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: Rs. 6000 is lent out in two parts. One part is lent at 5% p.a simple interest and the other is lent at 10% p.a simple interest. The total interest at the end of one year was Rs. 450. Find the ratio of the amounts lent at the lower rate and higher rate of interest?

 Option A: 5:1

 Option B: 5:5

 Option C: 5:8

 Option D: 5:4

 Option E: 5:2

Answer: Option B


Question: Question: For any positive integer Y, the sum of the first Y positive integers equals Y(Y+1)/2 . If X and Y are positive integers and X > Y, what is the sum of all the integers between X and Y, inclusive?

 Option A:  X(X+1

 Option B:  X(X+1

 Option C:  X(X+1

 Option D:  X(X+1

 Option E:  X(Y+1

Answer: Option B


Question: Question: Each of X alarm tolls at regular intervals. All of them tolls together twelve times a day. No two alarm at equal intervals of time. If each alarm tolls after a whole number of minutes, what is the maximum possible value of X?

 Option A: 14

 Option B: 16

 Option C: 18

 Option D: 20

 Option E: 22

Answer:
Option B