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PS Question - Value of B

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PS Question - Value of B

by MarceloBR » Mon Mar 24, 2014 6:56 pm
Hi,
Trying to Beat the GMAT I faced this PS question below that I couldn't overcome.. Can you guys give me a way out?

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) -2/3

I hope you can explain me how to solve this question!

Tnks a lot!
Marcelo
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by [email protected] » Mon Mar 24, 2014 8:15 pm
Hi MarceloBR,

This is an example of a Symbolism question (and you'll likely see 1 on Test Day). The idea is that you'll be given a "made up" math symbol, told what it "means" mathematically and then asked to solve some minor equation.

Here, we're told to substitute values in for A and B so that the equation....

A + B - AB = 0

We're asked which of the following answers CANNOT be the value of B? So 4 of the answers are POSSIBLE and one is IMPOSSIBLE.

There are a couple of ways to approach this prompt. You could work mathematically or you can TEST THE ANSWERS. I'm going to use the answers to my advantage and find the 4 that are possible solutions and the one the creates an impossible situation:

If B = 2, then we'd have...
A + 2 - 2A = 0
2 = A
So B COULD be 2

If B = 1, then we'd have...
A + 1 - A = 0
1 = 0???????
B CANNOT equal 1

At this point, we could stop. I'll show you why the other answers are possible though:

If B = 0, then we'd have...
A + 0 - 0 = 0
0 = A
So B COULD be 0

If B = -1, then we'd have...
A -1 -(-1)(A) = 0
2A = 1
1/2 = A
So B COULD be -1

If B = -2/3, then we'd have...
A - 2/3 -(-2/3)(A) = 0
A + 2A/3 = 2/3
5A/3 = 2/3
A = 6/15
So B COULD be -2/3

Final Answer: B

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
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