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
OA B
Source: GMAT Prep
For any numbers a and b, a#b=a + b - ab. If a#b=0, which of
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We have a#b = a + b - ab = 0BTGmoderatorDC 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
OA B
Source: GMAT Prep
From a + b - ab = 0, we have a = 1/(b - 1)
Since if b = 1, the value of a would be indeterminable, we have b ≠1.
The correct answer: B
Hope this helps!
-Jay
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BTGmoderatorDC 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
OA B
Source: GMAT Prep
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 b = 1 results in the inconsistent result of 1 = 0. Thus, the only value that b cannot assume is 1.
Answer: B
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