instruction:
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.
question:
Question: If k is an integer and 2 < k < 7, for how many different values of k is there a triangle with sides of lengths 2, 6, and k?

 Option A: one

 Option B: two

 Option C: three

 Option D: four

 Option E: five
answer:
Option B


question:
Question: X is a prime number bigger than 10. Also, Y = X+X^3+X^5+X^7. What is definitely true about Y?

 Option A: Y is a prime number.

 Option B: Y is odd.

 Option C: Y is even.

 Option D: Y is divisible by 3.

 Option E: Y is divisible by 7.
answer:
Option C


question:
Question: A merchant has 100 Kg of Sugar, part of which he sells at 7 % profit and the rest at 17 % profit. He gains 10 % in the whole. How much is sold at 17 % profit ?

 Option A: Rs. 70

 Option B: Rs. 36

 Option C: Rs. 27

 Option D: Rs. 67.5

 Option E: Rs. 77.5
answer:

Option E