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(1) \(a^2b=a\) --> \(a^2b-a=0\) --> \(a(ab-1)=0\) --> either \(a=0\) or \(ab=1\). Two different answers, not sufficient.

(2) \(ab^2=b\) --> \(ab^2-b=0\) --> \(b(ab-1)=0\) --> either \(b=0\) or \(ab=1\). Two different answers, not sufficient.

(1)+(2) either \(a=b=0\), so in this case \(ab=0\neq{1}\) and the answer to the question is NO, OR \(ab=1\) and the answer to the question is YES. Two different answers, not sufficient.

Answer: E.

onedayill wrote:

A/A cancels out to be 1 this means A*B = 1

When you cancel \(a\), what you are actually doing is dividing both parts of the equation by variable \(a\), thus assuming with no ground for it that this variable does not equal to zero.

Never reduce equation by variable (or expression with variable), if you are not certain that variable (or expression with variable) doesn't equal to zero. We can not divide by zero. _________________

(1) \(a^2b=a\) --> \(a^2b-a=0\) --> \(a(ab-1)=0\) --> either \(a=0\) (and \(b=any \ value\), including zero) so in this case \(ab=0\neq{1}\) OR \(ab=1\). Two different answers, not sufficient.

(2) \(ab^2=b\) --> \(ab^2-b=0\) --> \(b(ab-1)=0\) --> either \(b=0\) (and \(a=any \ value\), including zero) so in this case \(ab=0\neq{1}\) OR \(ab=1\). Two different answers, not sufficient.

(1)+(2) As from (1) \(a(ab-1)=0\) and from (2) \(b(ab-1)=0\) then \(a(ab-1)=b(ab-1)=0\) --> either \(a=b=0\), so in this case \(ab=0\neq{1}\) and the answer to the question is NO, OR \(ab=1\) and the answer to the question is YES. Two different answers, not sufficient.

Answer: E.

Side note on dividing (1) by \(a\) and (2) by \(b\): Never reduce equation by variable (or expression with variable), if you are not certain that variable (or expression with variable) doesn't equal to zero. We can not divide by zero.

It's not a good practice to divide the parts of an equation by the unknown (A or B here) because this unknown can be 0. As we know, division by 0 can't be done.

jainanurag78 wrote:

I think it should be D. Why can we divide A*B*A=A by A on both the sides and it would give us AB =1 same with the S2.

I don't agree with the answer. what do you guys think?

(1) ABA = A = ABA - A = 0 = A(AB-1) = 0 This means A=0 or AB=1 ---- Not Sufficient.

(2) BAB = B = BAB - B = 0 = B(AB-1) = 0 This means B=0 or AB=1 ---- Not Sufficient.

Combined - A=0 or B=0 or AB=1 ---Not Sufficient.

E

Putting Both statements together shouldn't it be sufficient? You know for sure that the only answers are 0 and 1. and if either A or B is 0, hten definetly the other is 1, IN this case answer is always zero right?

No they are not sufficient. The question asks is AB=1 ?

In data sufficiency with "is...?" questions we should arrive at either YES or NO. We cannot have both answers (ie) YES and NO from a single statement.

Statement 1 says --- > AB can be zero or one. So we can have No (AB is not 1) and Yes(AB is 1). so not sufficient Statement 2 says --- > AB can be zero or one. This is also not sufficient. Combined also says --> AB can be zero or one. So combined also not sufficient.

That is why we choose E. We are not able to arrive at definitive YES or NO with the given information.
_________________

"You have to find it. No one else can find it for you." - Bjorn Borg

(1) \(a^2b=a\) --> \(a^2b-a=0\) --> \(a(ab-1)=0\) --> in order a product to be zero ether of multiples (or both) must be zero --> so, either \(a=0\) (and \(b=any \ value\), including zero) so in this case \(ab=0\neq{1}\) OR \(ab=1\). Two different answers, not sufficient.

(2) \(ab^2=b\) --> \(ab^2-b=0\) --> \(b(ab-1)=0\) --> either \(b=0\) (and \(a=any \ value\), including zero) so in this case \(ab=0\neq{1}\) OR \(ab=1\). Two different answers, not sufficient.

(1)+(2) As from (1) \(a(ab-1)=0\) and from (2) \(b(ab-1)=0\) then \(a(ab-1)=b(ab-1)=0\) --> either \(a=b=0\), so in this case \(ab=0\neq{1}\) and the answer to the question is NO, OR \(ab=1\) and the answer to the question is YES. Two different answers, not sufficient.

I don't agree with the answer. what do you guys think?

(1) ABA = A = ABA - A = 0 = A(AB-1) = 0 This means A=0 or AB=1 ---- Not Sufficient.

(2) BAB = B = BAB - B = 0 = B(AB-1) = 0 This means B=0 or AB=1 ---- Not Sufficient.

Combined - A=0 or B=0 or AB=1 ---Not Sufficient.

E

Putting Both statements together shouldn't it be sufficient? You know for sure that the only answers are 0 and 1. and if either A or B is 0, hten definetly the other is 1, IN this case answer is always zero right?

We are saying that either A is 0 or AB=1. I was tempted to chose D because AB=1 from both and I dont care about A or B by themselves.

But the catch is either A is 0 or AB=1. We don't know which one of them is correct. either of them will satisfy the condition. If A =1 AB =0 irrespective of B. Hence AB can be both 0 or 1.

Never reduce equation by variable (or expression with variable), if you are not certain that variable (or expression with variable) doesn't equal to zero. We can not divide by zero.

Gottcha, Thanks once again!!!
_________________

GGG (Gym / GMAT / Girl) -- Be Serious

Its your duty to post OA afterwards; some one must be waiting for that...

E. AB = 1 doesn't mean A= 1 , B =1 They can be inverse of each other. E.g. A =2 , B = 1/2. Question doesn't say both are integers in which case AB =1 will imply A=B=1 and each one will be sufficient in that case. Also, you can't cancel out A with A because you don't know if A# 0.

Its D, ABA =A (Cancel A on both sides then Product of AB is equal to 1) BAB=B (Cancel B on both sides then product of AB =1)
_________________

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