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: 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: Sixty percent of the members of a swim club have passed the lifesaving test. Among the members who have not passed the test, 12 have taken the preparatory course and 30 have not taken the course. How many members are there in the swim club?

 Option A:  60

 Option B:  80

 Option C:  100

 Option D:  120

 Option E:  140

Answer: Option E


Question: Question: If p is the product of the integers from 1 to 36, inclusive, what is the greatest integer k for which 3^k is a factor of p?

 Option A: 13

 Option B: 15

 Option C: 17

 Option D: 19

 Option E: 21

Answer:
Option C