This is a confusing problem. As I read it, it kept going
in and out of focus. But I think I've got it now, and I also
think that NONE of the choices is correct.
We have to work with different values that 'a' and 'b' can be.
What are 'a' and 'b' ? The question says that they're integers
that we pick so that a·b is always 36. Can you think of another
way to say the same thing ?
'a' and 'b' are a factor pair of 36 ! That will help us write down
all the possible pairs of 'a' and 'b'. I'll do that in a second, but first ...
notice that the question is also going to talk about " a + b ",
so as I write down the factor pairs, I'll also write their sum next to
each one:
The factor pairs of 36 are:
1 and 36 . . . . . sum = 37
2 and 18 . . . . . sum = 20
3 and 12 . . . . . sum = 15
4 and 9 . . . . . . sum = 13
6 and 6 . . . . . . sum = 12 .
The question wants us to look through the list
for the biggest sum and the smallest sum, and
then figure out the difference between them.
That's easy !
The biggest sum is 37 .
The smallest sum is 12 .
The difference is (37 - 12) = 25 .
I don't see that among the choices.
But if I understand the question, then
that's my answer, and I'm sticking to it.
