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: Two alloys A and B are composed of two basic elements. The ratios of the compositions of the two basic elements in the two alloys are 5 : 3 and 1 : 2, respectively. A new alloy X is formed by mixing the two alloys A and B in the ratio 4 : 3. What is the ratio of the composition of the two basic elements in alloy X ?

 Option A: 1 : 1

 Option B: 2 : 3

 Option C: 5 : 2

 Option D: 4 : 3

 Option E: 7 : 9
answer:
Option A


question:
Question: A coin is tossed two times. What is the probability that there is at the least one tail?

 Option A: 3/4

 Option B: 31/37

 Option C: 31/18

 Option D: 31/10

 Option E: 31/19
answer:
Option A


question:
Question: In 1990 a total of p earthquakes occurred worldwide, some but not all of which occurred in Asia. If r of these earthquakes occurred in Asia, which of the following represents the ratio of the number of earthquakes that occurred in Asia to the number that did NOT occur in Asia?

 Option A: p/r

 Option B: r/p

 Option C: r/(p-r

 Option D: p/(p-r

 Option E: 1- (r/p
answer:

Option C