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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
If the three unique positive digits A,B, and C are arranged in all pos
[#permalink]
09 Jul 2021, 08:30
09 Jul 2021, 08:30
Expert Reply
4
Bookmarks
00:00
Question Stats:
81% (02:20) correct
18% (01:54) wrong based on 11 sessions
Hide Show timer Statistics
If the three unique positive digits A,B, and C are arranged in all possible sequences (ABC,ACB,BAC,ETC....),then the sum of all the resulting three -digit integers must be divisible by each of the following EXCEPT?
(A) 2
(B) 3
(C) 6
(D) 11
(E) 37
(A) 2
(B) 3
(C) 6
(D) 11
(E) 37
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Given Kudos: 172
Location: India
WE:Education (Education)
Re: If the three unique positive digits A,B, and C are arranged in all pos
[#permalink]
10 Jul 2021, 22:36
10 Jul 2021, 22:36
2
GeminiHeat wrote:
If the three unique positive digits A,B, and C are arranged in all possible sequences (ABC,ACB,BAC,ETC....),then the sum of all the resulting three -digit integers must be divisible by each of the following EXCEPT?
(A) 2
(B) 3
(C) 6
(D) 11
(E) 37
(A) 2
(B) 3
(C) 6
(D) 11
(E) 37
Remember: Any 3 digit number \(xyz\) can be written as \(100x + 10y + z\)
Now, ABC can be arranged in 3! ways = 6 ways
i.e. ABC, ACB, BAC, BCA, CAB, CBA
ABC = 100A + 10B + C
ACB = 100A + 10C + B
BAC = 100B + 10A + C
BCA = 100B + 10C + A
CAB = 100C + 10A + B
CBA = 100C + 10B + A
Sum = 222A + 222B + 222C = 222(A + B + C) = (2)(3)(37)(A + B + C)
Possible factors = 1, 2, 3, 6, 37, 74, 111, 222
Hence, option D
Re: If the three unique positive digits A,B, and C are arranged in all pos
[#permalink]
07 Mar 2024, 04:19
07 Mar 2024, 04:19
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.
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.
