er.twi.fb wrote:1.How many integers, x, satisfy the inequality b < x < a?
1) a - b = 78
2) a > 100 and b < 50

(1) If a = 78 and b = 0 then a - b = 78 and 0 < x < 78, which implies there will be 77 integers between a and b.
It is not given in the question that a and b are integers, so a = 78.5 and b = 0.5, so that a - b = 78 and 0.5 < x < 78.5, which implies there are 78 integers between a and b.
So, there is no unique answer.

Hence, (1) is NOT SUFFICIENT.

(2) If a = 101 and b = 49 then 49 < x < 101 implies x = 51
If a = 110 and b = 45 then 45 < x < 110 implies x = 64
So, there is no unique answer.

Hence, (2) is NOT SUFFICIENT.

Combining (1) and (2), a and b can take any values so that a - b = 78, so again we have a number of possible solutions.

The correct answer is (E).