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: In a certain school, the ratio of boys to girls is 5 to 13. If there are 160 more girls than boys, how many boys are there?

 Option A: 100

 Option B: 36

 Option C: 45

 Option D: 72

 Option E: 117

A: Option A
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Q: Question: If the operation ∆ is defined by a ∆ b = (b - a)^2/a^2 for all numbers a and b, and a ≠ 0, then what is the result when we evaluate this expression: (-5) ∆ (5 ∆ −5) ?

 Option A: 49/9

 Option B: 49/16

 Option C: 81/16

 Option D: 81/25

 Option E: 100/81

A: Option D
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Q: Question: If a and b are different positive integers and a + b+1 = a(a + b), then which of the following must be true?
I. a = 1
II. b = 1
III. a < b

 Option A: I only

 Option B: II only

 Option C: III only

 Option D: I and II

 Option E: I and III

A:
Option D
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