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by Stuart@KaplanGMAT » Tue Jul 20, 2010 2:49 pm
JeetGulia wrote:16. 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

Please help....
We often refer to this type of question as a "wacky symbol" or "symbolism" question; it's really a function question in disguise. For example, we could have restated this question as:

If f(a,b) = a + b - ab, and f(a,b) = 0, which of the following cannot be the value of b?

We start by applying a fundamental rule of math: no matter how weird things look, the same basic rules apply. We know that:

a · b = a + b - ab

and

a · b = 0

So, we can substitute in for the left side of the original equation to get:

0 = a + b - ab

ab = a + b

Rather than attacking this equation in the abstract, let's plug in the choices:

(A) 2

2a = a + 2
a = 2... works

(B) 1

a = a + 1
0 = 1... IMPOSSIBLE... therefore, (B) is the correct choice.
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by JeetGulia » Tue Jul 20, 2010 3:15 pm
Stuart Kovinsky wrote:
JeetGulia wrote:16. 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

Please help....
We often refer to this type of question as a "wacky symbol" or "symbolism" question; it's really a function question in disguise. For example, we could have restated this question as:

If f(a,b) = a + b - ab, and f(a,b) = 0, which of the following cannot be the value of b?

We start by applying a fundamental rule of math: no matter how weird things look, the same basic rules apply. We know that:

a · b = a + b - ab

and

a · b = 0

So, we can substitute in for the left side of the original equation to get:

0 = a + b - ab

ab = a + b

Rather than attacking this equation in the abstract, let's plug in the choices:

(A) 2

2a = a + 2
a = 2... works

(B) 1

a = a + 1
0 = 1... IMPOSSIBLE... therefore, (B) is the correct choice.
....You are the real dude!!
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by sumanr84 » Tue Jul 20, 2010 9:20 pm
JeetGulia wrote:16. 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

Please help....
Could you let us know the source of this question ?
I am on a break !!
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by JeetGulia » Wed Jul 21, 2010 11:59 am
sumanr84 wrote:
JeetGulia wrote:16. 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

Please help....
Could you let us know the source of this question ?
..Officail retired GMAT papers.
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by Testluv » Wed Jul 21, 2010 6:20 pm
We often refer to this type of question as a "wacky symbol"
We do?

Pray tell, Stuart: is that the official/technical way of referring to this problem?

:)
Kaplan Teacher in Toronto
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