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.
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Question: Question: Simplify: 250 x 250 - 100 x 100

 Option A: 761200

 Option B: 761400

 Option C: 52500

 Option D: 761500

 Option E: None of them

Answer: Option C


Question: Question: As a treat for her two children, a mother runs to the freezer in which she has three cherry ice pops, three orange ice pops, and four lemon ice pops. She chooses two at random to bring outside to the children, but realizes as she runs out the door that she cannot bring them different flavors without one being jealous of the other and getting even more upset. What is the probability that she has to return to the freezer to make sure that they each receive the same flavor?

 Option A: 2/5

 Option B: 3/7

 Option C: 7/12

 Option D: 11/15

 Option E: 17/25

Answer: Option D


Question: Question: The "factor count" of an integer n greater than 1 is the number of distinct prime factors of n. For example, the factor count of 36 is 2, since 2 and 3 are the distinct prime factors of 36 = 2 x 2 x 3 x 3. For which of the following integers is the factor count greatest?

 Option A: 60

 Option B: 61

 Option C: 62

 Option D: 63

 Option E: 64

Answer:
Option A