The product of four integers is-100. The difference between the greatest integer and the least integer is 7. What can the four integers be?
Let's call the integers a, b, c, and d. We know that their product is -100:
a * b * c * d = -100
We also know that the greatest integer minus the least integer is 7:
max(a, b, c, d) - min(a, b, c, d) = 7
We can look for possible combinations of integers that satisfy these conditions. One possible combination is:
a = -5, b = 2, c = -2, d = 5
-5 * 2 * -2 * 5 = -100
The greatest integer in this combination is 5 and the least integer is -5, and their difference is indeed 7.
Another possible combination is:
a = -10, b = 5, c = -1, d = 2
-10 * 5 * -1 * 2 = -100
In this case, the greatest integer is 5 and the least integer is -10, and their difference is also 7.
There may be other combinations that satisfy these conditions, but these are two examples.