I think you have a typo somewhere in your question (read through the explanation)
The trick to these questions is paying attention to how the question is worded. So, lets take a close look at the language in this question.
The most important part of the question is this phrase: "three consecutive odd" numbers. As you know, odd numbers are spaces apart by two (1 is two numbers away from 3, 3 is two numbers away from 5 and so one). Thus to get the third consecutive odd number we add or subtract 6 from an odd number (proved below).
Knowing this, we can create an equation to solve the question and find the greatest of these numbers.
From the first part of the question we see that we are dealing with a "number". Let's use 'y' to be a variable representing this number. If we say 'y' is the smallest consecutive number (out of 3 consecutive numbers) then the largest number is y+6.
From reading the question we can set up this equation:
2(y+6) = 1+3y
The left hand side is given by the phrase "twice the greatest number" and the right hand side is given by the other part of that question.
Solving the equation:
y = 11
From the way we set up our equation, y is the smallest of the three numbers. Therefore, 11 is the smallest number. To get the largest number simply add 6 to eleven: 6+11=17. And 17 is the largest of the numbers.
Proof for getting the 3rd odd number:
Lets use 9 as an example. We know that the three odd numbers below 9 are 7,5,3 and the three odd numbers above 9 are 11,12,15. If we subtract 6 from 9, we get 3, and if we add 6 to 9 we get 15. Thus, subtracting or adding 6 from any odd number gets the "3rd consecutive odd number."