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.

[EX Q]: Question: A number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34. Such a least possible number N is

 Option A: 74

 Option B: N=75

 Option C: N=175

 Option D: N=680

 Option E: 690
[EX A]: Option B

[EX Q]: Question: When n is divided by 19, the remainder is 7. When n is divided by 11, the quotient is equal to Z, and the remainder is equal to 7. Z must be divisible by which of the following numbers?

 Option A: 16

 Option B: 18

 Option C: 20

 Option D: 19

 Option E: 22
[EX A]: Option D

[EX Q]: Question: Given two fair dice, what is the probability W that the sum of their numbers is 4 if exactly one die shows a 3?

 Option A: a

 Option B: b

 Option C: c

 Option D: d

 Option E: e
[EX A]:
Option A