In the question below I understand that the *lowest possible* sum of a,b will be 5 (2,3 or 3,2). However, the situation where 4x5 = 10x2 also exists (a,b are integers and x,y are primes).

Why can we not say that x+y is 5+2 = z which is more than the *lowest possible* sum of a,b? 7 is more than 5, thus x+y = 7 in this situation is more than a+b=5.

So, by equal not equal the answer is D.

I think it’s because quantity A is “the lowest possible sum of a and b”, which is to say the lowest possible value of a plus the lowest possible value of b, for any valid x and y (given that they are positive). So for your example where a = 4 and b = 10, those are not the lowest possible values of a and b.

You said “which is to say the lowest possible value of a plus the lowest possible value of b, **for any valid x and y**” which is not something the question states. I considered that while solving as well but did not want to make an unstated assumption.

I think we must assume that the equation is true and that the conditions are upheld (valid values per the conditions), unless otherwise stated. So when you pick those distinct prime numbers for x and y, you then have to find the lowest possible sum of a and b that still keep that equation valid.

Put perhaps this is a question of convention, and what we can assume for the GRE without being explicitly stated (e.g. real roots, positive factors)