What is the least possible product of 4 different integers,

swerve 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

The OA is B

Source: GMAT Paper Tests

We want values with the greatest MAGNITUDE

So (10)(9)(8)(-5) = -3600

Answer: -3600

Answer: B

swerve 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

The OA is B

Source: GMAT Paper Tests

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