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
The OA is the option B.
Experts, how can I get an answer here? Should I try option by option? Could you give me some help, please? Thanks in advanced.
For any numbers a and b, a#b=a + b - ab. If a#b=0, which of
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a#b= 0 means that a +b -ab = 0 also.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
The OA is the option B.
Experts, how can I get an answer here? Should I try option by option? Could you give me some help, please? Thanks in advanced.
Which means that a+b=ab
Test the answers. Can b=2 ? Substitute 2 for b
a+2=2a works if a=2 so yes it's possible
Can b=1 ?
a+1=a > only possible if 1=0, which isn't true, therefore 1, B
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We are given that a#b=a + b - ab and that a#b=0. Thus we haveM7MBA 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
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
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