Question

Let x and y be two positive integers and p be a prime number. If x (x – p) – y (y + p) = 7p, what will be the minimum value of x – y?

• A. 1
• B. 3
• C. 5
• D. 7
• E. None of the above

Answer 1

Answer: (E)

None of the above

Answer 2

Given: x (x – p) – y (y + p) = 7p
x2 - xp + y2 - yp = 7p
x2 - y2 - p(x+y) = 7p
(x+y)(x-y) - p(x+y) = 7p
(x-y) = $\frac{p + 7p}{(x+y)}$
Hence, option E is the correct answer.
Note: The answer cannot be determined as it is not in the options. None of the above is selected.