To solve this problem, let's assume that the positive integer is represented by the variable "x."
According to the given information, the product of the positive integer and the integer that succeeds it (which is x + 1) is twelve.
So, we can write the equation:
x(x + 1) = 12
Expanding the equation:
x^2 + x = 12
Rearranging the equation:
x^2 + x - 12 = 0
We can now solve this quadratic equation by factoring or using the quadratic formula. Let's attempt to factor it.
The factors of -12 that add up to 1 are 4 and -3. Therefore, we can rewrite the equation as:
(x + 4)(x - 3) = 0
Setting each factor equal to zero:
x + 4 = 0 or x - 3 = 0
Solving for x:
x = -4 or x = 3
Since we are looking for a positive integer, the only valid solution is x = 3.
Therefore, the number that satisfies the given condition is 3.
The correct answer is A) 3.