To find the number of terms in a range;
Case I: when we have an odd and an even number as first and last term, the number of odd numbers and even numbers are same
Case II: when we have both first and last terms as odd or both even, the number of terms will have 1 more odd or even term.

Here, a number greater than 116,999 means 117,000 (First term)
and, less than 117,289 means 117,288 (Last term)

So, Case II applies

Number of even terms = \(\frac{Last - First}{2}\) + 1 = \(\frac{288}{2}\) + 1 = 145 terms
Number of odd terms = 288 - 145 = 143 terms

Hence, option E