• NEW! FREE Beat The GMAT Quizzes
Hundreds of Questions Highly Detailed Reporting Expert Explanations
• 7 CATs FREE!
If you earn 100 Forum Points

Engage in the Beat The GMAT forums to earn
100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## A is the set of 6-digit positive integers whose first three ##### This topic has 2 expert replies and 0 member replies ### GMAT/MBA Expert ## A is the set of 6-digit positive integers whose first three ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult A is the set of 6-digit positive integers whose first three digits are same as their last three digits, written in the same order. Which of the following numbers must be a factor of every number in the set A? A. 7 B. 11 C. 17 D. 19 E. 23 _________________ Math Revolution Finish GMAT Quant Section with 10 minutes to spare. The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Only$149 for 3 month Online Course
Free Resources-30 day online access & Diagnostic Test
Email to : info@mathrevolution.com

### GMAT/MBA Expert

GMAT Instructor
Joined
25 May 2010
Posted:
15344 messages
Followed by:
1864 members
13060
GMAT Score:
790
The GMAT is unlikely to test divisibility by 7.
An integer of the form XYZXYZ must be divisible by 7, but this issue seems irrelevant to the GMAT.
For this reason, I've replaced answer choice A with the value in red:

Max@Math Revolution wrote:
A is the set of 6-digit positive integers whose first three digits are same as their last three digits, written in the same order. Which of the following numbers must be a factor of every number in the set A?

A. 5
B. 11
C. 17
D. 19
E. 23
To determine whether an integer is divisible by 11:
1. From the left to right, sum alternating digits
2. Sum the remaining digits
3. Calculate the difference between the sums
4. If the difference is divisible by 11, so is the integer

Example: 587686
1. Sum of the blue digits = 5+7+8= 20
2. Sum of the red digits = 8+6+6 = 20
3. Difference between the sums = 20-20 = 0
4. Since the difference is divisible by 11, 587686 is divisible by 11

Each integer in set A is constructed as follows:
XYZXYZ

1. Sum of the blue digits = X+Z+Y
2. Sum of the red digits = Y+X+Z
3. Difference between the sums = (X+Z+Y) - (Y+X+Z) = 0
4. Since the difference is divisible by 11, XYZXYZ must be divisible by 11

_________________
Mitch Hunt
Private Tutor for the GMAT and GRE
GMATGuruNY@gmail.com

If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.

Available for tutoring in NYC and long-distance.
Student Review #1
Student Review #2
Student Review #3

Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.

### GMAT/MBA Expert

Legendary Member
Joined
24 Jul 2015
Posted:
2389 messages
Followed by:
32 members
19
GMAT Score:
Each number n in the set A is an integer of the form “xyz,xyz”. So,
n = 10^5x + 10^4y + 10^3z + 10^2x + 10y + z
= 10^3(10^2x + 10y + z) + (10^2x + 10y + z )
= 1000(10^2x + 10y + z) + (102x + 10y + z )
= 1001(10^2x + 10y + z )
= 11*91(10^2x + 10y + z )

Thus, n is a multiple of 11.

_________________

Math Revolution
Finish GMAT Quant Section with 10 minutes to spare.
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Only $149 for 3 month Online Course Free Resources-30 day online access & Diagnostic Test Unlimited Access to over 120 free video lessons-try it yourself Email to : info@mathrevolution.com • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

Available with Beat the GMAT members only code

• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• Award-winning private GMAT tutoring
Register now and save up to \$200

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

### Top First Responders*

1 Ian Stewart 57 first replies
2 Brent@GMATPrepNow 31 first replies
3 Jay@ManhattanReview 29 first replies
4 GMATGuruNY 20 first replies
5 ceilidh.erickson 15 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 Scott@TargetTestPrep

Target Test Prep

211 posts
2 Max@Math Revolution

Math Revolution

88 posts
3 Brent@GMATPrepNow

GMAT Prep Now Teacher

70 posts
4 Ian Stewart

GMATiX Teacher

65 posts
5 GMATGuruNY

The Princeton Review Teacher

39 posts
See More Top Beat The GMAT Experts