Problem Solving

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

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

The correct answer is B.

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.

Therefore, B is the answer.