The square of twice 45

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.