in Practice 1 the question about which n is even i didnt understand the solution?

Question

Krishna kumar · Accepted Answer

To determine which of the given expressions is always even for any value of  (n), we need to check whether each expression is guaranteed to have at least one even factor, making the product even.
1. Option 1: ((n-1)(n-3)(n-5))   - (n-1): Can be even or odd.   - (n-3): Can be even or odd.   - (n-5): Can be even or odd.   - This product can be all odd if (n) is even, hence not always even.
2. Option 2: ((n-2)(n-4)(n-6))   - (n-2): Can be even or odd.   - (n-4): Can be even or odd.   - (n-6): Can be even or odd.   - This product can be all odd if (n) is even, hence not always even.
3. Option 3: ((n-1)(n-2)(n-3))   - (n-1): Can be even or odd.   - (n-2): Can be even or odd.   - (n-3): Can be even or odd.   - This product will always contain (n-2), which is a consecutive integer to n . Among any three consecutive integers, there is always one even number. Therefore, this product will always have at least one even number, making it always even.
4. Option 4: None of these   - Based on our analysis, Option 3 is always even.
Hence, the correct answer is:
Option 3: (n-1)(n-2)(n-3))