For any numbers a and b, a#b = ab(3 − b). If a and a#b both represent positive numbers, which of the following could be a value of b? Select:
A) −5
B) −2
C) 2
D) 4
E) 7
if a#b is positive then there are 2 cases   either ab &amp;(3-b) both are negatives or both positives   let both are positives then for (3-b) to be positive b has to less than 3 (3-b&gt;0---&gt;3&gt;b)   from options b can be -5,-2,or 2   but if we take negative value of b then ab will negative &amp; hence a#b which is not possible.   also if we do both negative then (3-b) to be negative b has to be greater than 3 which from options are only 4&amp;7   if we take any value then the term ab will positive leaving a#b negative.which is not possible   Hence b=2   ANSWER:2
<result>C</result>
For any numbers a and b, a#b = ab(3 − b). If a and a#b both represent positive numbers, which of the following could be a value of b?