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.

Q: 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

A: Option B
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Q: Question: The functions f and g are defined for all the positive integers n by the following rule: f(n) is the number of perfect squares less than n and g(n) is the number of primes numbers less than n. If f(x) + g(x) = 16, then x is in the range:

Option A: 30 < x < 36

Option B: 30 < x < 37

Option C: 31 < x < 37

Option D: 31 < x < 38

Option E: 32 < x < 38

A: Option C
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Q: Question: A man buys an article for $100. and sells it for $120. Find the gain percent?

Option A: 10%

Option B: 15%

Option C: 25%

Option D: 20%

Option E: 30%

A:
Option D
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