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 350,000 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:

1. Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient 2. Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient 3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient 4. EACH statement ALONE is sufficient 5. Statements (1) and (2) TOGETHER are NOT sufficient

Please justify your answer, as I am not sure if the OA is correct. Thanks.

1. \(A^2B-A=0\) \(A(AB-1)=0\)

Either A=0 OR AB=1 If A=0; AB=0 OR AB=1 AB can be 0 or 1. Not Sufficient.

2. \(B^2A-B=0\) \(B(AB-1)=0\)

Either B=0 OR AB=1 If B=0; AB=0 OR AB=1 AB can be 0 or 1. Not Sufficient.

Combining both statements:

Either A and B are both 0 OR AB=1 If A and B are both zeros: AB=0 or AB=1 Not Sufficient.

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.

For all who think we can divide both sides by A to have AB=1; Ok, we can try it, but just like absolute values, we have to consider two scenarios:

1) A is NOT equal to 0 : Well here AB=1

2) A is EQUAL to zero. Here since we can not divide, we have to find other ways to manipulate the statements. We arrive at A(AB-1)=0. Analyzing it, we can see AB can be both 1 and 0. Insuf.

I think D is irrelevant and if we are gonna become dubious b/w two choices, they are more likely to be C and E. As you know the general guideline is to choose C b/w C and E on tough questions when it comes to guessing. Solving it, I couldn't make my brain free of the thought that the statements together may be suf. _________________

Ambition, Motivation and Determination: the three "tion"s that lead to PERFECTION.

World! Respect Iran and Iranians as they respect you! Leave the governments with their own.

What are wonderful question ! Reminds me of the Mona lisa.. Wonderfully simple in its presentation, yet on closer inspection, the painting reveals so many subtleities. Anyway, the key point to remember is that , on the GMAT, a) If the questions pertains to the "=" symbol, never ever cancel terms on both ends unless one is sure that the variable is not equal to 0. Remember that there is no such mathematical action as "Cancellation". Cancellation is division in disguise. b) If the question pertains to the ">" or "<" symbol, never ever divide, or cross multiply unless one is certain that the variable being acted upon is >0. Remember that there is no such mathematical operation as "Cross multiplying". It is multiplication in disguise

Apply the FOIN tests to ensure that you have covered all the values that a variable may assume :- F - Fraction o - ZERO i - Integer or Irrational N - Negative _________________

----------------------------------------------------------------------------------------------------- IT TAKES QUITE A BIT OF TIME AND TO POST DETAILED RESPONSES. YOUR KUDOS IS VERY MUCH APPRECIATED -----------------------------------------------------------------------------------------------------

well, i first chose E but on a second thought, i chose A , cos, drug related is an entity and others' is another entity that must be recognised as well. so i go for A, i hope am right.

well, i first chose E but on a second thought, i chose A , cos, drug related is an entity and others' is another entity that must be recognised as well. so i go for A, i hope am right.

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 or its sign. We can not divide by zero.

BAB = B. =>BAB/B = 1 => BA = 1 => AB = 1 .... Suff.

Hence either of them is sufficient Hence D.

I thought of this in the beginning, but A or B might equal zero, which makes dividing by A or B undefined. There is nothing in the question that tells you that A and B are not zero. I think if the questions states that A and B are not zero, then your solution will be correct.

(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.

Hope it helps.

Hi Bunnel, per my understanding when we combine the solution from 2 equations we look for common solution. from 2 equations we have a=0 OR b=0 OR ab=1 a=0, is not a solution since it doesn't satisfy II b=0, is not a solution since it doesn't satisfy I ab=1 satisfy both I and II so this is the solution or we have single solution for the problem.

(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.

Hope it helps.

Hi Bunnel, per my understanding when we combine the solution from 2 equations we look for common solution. from 2 equations we have a=0 OR b=0 OR ab=1 a=0, is not a solution since it doesn't satisfy II b=0, is not a solution since it doesn't satisfy I ab=1 satisfy both I and II so this is the solution or we have single solution for the problem.

When we consider two statements together we should take the values which satisfy both statements. For this question \(ab=1\) satisfies both statement, but \(a=b=0\) also satisfies both statements. So what you call "common solution" for this question is: \(ab=1\) OR \(ab=0\neq{1}\).