Final answer:
The only way for the sum of two numbers, p and q, to equal zero is if one number is positive and the other is negative. Neither both positive nor both negative numbers can add up to zero, and one number cannot be zero and the other positive if their sum is zero.
Step-by-step explanation:
The student has asked a question about the sum of two numbers, p and q, given that p + q = 0. With the condition that the sum of the two numbers is zero, we can rule out certain possibilities for the values of p and q. Let's consider each of the given options:
(a) Both numbers are positive. This cannot be true because the sum of two positive numbers would result in a positive number, not zero.
(b) Both numbers are negative. This is also not possible, as the sum of two negative numbers would result in a negative number.
(c) One number is zero and the other is positive. This is not correct because if one of the numbers was zero, the sum would be equal to the other number, which is positive, therefore not zero.
(d) One number is positive and the other is negative. This is the correct answer. When two numbers with opposite signs are added together, their magnitudes can cancel each other out, resulting in a sum of zero.
Therefore, the correct statement is: One number is positive and the other is negative (d).