Question

The sum of three consecutive odd numbers is 20 more than the first number. What is the middle number ?

• A. 7
• B. 9
• C. 11
• D. Data inadequate

Answer 1

The Correct Option is B

To solve the problem of finding the middle number of three consecutive odd numbers, we can follow these steps:

1. Let's denote the three consecutive odd numbers. If we assume the first odd number is x, the second odd number would be x + 2, and the third odd number would be x + 4.
2. According to the problem, the sum of these three numbers is 20 more than the first number. This can be set up as an equation: x + (x + 2) + (x + 4) = x + 20
3. Simplify the left side of the equation: 3x + 6 = x + 20
4. Subtract x from both sides: 2x + 6 = 20
5. Subtract 6 from both sides to isolate 2x: 2x = 14
6. Divide both sides by 2 to solve for x: x = 7
7. Thus, the three consecutive odd numbers are 7, 9, and 11. The middle number is, therefore, 9.

Hence, the correct answer is 9.