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For any numbers a and b, a · b

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Nicky
 Post subject: For any numbers a and b, a · b
 Post Posted: Mon Sep 08, 2008 8:07 pm 
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) 2

Source: My GMAT Prep School.
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RonPurewal
 Post subject:
 Post Posted: Mon Sep 29, 2008 6:17 am 
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ManhattanGMAT Staff


Posts: 6765
"gmat prep school"? huh?

--

go ahead and try the choices in succession, substituting them into the given equation, and see if any of them gives an absurdity (reductio ad absurdum).

(a) gives a + 2 - 2a = 0, or 2 - a = 0. this is perfectly possible, if a = 2.
(b) gives a + 1 - a = 0, or 1 = 0. impossible.
at this point there's no need to try the later choices, as it's clear that this is the absurdity. nevertheless, if you insist on trying the other 3 choices, you'll find that each of them gives one perfectly valid solution for a.

moral of the story = takeaway: in problems that define strange symbols or functions, pretty much the entire challenge will consist in just following the directions. these problems are paper tigers: they're intimidating to look at, but, once you realize that all you have to do is plug into the expression and watch what happens, they usually aren't that bad.
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Guest
 Post subject:
 Post Posted: Tue Sep 30, 2008 12:35 am 
There is easier way to go about it.

a · b = a + b – ab

0 = a + b - ab

so a = b/(b-1)

so b cannot equal 1.
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RonPurewal
 Post subject:
 Post Posted: Tue Sep 30, 2008 4:06 am 
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ManhattanGMAT Staff


Posts: 6765
Anonymous wrote:
There is easier way to go about it.

a · b = a + b – ab

0 = a + b - ab

so a = b/(b-1)

so b cannot equal 1.


well played.
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