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# For any numbers a and b, aXb = a+b-ab. If axb = 0, which of

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Intern
Joined: 08 Nov 2006
Posts: 34
For any numbers a and b, aXb = a+b-ab. If axb = 0, which of  [#permalink]

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22 Nov 2006, 11:48
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For any numbers a and b, aXb = a+b-ab.
If axb = 0, which of the following CANNOT be a value of b?
(A) 2
(B) 1
(C) 0
(D) -1
(E) -3/2

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Director
Joined: 28 Dec 2005
Posts: 891

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22 Nov 2006, 12:22
I get B.

axb= 0
=> a+b-ab = 0
=> a(1-b)+b = 0
=> a = -b/(1-b) = b/b-1

=> if b is 1 then a will be undefined.
Intern
Joined: 08 Nov 2006
Posts: 34

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22 Nov 2006, 12:37
How can A be 2? or any of the other answers besides zero?

Thats what I don't understand. Is there some rule I am missing?
Intern
Joined: 08 Nov 2006
Posts: 34

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22 Nov 2006, 14:08
For any numbers a and b, aXb = a+b-ab.
If axb = 0, which of the following CANNOT be a value of b?
(A) 2
(B) 1
(C) 0
(D) -1
(E) -3/2
---------------------------------------------------------------------------

I'm saying that value cannot be a, b, d or e.
If you have
aXb = 0
and
aXb = a+b-ab
then you have
a+b-ab = 0
and
axb = 0
If aXb = 0, that means either a or b or both have to be zero.

If thats the case, then you have:
0 +b-0 =0
or
a+0-0 =0
which means both a and b have to be zero to have both those statements hold true. Which also means the answer cannot be a,b,d or e.

Can you explain this to me?
Senior Manager
Joined: 24 Oct 2006
Posts: 334

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22 Nov 2006, 14:20
"X" denotes an operation for any value of a and b and not multiplication.
aXb = a+b-ab, aXb = 0

Then,
a+b-ab=0

for example, if b=2,

a+2-2a=0
a=2

if b=-1,
a-1+a=0
a=1/2

The only no. for b that does not satisfy the equation is B, b=1
a+1-a=0
Non-Human User
Joined: 09 Sep 2013
Posts: 9457
Re: For any numbers a and b, aXb = a+b-ab. If axb = 0, which of  [#permalink]

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15 Dec 2017, 13:37
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Re: For any numbers a and b, aXb = a+b-ab. If axb = 0, which of &nbs [#permalink] 15 Dec 2017, 13:37
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