M7MBA wrote:For any numbers a and b, a#b=a + b - ab. If a#b=0, which of the following CANNOT be a value of b?

A. 2
B. 1
C. 0
D. -1
E. -3/2

We are given that a#b=a + b - ab and that a#b=0. Thus we have

a + b - ab = 0

a + b = ab

Now let's look at the choices:

A. If b = 2, then

a + 2 = a(2)

2 = a

So b can be 2.

B. If b = 1, then

a + 1 = a(1)

We see that a + 1 (1 more than a) can't be equal to a itself. So b CANNOT be 1, and that is the number we are looking for.

Alternate Solution:

We are given that a#b=a + b - ab and that a#b=0. Thus we have

a + b - ab = 0

a + b = ab

b = ab - a

b = a(b - 1)

We observe here that for any value of b other than 1, we can divide each side of the equality by b - 1 and express a as b/(b - 1). Thus, the only value that b cannot assume is 1.

Answer: B