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# Is the product of A and B equal to 1? (1) A B A = A (2) B A

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Is the product of A and B equal to 1? (1) A B A = A (2) B A [#permalink]

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19 Nov 2007, 19:29
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Is the product of A and B equal to 1?

(1) A B A = A
(2) B A B = B
SVP
Joined: 29 Aug 2007
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19 Nov 2007, 20:54
sujitmgmat wrote:
Is the product of A and B equal to 1?

(1) A B A = A
(2) B A B = B

E.
(1) A B A = A
ABA - A = 0
A (AB - 1) = 0
A = 0
AB = 1 but this not possible because if A = 0, AB cannot be 1.

(2) B A B = B

BAB - B = 0
B (AB - 1) = 0
B = 0
AB = 1 again this is also not possible as above.

So E.
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19 Nov 2007, 21:01
Thanks GMAT TIGER for responding. However, I am difficulty understanding it.

Statement 1 implies that either A = 0 "or" AB=1. From this how can we conclude that AB=1 is not possible?

Similarly Statement 2 implies that either B=0 "or" AB=1.

Therefore, Statement 1 and 2 will imply that AB=1. That is, I think answer should be (C).

But the answer in GMATCLUB Challenge is given as (E).
Director
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19 Nov 2007, 21:38
sujitmgmat wrote:
Is the product of A and B equal to 1?

(1) A B A = A
(2) B A B = B

Does A B A mean A*B*A? Can you clarify? Thanks.
VP
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19 Nov 2007, 21:54
sujitmgmat wrote:
Thanks GMAT TIGER for responding. However, I am difficulty understanding it.

Statement 1 implies that either A = 0 "or" AB=1. From this how can we conclude that AB=1 is not possible?

Similarly Statement 2 implies that either B=0 "or" AB=1.

Therefore, Statement 1 and 2 will imply that AB=1. That is, I think answer should be (C).

But the answer in GMATCLUB Challenge is given as (E).

This is data sufficiency problem - since you have two options for AB (i.e 0 or 1) then you don't have sufficient data to answer the problem.

Assume A=0 B=0 then AB = 0 in option (C) !

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20 Nov 2007, 17:51
This might be a silly question, but why can we not do this:

ABA=A
(AB)A=A
AB=1

is it because we dont know whether A is positive or negative ?
CEO
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20 Nov 2007, 18:13
sujitmgmat wrote:
Is the product of A and B equal to 1?

(1) A B A = A
(2) B A B = B

ABA=A can be 0 1

BAB=B can be 0 or 1

Again A could = B and be 0 or 1.

Insuff.

E
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20 Nov 2007, 19:36
KS,
Why can't the answer be C?
Stmt 1: A= 0 or AB =1
Stmt 2: B=0 or BA =1
When we combine both, don't we get AB = 1

I thought when we combine 2 stmts we take common solution.
Here is one example
http://www.gmatclub.com/forum/t55909

Please explain if I am missing something.
thanks.
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20 Nov 2007, 19:54
Good question!
Thanks everybody. I got this Q wrong initially ...
20 Nov 2007, 19:54
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