Three integers have a sum of 7 and a product of 0. If the difference of the greatest number and the least number is 11, then the least of these numbers is?

Answer 1

If they have a product of 0, then at least one of the numbers is 0.

The greatest number cannot be 0, otherwise the sum would be negative.

Now, let x = the greatest number
x - 11 = the least number

x + x - 11 + 0 = 7
2x - 11 = 7
2x = 18
x = 9

The least number is 9-11, or -2.

Answer 2

If their product is zero, then one of them had to be a zero
so the 3 numbers can be called x,0, and y
x+y+0 = 7 or
x+y = 7 and
x-y = 11

adding them: 2x = 18
x = 9
if x=9 then y = -2

the 3 numbers are -2,0, and 9

check: is their sum = 7 ? YES
is the largest - the smallest = 11 ? YES