Question 6

The least integer value of a/b is -2.

To find the least integer value of a/b given the constraints -5 ≤ a ≤ 5 and 1 < b < 5, we can analyze the possible values of a and b. The minimum ratio occurs when a is at its lowest value and b is at its highest value while still satisfying the inequalities.

A) 2

The value of 2 would imply that a/b is positive. Given that a can be negative (as low as -5), this option cannot be correct since we are seeking the least integer value which must be negative or zero.

B) -1

While -1 is a negative value, it is not the least integer possible given the constraints. For example, if a = -5 and b = 4, then a/b = -5/4 = -1.25, which is less than -1, indicating that -1 is not the minimum.

C) -2

This option is correct as the least integer value of a/b. By selecting a = -5 and b = 2, we find a/b = -5/2 = -2.5, which rounds up to -2 as the least integer value satisfying the constraints.

D) -4

The value -4 is less than -2, but cannot be attained under the given conditions. With a = -5 and b = 2, the calculation yields -2.5, indicating that -4 is not achievable with any integer values for a and b defined by the inequalities.

Conclusion

The least integer value of a/b is definitively -2, as verified by checking the possible values of a and b within the specified ranges. All other options fail to meet the criteria set by the inequalities or do not represent the least integer value achievable under these conditions. Thus, -2 stands as the only valid solution.