Discussion
If n3 is an odd integer, which one of the following expressions is an even integer?
*This question is included in Nova Math - Problem Set F: Number Theory, question #29
| (A) | 2n2 + 1 |
| (B) | ... |
| (C) | ... |
| (D) | ... |
| (E) | ... |
| (F) | ... |
The solution is
Posted: 02/12/2016 20:40
Well suppose we used n=3 then the answer would be n(n+2)
Posted: 02/12/2016 21:52
Hi Joelene,
If chose n = 3, then n(n + 2) = 3(3 + 2) = 3(5) =15, which is an odd number. But we are looking for an even number, so n(n + 2) is not correct.
With n = 3, Choice (C) becomes 3^2 + 1 = 9 + 1 = 10, which is even. So, again (C) is the correct answer.
Nova Press
If chose n = 3, then n(n + 2) = 3(3 + 2) = 3(5) =15, which is an odd number. But we are looking for an even number, so n(n + 2) is not correct.
With n = 3, Choice (C) becomes 3^2 + 1 = 9 + 1 = 10, which is even. So, again (C) is the correct answer.
Nova Press
Posted: 02/12/2016 20:40
How do we determine weather to use n=1 or another number
Posted: 02/12/2016 21:54
Hi Joelene,
Any odd number will work.
We chose n = 1 because it is the easiest odd number to work with.
Nova Press
Any odd number will work.
We chose n = 1 because it is the easiest odd number to work with.
Nova Press