Select the odd number from the given alternatives: 1, -2, -(-3), and 5.

Introduction / Context:
This question tests your understanding of integers, signs, and the concept of even and odd numbers. It presents some numbers in standard form and one in a slightly tricky form using a double negative. Your task is to simplify where needed and then identify which number has a different parity, that is, whether it is even or odd, compared to the others.

Given Data / Assumptions:

• The given numbers are 1, -2, -(-3), and 5.
• The expression -(-3) should be simplified using the rule that a negative times a negative gives a positive.
• We classify numbers as even if they are divisible by 2 and odd if they are not divisible by 2.
• Exactly one number has different parity from the others.

Concept / Approach:
The first step is to simplify -(-3). Using basic rules of signs, a negative of a negative number is positive, so -(-3) becomes +3. Once all numbers are in simple form, the idea is to check whether each is even or odd. Odd one out questions involving integers often use parity as the distinguishing property. If three numbers are odd and one is even, or vice versa, the number with different parity is the odd one out.

Step-by-Step Solution:
Step 1: Simplify -(-3). A negative of a negative gives a positive, so -(-3) = 3. Step 2: List the simplified numbers: 1, -2, 3, and 5. Step 3: Check the parity of 1. Since 1 is not divisible by 2, it is an odd number. Step 4: Check the parity of -2. Because -2 is divisible by 2 (that is, -2 / 2 = -1), it is an even number. Step 5: Check the parity of 3. Since 3 is not divisible by 2, it is odd. Step 6: Check the parity of 5. Since 5 is not divisible by 2, it is odd. Step 7: Group the odd numbers: 1, 3, and 5 are all odd integers. Step 8: Observe that -2 is the only even integer among the four. Step 9: Conclude that -2 is the odd number out based on parity.

Verification / Alternative check:
You can verify by thinking in terms of multiples of 2. Any integer that can be written as 2 * k for some integer k is even. -2 fits this definition because -2 = 2 * (-1). The numbers 1, 3, and 5 cannot be expressed as 2 times an integer without involving fractions, so they are odd. Also, ignoring the sign and checking absolute values, 1, 3, and 5 are odd absolute values while 2 is even. The sign does not affect evenness or oddness, so this reinforces the conclusion that -2 is the unique even number and hence the odd one out.

Why Other Options Are Wrong:
1 is an odd integer and shares this property with 3 and 5, so it is not the odd one out.
-(-3) simplifies to 3, which is an odd number and belongs with 1 and 5.

5 is also an odd number and matches the parity of 1 and 3, so it cannot be considered the odd one out.

Common Pitfalls:
One common pitfall is to be confused by the expression -(-3) and treat it as some kind of special or different number. Another mistake is to focus on the sign rather than on evenness and oddness, thinking that the only negative number must be the odd one out without checking parity. However, even negative numbers are still considered even. To avoid such errors, always simplify expressions first and then apply clear definitions of even and odd numbers. Remember that parity is based only on divisibility by 2 and not on whether the number is positive or negative.

Final Answer:
The odd number is -2.