Given: Each child received the same number of presents
So, let's say that each child received k presents.
So, 13k = the the number of presidents that were distributed.
Since there were 11 undistributed presents, then 13k + 11 = the total number of presents that Santa brought.

In other words, n = 13k + 11
So, by plugging in different integer values of k we get different values of n.
Some possible values of n are: 24, 37, 50, 63, 76, 89, 102....

If n = 24, we get:
QUANTITY A: 24 gifts divided among 14 children leaves a remainder of 10 gifts
QUANTITY B: 24 gifts divided among 15 children leaves a remainder of 9 gifts
Quantity A is greater.

If n = 89, we get:
QUANTITY A: 89 gifts divided among 14 children leaves a remainder of 5 gifts
QUANTITY B: 89 gifts divided among 15 children leaves a remainder of 14 gifts
Quantity B is greater.

Answer: D

I set up a table and starred the higher remainder.

# presents | Remainder 14 children | Remainder w/15 children
1*13+11 = 24 | 10* | 9
2*13+11 = 37 | 9* | 7
3*13+11 = 50 | 8* | 5
noticing a pattern, I guessed if I counted several up, the 15 children column would cycle around past zero and get high while the 14 children column would continue going down, and this proved correct
.
.
6*13+11=89 | 5 | 14*


Since the higher remainder switched columns, the answer is D.

A rather simple way to solve this by taking two conditions
First assume he had 13 gifts for each making it 24 (13 given 11 left) so A answer is correct
Now is the cheeky part I have used to solve.
What is santa did not give any present and carried 11 home?
Condition All orphans gets the same number of presents -- technically yes (0)
So even if you add 1 or 100 it wont matter cause none of them will get a present
So D