Question

The sum of two consecutive odd integers is 32. What is the value of the next consecutive odd integer?

• A. 33
• B. 21
• C. 17
• D. Cannot be determined
• E. 19

Hint:

Read the question carefully. A common mistake is to solve for one of the two integers (like 17) and select that as the answer. The question here asks for the *next* integer in the sequence, not one of the integers in the sum.

Answer 1

Answer: (E)

Step 1: Understanding the Concept:
Consecutive odd integers are odd numbers that follow each other in sequence, such as 3, 5, 7. They always have a difference of 2. We can set up an algebraic equation to find the integers.
Step 2: Key Formula or Approach:
Let the first odd integer be \(n\). Then the next consecutive odd integer is \(n + 2\). Their sum is 32: \[ n + (n + 2) = 32 \] We need to find the integers and then identify the *next* one in the sequence.
Step 3: Detailed Explanation:
Solve the equation for n: \[ 2n + 2 = 32 \] Subtract 2 from both sides: \[ 2n = 30 \] Divide by 2: \[ n = 15 \] So, the first odd integer is 15. The second consecutive odd integer is \(n + 2 = 15 + 2 = 17\). Check: \(15 + 17 = 32\). This is correct. The problem asks for the *next* consecutive odd integer after these two. The sequence is 15, 17, ... The next odd integer after 17 is \(17 + 2 = 19\).
Step 4: Final Answer:
The value of the next consecutive odd integer is 19.