Gmat_mission wrote:What is the least possible product of 4 different integers, each of which has a value between -5 and 10, inclusive?

(A) -5040
(B) -3600
(C) -720
(D) -600
(E) -120

[spoiler]OA=B[/spoiler].

Hello, I have this doubt, how can I determine the correct option? Why are all the answers negative? <i class="em em-frowning"></i>

Since you want to LEAST (or LOWEST number) you want to increase magnitude of the product but also ensure that the number is negative. To get a negative number you want 1 or 3 negative numbers in the product. Given the range here you only want 1!

To keep it simple what 4 numbers would you choose for the largest number? Well that's 10*9*8*7. Now let's make it negative by getting rid of 7 (the lowest impact number) and substituting -5 (the highest impact negative number): now we have 10*9*8*(-5) and we get -3600.

Gmat_mission wrote:What is the least possible product of 4 different integers, each of which has a value between -5 and 10, inclusive?

(A) -5040
(B) -3600
(C) -720
(D) -600
(E) -120

We want to create the smallest negative number possible. As we can see from the answer choices, the smallest product is negative; therefore, an odd number of factors (either 1 factor or 3 factors) must be negative. Moreover, in order for the product to be as small as possible, we should aim for the greatest absolute value. Within the given bounds, this can be achieved by picking three positive numbers that are as large as possible and one negative number that is as small as possible. Thus, the smallest product would be:

-5 x 10 x 9 x 8 = -3600

Answer: B