Question: If n is an even integer, which of the following is always odd?
Options:
n + 1
n + 2
n - 2
n - 1
Correct Answer: n - 1
Solution:
n - 1 is odd since subtracting 1 from an even number results in an odd number.
If n is an even integer, which of the following is always odd?
Practice Questions
Q1
If n is an even integer, which of the following is always odd?
n + 1
n + 2
n - 2
n - 1
Questions & Step-by-Step Solutions
If n is an even integer, which of the following is always odd?
Correct Answer: n - 1
Step 1: Understand what an even integer is. An even integer is any whole number that can be divided by 2 without a remainder (e.g., 0, 2, 4, 6, ...).
Step 2: Recognize that if n is an even integer, it can be represented as n = 2k, where k is any integer.
Step 3: Consider the expression n - 1. If n is even, then n - 1 means you are subtracting 1 from an even number.
Step 4: When you subtract 1 from an even number (2k), you get 2k - 1, which is an odd number because it cannot be divided evenly by 2.
Step 5: Conclude that n - 1 is always odd when n is an even integer.
Even and Odd Integers – Understanding the properties of even and odd integers, specifically that subtracting 1 from an even integer results in an odd integer.
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