Answer:
13
Explanation:
Two factors of -48... that means two numbers which multiplied together give a result of -48, like -6 and 8 for example.
The difference of those two factors is -19. There not that many possible factors for -48, so if we list them we'll be able to spot a pair with a difference of 19.
A first list of factors for -48 is: -1 and 48, -2 and 24, -3 and 16, -4 and 12, -6 and 8.
We can create another list by inverting the signs: 1 and -48, 2 and -24, 3 and -16, 4 and -12, 6 and -8.
The question says the difference of the two factors is 19... can you spot in each list a pair of factors having a difference of 19? I see -3 and 16 and also 3 and -16.
The question also say the one of the greatest absolute value is positive... so that means it's a pair with +16, not -16.
The pair of factors we're looking for is then -3 and 16. They are factors of -18, they have a difference of 19, and the one with the greatest absolute value is positive.
The sum of -3 and 16 is 13.