1+1)
last 1+1 is for 2 factors of k
Where is my reasoning wrong?

What is the differnece between factors of a number and distinct factors ?

12 has 2*2*3=2^2*3
i.e (2+1)*(1+1)=6 factors
Are these distinct ?
1,2,3,4,6,12 are all distinct only.So what are non distinct factors?


First, you got the problem wrong for a reason that has nothing to do with distinct factors!

Here's why you missed it. The formula you're using is completely correct. In fact, if k = 7 or if k = 11, your reasoning is 100% right. (2+1)(1+1)(1+1) = 12 factors, and that's the number of factors in 20(7) = 140. It's also the number of factors of 20(11) = 220.

The problem is, k could equal 2 or 5. If that's true, your formula doesn't work. If k = 2, then you'd actually be finding the number of factors of (2^3 * 5), which is a different formula: (3+1)(1+1) = 8 factors.

Or if k = 5, you'd be finding the factors of (2^2 * 5^2), which is (2+1)(2+1) = 9 factors.

So, the number of factors isn't always 12. It's only 12 if k is a different prime.

I'll also answer your question about distinct factors below!
There are actually three different terms, not just two:

1. prime factors (or 'prime factorization')
2. distinct prime factors
3. factors

The prime factors of a number are the primes you get when you 'break down' that number as much as possible. For instance:

12 = 2 * 2 * 3

Prime factors are 2, 2, and 3.

The distinct prime factors of a number are just the unique prime factors, without any repeats.

The distinct prime factors of 12 are 2 and 3.

The factors of a number don't have to be prime at all! If a problem just says 'factors', it's talking about all of the positive integers that can be divided evenly into that number. Not just the primes!

The factors of 12 are 1, 2, 3, 4, 6, and 12.

If a problem says 'different factors', this is what the problem means. It doesn't technically have to say 'different factors'; if it just says 'factors', you should usually assume that it's looking for all of the factors of the number, like 1, 2, 3, 4, 6, 12, and that you shouldn't skip any or count any twice.
_________________

Image

Chelsey Cooley | Manhattan Prep | Seattle and Online

My latest GMAT blog posts | Suggestions for blog articles are always welcome!

GMAT Club Bot
Re: Distinct Factors &nbs [#permalink] 05 Nov 2018, 12:51
Display posts from previous: Sort by

Distinct Factors

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.