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: When positive integer k is divided by 5, the remainder is 2. When k is divided by 6, the remainder is 5. If k is less than 24, what is the remainder when k is divided by 7?

 Option A: 2

 Option B: 5

 Option C: 6

 Option D: 3

 Option E: 8
answer:
Option D


question:
Question: If x and y are negative integers, which of the following statements must be true?
I. (-x)^y is positive.
II. (-x)^(-y) is positive.
III. x^(-y) is positive.

 Option A: None

 Option B: II only

 Option C: I and II

 Option D: I and III

 Option E: I, II and III
answer:
Option C


question:
Question: In an examination 35% of the students passed and 455 failed. How many students appeared for the examination?

 Option A: 540

 Option B: 400

 Option C: 700

 Option D: 650

 Option E: 840
answer:

Option C