Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 22 Jul 2019, 01:11 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # a, b, and c are positive integers. If a, b, and c are assembled into

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 56332
a, b, and c are positive integers. If a, b, and c are assembled into  [#permalink]

### Show Tags 00:00

Difficulty:   95% (hard)

Question Stats: 40% (01:50) correct 60% (01:20) wrong based on 155 sessions

### HideShow timer Statistics a, b, and c are positive integers. If a, b, and c are assembled into the six-digit number abcabc, which one of the following must be a factor of abcabc?

(A) 16
(B) 13
(C) 5
(D) 3
(E) none of the above

_________________

Originally posted by Bunuel on 22 May 2016, 14:36.
Last edited by Bunuel on 23 May 2017, 05:20, edited 2 times in total.
Edited the OA.
Retired Moderator D
Joined: 13 Apr 2015
Posts: 1676
Location: India
Concentration: Strategy, General Management
GMAT 1: 200 Q1 V1 GPA: 4
WE: Analyst (Retail)
Re: a, b, and c are positive integers. If a, b, and c are assembled into  [#permalink]

### Show Tags

4
1
abcabc = $$10^5a + 10^4b + 10^3c + 10^2a + 10b + c$$
= $$(10^5 + 10^2)a + (10^4 + 10)b + (10^3 + 1)c$$
= $$10^2(10^3 + 1)a + 10(10^3 + 1)b + (10^3 + 1)c$$
= $$(10^3 + 1)(10^2a + 10b + c)$$
= $$1001 (100a + 10b + c)$$

1001 = 7 * 11 * 13

Hence the integer abcabc must be divisible by 7, 11 and 13

##### General Discussion
Board of Directors P
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4512
Location: India
GPA: 3.5
Re: a, b, and c are positive integers. If a, b, and c are assembled into  [#permalink]

### Show Tags

1
Bunuel wrote:
a, b, and c are positive integers. If a, b, and c are assembled into the six-digit number abcabc, which one of the following must be a factor of abcabc?

(A) 16
(B) 13
(C) 5
(D) 3
(E) none of the above

Plug in some values and check -

abcabc = 123123

Not divisible by 16 and 5

let abcabc = 125125

Not divisible by 3

Only option (B) and (E) is left in both the cases...

Check once more to marke (B) as correct answer

let abcabc = 135135

Again divisible by 13

So, mark answer as (B) 13

_________________
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 )
Retired Moderator V
Joined: 27 Oct 2017
Posts: 1232
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: a, b, and c are positive integers. If a, b, and c are assembled into  [#permalink]

### Show Tags

1
1
it is clearly visible that abcabc = 1001*abc
now checking with options, we get that 1001 is divisible by 13. hence B is the answer.
_________________
Intern  B
Joined: 19 Jul 2017
Posts: 43
a, b, and c are positive integers. If a, b, and c are assembled into  [#permalink]

### Show Tags

Bunuel wrote:
a, b, and c are positive integers. If a, b, and c are assembled into the six-digit number abcabc, which one of the following must be a factor of abcabc?

(A) 16
(B) 13
(C) 5
(D) 3
(E) none of the above

Remember that
any three digit number when multiplied by 1001 , the result is the same three digit number side by side
abc X 1001 = abcabc

or, abc X 13 X 11 X 7 = abcabc

which is surely divisible by 13, 11 and 7

answer is B _________________
He gives power to the faint; and to them that have no might he increases strength. Isaiah 40:29

You never FAIL until you stop TRYING
CEO  V
Joined: 12 Sep 2015
Posts: 3857
Re: a, b, and c are positive integers. If a, b, and c are assembled into  [#permalink]

### Show Tags

1
Top Contributor
Bunuel wrote:
a, b, and c are positive integers. If a, b, and c are assembled into the six-digit number abcabc, which one of the following must be a factor of abcabc?

(A) 16
(B) 13
(C) 5
(D) 3
(E) none of the above

Let's think of abc as a number (NOT a product).
So, for example, if a = 1, b = 2 and c = 5, then abc = 125, and abcabc = 125125

In this regards, abcabc = abc000 + abc
= abc(1000 + 1)
= abc(1001)
= abc(7)(11)(13)

So, abcabc must be divisible by 7, 11 and 13

Cheers,
Brent
_________________ Re: a, b, and c are positive integers. If a, b, and c are assembled into   [#permalink] 27 Nov 2018, 19:02
Display posts from previous: Sort by

# a, b, and c are positive integers. If a, b, and c are assembled into  