Greg did not manipulate the quantities and directly jumped to choosing numbers. Why? If we manipulate the quantities, A becomes 1, and B becomes a – b, and the correct answer seems B after choosing all possible sets of numbers. But Greg’s approach gives D as the correct answer. Why does manipulating the answer choices does not work here?

Watch out: if you manipulate the quantities, you would divide by a + b. This causes issues if a + b = 0.

Also, notice that the numbers can be negative.

But we already know that ab=15, and with all the possible values of a and b none of the sets give a + b = 0.

The problem is this: **can you** actually make the manipulation you described? What happens to the quantities if (a + b) is negative?