Processing math: 100%

Last visit was: 07 Apr 2025, 21:20 It is currently 07 Apr 2025, 21:20
Decision Tracker
My Rewards
New comers' posts
New posts
Unanswered

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.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel
PREVIOUS TOPIC
NEXT TOPIC

k is a positive integer and 225 and 216 are both divisors of

Tags :
Find Similar Topics  About  Add a Tag

Show Tags
Hide Tags

User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 31489
Own Kudos [?]: 37683 [10]
Given Kudos: 26234
Send PM
k is a positive integer and 225 and 216 are both divisors of [#permalink] New post   Updated on: 02 Feb 2020, 13:29
5
1
Expert Reply
4
Bookmarks
00:00
A
B
C
D
E

Question Stats:

68% (02:04) correct 31% (01:58) wrong based on 297 sessions

Show timer Statistics

k is a positive integer and 225 and 216 are both divisors of k. If k=2a×3b×5c, where a, b and are positive integers, what is the least possible value of a+b+c?

(A) 4

(B) 5

(C) 6

(D) 7

(E) 8


Kudos for the right answer and explanation
ShowHide Answer
Official Answer
E

Originally posted by Carcass on 02 Feb 2020, 09:43.
Last edited by Carcass on 02 Feb 2020, 13:29, edited 1 time in total.
Updated
Most Helpful Community Reply
User avatar
sujoykrdatta
GRE Instructor
Joined: 19 Jan 2020
Status:Entrepreneur | GMAT, GRE, CAT, SAT, ACT coach & mentor | Founder @CUBIX | Edu-consulting | Content creator
Posts: 117
Own Kudos [?]: 272 [11]
Given Kudos: 0
GPA: 3.72
Send PM
Re: k is a positive integer and 225 and 216 are both divisors of [#permalink] New post   02 Feb 2020, 11:19
9
2
Bookmarks
Carcass wrote:
k is a positive integer and 225 and 216 are both divisors of k. If k−2a×3b×5c, where a, b and are positive integers, what is the least possible value of a+b+c?

(A) 4

(B) 5

(C) 6

(D) 7

(E) 8


Kudos for the right answer and explanation



225=52∗32 and 216=23∗33

Since 225 and 216 are both divisors of k, it must be that k is a multiple of the LCM of 225 and 216

=> k = Multiple of 52∗33∗23

Since k=2a×3b×5c, and we need the minimum values of a,b,c, we take:

=> k = 52∗33∗23 = 5c∗3b∗2a

=> a=3, b=3, c=2

=> a+b+c=8

Answer E
General Discussion
avatar
rubytuesdays21
Intern
Intern
Joined: 16 Jul 2021
Posts: 17
Own Kudos [?]: 18 [3]
Given Kudos: 22
Send PM
Re: k is a positive integer and 225 and 216 are both divisors of [#permalink] New post   26 Jul 2021, 06:00
3
Easiest way to solve this question is to do the prime factorization of both 225 and 216.
225: (3)^2 (5)^1
216:(3)^3 * (2)^3 * (5)^2

The least common multiple is therefore a = 3, b =3, c = 2.
Finally, 3 + 3 + 2 = 8.
B.O.L
User avatar
P
Ks1859
Retired Moderator
Joined: 09 Jan 2021
Posts: 576
Own Kudos [?]: 852 [3]
Given Kudos: 194
GRE 1: Q167 V156
GPA: 4
WE:Analyst (Investment Banking)
Send PM
Reviews Badge
Re: k is a positive integer and 225 and 216 are both divisors of [#permalink] New post   26 Jul 2021, 06:12
3
rubytuesdays21 wrote:
Easiest way to solve this question is to do the prime factorization of both 225 and 216.
225: (3)^2 (5)^1
216:(3)^3 * (2)^3 * (5)^2

The least common multiple is therefore a = 3, b =3, c = 2.
Finally, 3 + 3 + 2 = 8.
B.O.L


Hi rubytuesdays21

Great explanation!

Out of curiosity what is B.O.L?

Regards
S

Posted from my mobile device
avatar
rubytuesdays21
Intern
Intern
Joined: 16 Jul 2021
Posts: 17
Own Kudos [?]: 18 [1]
Given Kudos: 22
Send PM
Re: k is a positive integer and 225 and 216 are both divisors of [#permalink] New post   26 Jul 2021, 06:24
1
Best of luck! Thank you :D Ks1859
User avatar
bumpbot
GRE Prep Club Legend
GRE Prep Club Legend
Joined: 07 Jan 2021
Posts: 5234
Own Kudos [?]: 77 [0]
Given Kudos: 0
Send PM
Re: k is a positive integer and 225 and 216 are both divisors of [#permalink] New post   03 Jan 2025, 05:48
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
gmatclubot
Re: k is a positive integer and 225 and 216 are both divisors of [#permalink]
03 Jan 2025, 05:48
Moderators:
adewale223
GRE Instructor
108 posts
bronaugust
GRE Forum Moderator
37 posts
BrushMyQuant
Moderator
1131 posts
VibhuAnurag
GRE Instructor
234 posts

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

Main navigation

Partners

GRE Resources

www.ets.org/gre | About | Terms and Conditions and Privacy Policy | Prep Club for GRE Rules | Contact