M2. A (Estimated Difficulty Level: 3)
Try plugging in some real numbers until you get one of the answers. For example, if you choose 4, then calcu- late 2×4+42 +1 = 25. The answers don’t list 25, so choose another integer to start with. If you choose 5, you’ll get 2 × 5 + 52 + 1 = 36, so the answer is A.
If you are an algebra fiend, you may notice that if the integer is x, then the calculation is 2x+x2+1 = (x+1)2, so the final sum must be the square of an integer. Only answer A is a perfect square.