Final answer:
The greatest number of odd-sum triples is infinite. Odd-sum triples are sets of three numbers, where the sum of the three numbers is an odd number. These triples can be generated by adding odd numbers together in different combinations.
Step-by-step explanation:
The greatest number of odd-sum triples is infinite (d).
To understand why there are an infinite number of odd-sum triples, we need to understand what an odd-sum triple is. An odd-sum triple is a set of three numbers such that the sum of the three numbers is an odd number. For example, (1, 3, 5) is an odd-sum triple because 1 + 3 + 5 = 9, which is an odd number.
Now, let's take a look at how we can generate odd-sum triples. We can start with any odd number, let's say 1. Then, we can add any two odd numbers to it. So, we can have (1, 3, 5), (1, 7, 9), (1, 11, 13), and so on. Since there are an infinite number of odd numbers, we can keep generating odd-sum triples by adding different combinations of odd numbers together.
Therefore, the greatest number of odd-sum triples is infinite.