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

 It is currently 20 Nov 2019, 05:14

### 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

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

# How many odd positive divisors does 9000 have?

Author Message
TAGS:

### Hide Tags

GMAT Club Legend
Joined: 12 Sep 2015
Posts: 4068
How many odd positive divisors does 9000 have?  [#permalink]

### Show Tags

12 Feb 2017, 07:53
Top Contributor
6
00:00

Difficulty:

25% (medium)

Question Stats:

68% (01:15) correct 32% (01:52) wrong based on 218 sessions

### HideShow timer Statistics

How many odd positive divisors does 9000 have?

A) 6
B) 8
C) 10
D) 12
E) 15

* kudos for all correct solutions

_________________
Test confidently with gmatprepnow.com
Intern
Joined: 09 Sep 2016
Posts: 35
Location: Georgia
GPA: 3.75
WE: Analyst (Investment Banking)
Re: How many odd positive divisors does 9000 have?  [#permalink]

### Show Tags

12 Feb 2017, 08:59
3
2
first find out prime factors of 9000

that is 3^2*5^3*2^3 . so we have 48 distinct factors. we need odd. We can only get odd by multiplying odd factors. so we must use only 5^3*3^2.
from that we can calculate odd distinct factors: (3+1)*(2+1)=12

##### General Discussion
Director
Joined: 14 Nov 2014
Posts: 593
Location: India
GMAT 1: 700 Q50 V34
GPA: 3.76
Re: How many odd positive divisors does 9000 have?  [#permalink]

### Show Tags

13 Feb 2017, 04:00
1
GMATPrepNow wrote:
How many odd positive divisors does 9000 have?

A) 6
B) 8
C) 10
D) 12
E) 15

* kudos for all correct solutions

9000 = 2^3 * 3 ^2 * 5^3
we need only odd factor ,so rejecting all the factor containing 2 as one of the factor..
odd factor - (2+1)(3+1)
12.
D.
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4835
Location: India
GPA: 3.5
Re: How many odd positive divisors does 9000 have?  [#permalink]

### Show Tags

13 Feb 2017, 09:53
1
GMATPrepNow wrote:
How many odd positive divisors does 9000 have?

A) 6
B) 8
C) 10
D) 12
E) 15

* kudos for all correct solutions

$$9000 = 2^3 * 3 ^2 * 5^3$$

The trick here is considering all the factors except 2 ( Because 2 will always create an even number )

Hence, the required number of odd Positive is ( 3 + 1 )( 2 + 1 ) = 12

_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 4068
Re: How many odd positive divisors does 9000 have?  [#permalink]

### Show Tags

12 Feb 2017, 10:02
Top Contributor
1
GMATPrepNow wrote:
How many odd positive divisors does 9000 have?

A) 6
B) 8
C) 10
D) 12
E) 15

* kudos for all correct solutions

IMPORTANT RULE
If the prime factorization of N = (p^a)(q^b)(r^c) . . . (where p, q, r, etc are different prime numbers), then N has a total of (a+1)(b+1)(c+1)(etc) positive divisors.

Example: 14000 = (2^4)(5^3)(7^1)
So, the number of positive divisors of 14000 = (4+1)(3+1)(1+1) =(5)(4)(2) = 40

9000 = (2)(2)(2)(3)(3)(5)(5)(5)
= (2³)(3²)(5³)

We want ODD divisors only, so we need to disregard the 2's, because they will give us EVEN divisors.
In other words, if we examine the divisors of (3²)(5³), we will find that ALL of them are ODD (since any product of odd integers will be odd)
The number of positive divisors of (3²)(5³) = (2+1)(3+1) =(3)(4) = 12

RELATED VIDEO FROM OUR COURSE

_________________
Test confidently with gmatprepnow.com
Non-Human User
Joined: 09 Sep 2013
Posts: 13614
Re: How many odd positive divisors does 9000 have?  [#permalink]

### Show Tags

16 Jun 2018, 23:43
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.
_________________
Re: How many odd positive divisors does 9000 have?   [#permalink] 16 Jun 2018, 23:43
Display posts from previous: Sort by