You are given a math word problem and you are supposed to make use of mathematical concepts like probability, combinatorics, linear equations, sequences/series, or simple operators like addition, subtraction, division, or multiplication to answer the given question. Choose the best option from the 5 given options and report that option.

[Q]: Question: For any positive integer Y, the sum of the first Y positive integers equals Y(Y+1)/2 . If X and Y are positive integers and X > Y, what is the sum of all the integers between X and Y, inclusive?

 Option A:  X(X+1

 Option B:  X(X+1

 Option C:  X(X+1

 Option D:  X(X+1

 Option E:  X(Y+1
[A]: Option B


[Q]: Question: To save money, Arkadelphia Cream Cheese will reduce each dimension of its rectangular box container (which is entirely full of cream cheese) by 25%, and reduce the price it charges its consumers by 25% as well. By what percentage does this increase the price-per-cubic-inch that each consumer will pay for cream cheese?

 Option A: 1. No change

 Option B: 2. 78%

 Option C: 3. 100%

 Option D: 4. 300%

 Option E: 5. 400%
[A]: Option B


[Q]: Question: A box contains 12 mangoes out of which 4 are spoilt. If four mangoes are chosen at random, find the probability that A number is selected at random from first thirty natural numbers. What is the chance that it is a multiple of either 3 or 13?

 Option A: 17/30

 Option B: 2/5

 Option C: 11/30

 Option D: 4/15

 Option E: 7/15
[A]:
Option B