Problem Solving

If x > y, x < 6, and y> -3, what is the largest prime number that could be equal to x+ y?

Good Day Sir,

This was my way of solving the problem :

x < 6. So I considered x = 5

-3 < y < x. So y can be -3,-2,-1,0,1,2,3,4

From this max prime value of x + y = 7

To get x + y = 11, x needs to be 6 and y needs to be 5. But this is not possible as x < 6. Y cannot be 6 or more as y< x. So how can we get the sum as 11?

Please advise if there is a mistake in my understanding..

One error,

I meant y can be -2,-1,0,1,2,3,4...

From the problem statement, it can be deduced that -

-3< y < x <6.

The greatest value of x can be 5 which means y should then be less than 5.

Replacing the value of x as 5 in (x+y) and testing for the values of y < 5

5 + y (=4) => not prime
5 + y (=3) => not prime
5 + y (=2) => prime (Ans).

Nowhere given that x and y are integers and thus 11 is the largest possible prime value of x+y