Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: One more .... help needed [#permalink]
07 Jul 2010, 04:04

5

This post received KUDOS

Expert's post

Is the product of A and B equal to 1?

Question: \(ab=1\)?

(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.

Re: One more .... help needed [#permalink]
07 Jul 2010, 04:26

1

This post was BOOKMARKED

Bunuel wrote:

Question: \(ab=1\)?

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...

Re: One more .... help needed [#permalink]
12 Jul 2010, 06:48

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.