Problem Solving

Ahmed MS wrote:Q: If x>y, x<6, and y>-3, what is the largest prime number that could be equal to x+y? ( source: Manhattan equation, chapter 12 problem set).

-3 < y < x < 6

To find the largest prime number which is equal to (x + y), we have to maximize both x and y such that their sum is a prime number. Note that this does not mean that x and y have to be integer.

Maximum possible value for x and y is just less than 6.
Hence, maximum possible sum of x and y will be just less than (6 + 6) = 12

The largest prime number less than 12 is 11.
If we take x = 5.9 and y = 5.1, (x + y) = (5.9 + 5.1) = 11
Hence, it is possible that (x + y) can be equal to 11.

Therefore, 11 is the largest prime number that could be equal to (x + y).