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If n is an even integer, which of the following is always odd?
If n is an even integer, which of the following is always odd?
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Practice Questions
1 question
Q1
If n is an even integer, which of the following is always odd?
n + 1
n + 2
n - 2
n - 1
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n - 1 is odd since subtracting 1 from an even number results in an odd number.
Questions & Step-by-step Solutions
1 item
Q
Q: If n is an even integer, which of the following is always odd?
Solution:
n - 1 is odd since subtracting 1 from an even number results in an odd number.
Steps: 5
Show Steps
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.
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