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: 2508
Given Kudos: 1053
GPA: 3.39
If x represents the sum of all the positive three-digit numbers that c
[#permalink]
04 Apr 2021, 22:51
04 Apr 2021, 22:51
2
Expert Reply
16
Bookmarks
00:00
Question Stats:
49% (02:21) correct
50% (02:07) wrong based on 73 sessions
Hide Show timer Statistics
If x represents the sum of all the positive three-digit numbers that can be constructed using each of the distinct nonzero digits a, b, and c exactly once, what is the largest integer by which x must be divisible?
(A) 3
(B) 6
(C) 11
(D) 22
(E) 222
(A) 3
(B) 6
(C) 11
(D) 22
(E) 222
If x represents the sum of all the positive three-digit numbers that c
[#permalink]
13 Oct 2021, 21:28
13 Oct 2021, 21:28
10
2
Bookmarks
If we consider the non-zero distinct numbers a,b,c - total 6 3-digit numbers can be constructed.
abc
acb
bca
bac
cba
cab
We can write abc as 100a + 10b +c. If we write every number in this format and add all these 6 numbers we get 200(a+b+c) + 20(a+b+c) + 2(a+b+c).
Now we take (a+b+c) as common and rewrite it as (a+b+c)(200 + 20 + 2) i.e (a+b+c)(222).
Hence it is conspicuous that 222 is the largest number we can divide with. So the ans is E
abc
acb
bca
bac
cba
cab
We can write abc as 100a + 10b +c. If we write every number in this format and add all these 6 numbers we get 200(a+b+c) + 20(a+b+c) + 2(a+b+c).
Now we take (a+b+c) as common and rewrite it as (a+b+c)(200 + 20 + 2) i.e (a+b+c)(222).
Hence it is conspicuous that 222 is the largest number we can divide with. So the ans is E
General Discussion
If x represents the sum of all the positive three-digit numbers that c
[#permalink]
06 Apr 2021, 10:35
06 Apr 2021, 10:35
4
Quote:
what is the largest integer by which x must be divisible
The answer choices are factors of x. Let's find the minimum value that x can have since the factor must be for any value of x.
Quote:
constructed using each of the distinct nonzero digits a, b, and c exactly once
Basically, there can be 6 such integers that can be constructed. To find the minimum sum of these integers, let's assume least values that a, b, and c can have: a=1, b=2, and c=3.
Next step is to arrange these digits, construct integers, and add to produce x.
1 2 3
1 3 2
2 1 3
2 3 1
3 1 2
3 2 1
Add up. x = 1332. This must be divisible by 3. Try dividing by 6, you get 222 as quotient. So, 222 must also divide x completely. We are looking for the largest divisor among the answer choices. Hence, E is the correct answer.
