For integers a and b, where 4 is less than or equal to a, which is less than or equal to 6 and 8 is less than or equal to b, which is less than or equal to 10, what is the greatest possible value of 3/(b-a)? Shouldn’t the answer be 3? (since 7-6 is 1 and the greatest value will be 3).. The answer was 1.5.

So 4 ≤ a ≤ 6 and 8 ≤ b ≤ 10? The greatest possible value of that fraction will be when (b – a) is as small as possible without reaching 0. The smallest b is 8, and the biggest a is 6. Using those will give you the smallest b – a, which will be 2. 3/2 = 1.5.