motion2020 wrote:
What is the number of odd integers that are greater than \(116,999\) and less than \(117,289\)?
(A) 147
(B) 146
(C) 145
(D) 144
(E) 143
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