Sum of odd numbers between 100 and 200 — Aptitude Question
Sum of odd numbers between 100 and 200: What is the sum of all odd numbers between 100 and 200? Answer and worked solution on CodeKairo.
- Topic: Number System
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 60 seconds
Question
What is the sum of all odd numbers between 100 and 200?
Options
- 7000
- 7250
- 7500
- 7750
Show the answer and the worked solution
Correct answer: C. 7500
Worked solution
- The odd numbers run 101, 103, …, 199.
- Count = (199 − 101)/2 + 1 = 50.
- Sum = 50 × (101 + 199)/2 = 50 × 150 = 7500.
Answer: 7500.
The idea
Any evenly spaced list sums to count × average, and the average is (first + last)/2. Getting the count right is the only real work: (last − first)/step + 1.
Shortcut. The first n odd numbers sum to n². Odd numbers up to 199 are the first 100 (sum 10,000) and up to 99 the first 50 (sum 2,500), so 10,000 − 2,500 = 7500.
Common trap. Counting the terms as (199 − 101) ÷ 2 = 49, without the + 1 for the first term, gives 49 × 150 = 7350, and the nearest option to that is 7250; the run 101, 103, …, 199 has 50 terms, so the sum is 50 × 150 = 7500.