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

 It is currently 24 May 2019, 22:19

### 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

# If k is a positive integer and the greatest common divisor of k and 45

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

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 55271
If k is a positive integer and the greatest common divisor of k and 45  [#permalink]

### Show Tags

16 Nov 2016, 04:55
1
4
00:00

Difficulty:

45% (medium)

Question Stats:

70% (01:56) correct 30% (01:56) wrong based on 138 sessions

### HideShow timer Statistics

If k is a positive integer and the greatest common divisor of k and 45 is 15, then the greatest common divisor of k and 900 may be any of the following EXCEPT

A. 15
B. 45
C. 60
D. 150
E. 300

_________________
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14198
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If k is a positive integer and the greatest common divisor of k and 45  [#permalink]

### Show Tags

14 Mar 2018, 19:41
3
2
Hi All,

This question is ultimately about "prime factorization" (the idea that a positive integer is either prime or can be "broken down" into the product of a bunch of primes).

We're told that the greatest common divisor of K and 45 is 15.

Since 45 = (3)(3)(5)
and 15 = (3)(5)
then K, at the minimum is (3)(5). It might have OTHER prime factors as well, BUT it can't have another 3. Here's why…

If K = (2)(3)(5) = 30, then the greatest common divisor of 30 and 45 is 15, so the above statement holds true.
If K = (3)(3)(5) = 45, then the greatest common divisor of 45 and 45 is 45, and the above statement doesn't make sense.

We're asked which of the following could be the greatest common divisor of K and 900 EXCEPT….

900 = (3)(3)(2)(2)(5)(5)
K = (3)(5)(possibly some other primes other than 3)

We can now use the answer choices to eliminate the possibilities:

A = 15 = (3)(5) IS possible
B = 45 = (3)(3)(5) is NOT possible
C = 60 = (3)(5)(2)(2) IS possible
D = 150 = (3)(5)(2)(5) IS possible
E = 300 = (3)(5)(2)(2)(5) IS possible

GMAT assassins aren't born, they're made,
Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/
##### General Discussion
Senior Manager
Joined: 06 Jun 2016
Posts: 258
Location: India
Concentration: Operations, Strategy
Schools: ISB '18 (D)
GMAT 1: 600 Q49 V23
GMAT 2: 680 Q49 V34
GPA: 3.9
If k is a positive integer and the greatest common divisor of k and 45  [#permalink]

### Show Tags

16 Nov 2016, 06:26
Bunuel wrote:
If k is a positive integer and the greatest common divisor of k and 45 is 15, then the greatest common divisor of k and 900 may be any of the following EXCEPT

A. 15
B. 45
C. 60
D. 150
E. 300

IMO B

A. 15== GCD(15,45)= 15 GCD(15,900)= 15
B. 45== GCD(45,45)= 45 GCD(45,900)= 45 Violates the given GCD(k,45)=15
C. 60== GCD(60,45)= 15 GCD(60,900)= 60
D. 150== GCD(150,45)= 15 GCD(150,900)=150
E. 300== GCD(300,45)= 15 GCD(300,900)= 300
If k is a positive integer and the greatest common divisor of k and 45   [#permalink] 16 Nov 2016, 06:26
Display posts from previous: Sort by

# If k is a positive integer and the greatest common divisor of k and 45

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

 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®.