Find all School-related info fast with the new School-Specific MBA Forum

It is currently 28 Apr 2016, 15:56
GMAT Club Tests

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If @x is the number of distinct positive divisors of x, what is the va

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

1 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 06 Jul 2006
Posts: 295
Location: SFO Bay Area
Schools: Berkeley Haas
Followers: 2

Kudos [?]: 46 [1] , given: 0

If @x is the number of distinct positive divisors of x, what is the va [#permalink]

Show Tags

New post 28 Feb 2008, 09:23
1
This post received
KUDOS
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

62% (01:39) correct 38% (01:04) wrong based on 107 sessions

HideShow timer Statictics

If \(@x\) is the number of distinct positive divisors of \(x\), what is the value of \(@(@90)\)?

A. 3
B. 4
C. 5
D. 6
E. 7

M01-35
[Reveal] Spoiler: OA

Last edited by Bunuel on 27 Sep 2014, 05:56, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
CEO
CEO
User avatar
Joined: 29 Mar 2007
Posts: 2583
Followers: 18

Kudos [?]: 320 [0], given: 0

Re: If @x is the number of distinct positive divisors of x, what is the va [#permalink]

Show Tags

New post 28 Feb 2008, 09:30
suntaurian wrote:
\(@x\) is the number of distinct positive divisors of \(x\) . What is the value of \(@@90\) ?

* 3
* 4
* 5
* 6
* 7


D.

Factors of 90: 1,2,3,5,6,9,10,15,18,30,45,90

thus @90 = 12. @12= 6
SVP
SVP
avatar
Joined: 28 Dec 2005
Posts: 1575
Followers: 3

Kudos [?]: 117 [0], given: 2

Re: If @x is the number of distinct positive divisors of x, what is the va [#permalink]

Show Tags

New post 28 Feb 2008, 13:38
is there a quick way to find all the factors of 90, or do you just have to go through all the numbers ?
CEO
CEO
User avatar
Joined: 29 Mar 2007
Posts: 2583
Followers: 18

Kudos [?]: 320 [0], given: 0

Re: If @x is the number of distinct positive divisors of x, what is the va [#permalink]

Show Tags

New post 28 Feb 2008, 14:46
pmenon wrote:
is there a quick way to find all the factors of 90, or do you just have to go through all the numbers ?


You can find out all the prime factors. But you probably wont save too much time here. might be a better approach on bigger numbers though.


2,3,3,5 dont forget 1 at the end. multiply all the possible combinations by.

Ex/ 2*3, 3*3, etc...

I cannot come up with an actual combinatorics solution yet, but im done w/ my work for the day and got bout 20min til i go home so il try and see if i can think of something...
VP
VP
User avatar
Joined: 22 Oct 2006
Posts: 1443
Schools: Chicago Booth '11
Followers: 8

Kudos [?]: 165 [0], given: 12

Re: If @x is the number of distinct positive divisors of x, what is the va [#permalink]

Show Tags

New post 28 Feb 2008, 16:48
1
This post was
BOOKMARKED
The quick way to get # of factors is to find prime factor the number:

90 = 3^2 * 5^1 * 2^1

Then you add the number 1 to exponent and multiply exponents together.

so (2+1) (1+1) (1+1) = 3*2*2 = 12

12 is number of factors of 90

do the same to get number of factors of 12

12 = 2^2 * 3^1

(2+1) * (1+1) = 6
SVP
SVP
avatar
Joined: 28 Dec 2005
Posts: 1575
Followers: 3

Kudos [?]: 117 [0], given: 2

Re: If @x is the number of distinct positive divisors of x, what is the va [#permalink]

Show Tags

New post 28 Feb 2008, 18:37
terp26 wrote:
The quick way to get # of factors is to find prime factor the number:

90 = 3^2 * 5^1 * 2^1

Then you add the number 1 to exponent and multiply exponents together.

so (2+1) (1+1) (1+1) = 3*2*2 = 12

12 is number of factors of 90

do the same to get number of factors of 12

12 = 2^2 * 3^1

(2+1) * (1+1) = 6


right, thats the trick i remember reading somewhere on this forum !! thanks !!
Manager
Manager
avatar
Joined: 28 Sep 2007
Posts: 213
Followers: 1

Kudos [?]: 17 [0], given: 0

Reviews Badge
Re: If @x is the number of distinct positive divisors of x, what is the va [#permalink]

Show Tags

New post 29 Feb 2008, 09:13
I got D a different way. I found the primes of 90, distinct, which came out to 2,3,5. Since there are two OO, i multiplyed 3 * 2 = 6.
Did I do it correctly?
Senior Manager
Senior Manager
avatar
Joined: 08 Apr 2012
Posts: 464
Followers: 1

Kudos [?]: 36 [0], given: 58

Re: If @x is the number of distinct positive divisors of x, what is the va [#permalink]

Show Tags

New post 27 Sep 2014, 05:52
terp26 wrote:
The quick way to get # of factors is to find prime factor the number:

90 = 3^2 * 5^1 * 2^1

Then you add the number 1 to exponent and multiply exponents together.

so (2+1) (1+1) (1+1) = 3*2*2 = 12

12 is number of factors of 90

do the same to get number of factors of 12

12 = 2^2 * 3^1

(2+1) * (1+1) = 6

Is this how to calculate the number of distinct factors?
In the number 12, we have 2,3,4,6... but 6 is made up from 2 and 3, so does it count in the distinct?
what about 216? it's 6*6*6... so does 6*6 count as distinct, or do we just count 6?
I got confused here....
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 32508
Followers: 5620

Kudos [?]: 68150 [0], given: 9797

Re: If @x is the number of distinct positive divisors of x, what is the va [#permalink]

Show Tags

New post 27 Sep 2014, 06:00
Expert's post
ronr34 wrote:
terp26 wrote:
The quick way to get # of factors is to find prime factor the number:

90 = 3^2 * 5^1 * 2^1

Then you add the number 1 to exponent and multiply exponents together.

so (2+1) (1+1) (1+1) = 3*2*2 = 12

12 is number of factors of 90

do the same to get number of factors of 12

12 = 2^2 * 3^1

(2+1) * (1+1) = 6

Is this how to calculate the number of distinct factors?
In the number 12, we have 2,3,4,6... but 6 is made up from 2 and 3, so does it count in the distinct?
what about 216? it's 6*6*6... so does 6*6 count as distinct, or do we just count 6?
I got confused here....


First of all, the factors of 12 are 1, 2, 3, 4, 6, and 12. Next, how is 6 and 6 different from one another? You should count it once.

If \(@x\) is the number of distinct positive divisors of \(x\), what is the value of \(@(@90)\)?

A. 3
B. 4
C. 5
D. 6
E. 7

Finding the Number of Factors of an Integer

First make prime factorization of an integer \(n=a^p*b^q*c^r\), where \(a\), \(b\), and \(c\) are prime factors of \(n\) and \(p\), \(q\), and \(r\) are their powers.

The number of factors of \(n\) will be expressed by the formula \((p+1)(q+1)(r+1)\). NOTE: this will include 1 and \(n\) itself.

Example: Finding the number of all factors of 450: \(450=2^1*3^2*5^2\)

Total number of factors of 450 including 1 and 450 itself is \((1+1)*(2+1)*(2+1)=2*3*3=18\) factors.

Back to the original question:

The question defines \(@x\) as the number of distinct positive divisors of \(x\). Say \(@6=4\), as 6 have 4 distinct positive divisors: 1, 2, 3, 6.

Question: \(@(@90)=\)?

\(90=2*3^2*5\), which means that the number of factors of 90 is: \((1+1)(2+1)(1+1)=12\). So \(@90=12\). Next, \(@(@90)=@12\). Now, since \(12=2^2*3\), then the number of factors of 12 is: \((2+1)(1+1)=6\).

Answer: D
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1858
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 34

Kudos [?]: 1470 [0], given: 193

Re: If @x is the number of distinct positive divisors of x, what is the va [#permalink]

Show Tags

New post 29 Sep 2014, 01:08
suntaurian wrote:
If \(@x\) is the number of distinct positive divisors of \(x\), what is the value of \(@(@90)\)?

A. 3
B. 4
C. 5
D. 6
E. 7

M01-35


\(90 = 2^1 * 3^2 * 5^1\)

\(@90 = (1+1) (2+1) (1+1) = 3*4 = 12\)

\(@90 = 2^2 * 3^1\)

\(@(@90) = (2+1) (1+1) = 6\)

Answer = D
_________________

Kindly press "+1 Kudos" to appreciate :)

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 9201
Followers: 453

Kudos [?]: 114 [0], given: 0

Premium Member
Re: If @x is the number of distinct positive divisors of x, what is the va [#permalink]

Show Tags

New post 12 Apr 2016, 03:51
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 Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: If @x is the number of distinct positive divisors of x, what is the va   [#permalink] 12 Apr 2016, 03:51
    Similar topics Author Replies Last post
Similar
Topics:
8 Experts publish their posts in the topic A positive integer x has 60 divisors and 7x has 80 divisors. What is t manpreetsingh86 9 22 Jan 2015, 02:01
17 Experts publish their posts in the topic If two distinct positive divisor of 64 are randomly selected goodyear2013 10 18 Mar 2014, 16:04
3 Experts publish their posts in the topic If x is a positive number and a=√x∗x−x, gmatgambler 5 03 Feb 2014, 05:41
6 Experts publish their posts in the topic If 3|3 – x| = 7, what is the product of all the possible va nave 8 28 Mar 2013, 21:09
3 Experts publish their posts in the topic If x is an integer that has exactly three positive divisors nades09 6 16 May 2012, 20:10
Display posts from previous: Sort by

If @x is the number of distinct positive divisors of x, what is the va

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.