Select the choice in which the fifth quantity bears the identical mathematical relation to the sixth quantity as the second quantity does to the first, and the fourth does to the third. (Note: Arithmetic procedures must be executed on the numbers in their entirety, rather than splitting them into individual digits.)
3571 : 3615 :: 6423 : 6467 :: 9753 : ?

The correct answer is 9797.

To solve this number analogy problem, we need to determine the mathematical relationship governing the given pairs of numbers.
Let us analyze the relationship between the first and second terms, as well as the third and fourth terms.

Step 1: Analyze the first pair (3571 : 3615)
Subtract the first number from the second number to find the difference:

$3615-3571=44$

Step 2: Analyze the second pair (6423 : 6467)
Subtract the third number from the fourth number to check if the same difference applies:

$6467-6423=44$

Step 3: Apply the pattern to find the missing quantity (9753 : ?)
We can see that the rule across the pairs is to add 44 to the first quantity to get the second quantity.
Now, add 44 to the fifth quantity (9753):

$9753+44=9797$

Therefore, the sixth quantity that completes the mathematical relationship is 9797.