Question

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?

Answer 1

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.