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:

Please help me in understanding this question. I am confused between C and D.

First of all, we can eliminate answer choices A, B, and E right away. There is no reason to distinguish between \(a\) and \(b\), so if \(a\) cannot be a product, then \(b\) cannot be either and since we cannot have two correct answers in PS problems, then neither A nor B can be correct. As for E it's clearly cannot be correct answer.

So, we are left with options C and D.

For C, can \(ab=3b+2a\)? --> \(ab-2a=3b\) --> \(a(b-2)=3b\) --> \(a=\frac{3b}{b-2}\). Now, if \(b=3\), then \(a=9\), so in this case \(ab=3b+2a\) is possible.

Only option left is D.

Answer: D.

Else, you can notice that since \(a\) and \(b\) are positive integers, then their product MUST be greater than their difference, so D is not possible.

Please help me in understanding this question. I am confused between C and D.

Thanks & Regards Vinni

(A) \(a=ab\) for \(b=1\) and any positive integer \(a>1.\) (B) \(b=ab\) for \(a=1\) and any positive integer \(b>1.\) (C) \(3b+2a=ab\) can be written as \(ab-2a-3b=0\) or \(a(b-2)-3(b-2)=6\) and finally \((a-3)(b-2)=6.\) Then we can have for example \(a-2=1\) and \(b-2=6\) or \(a=3\) and \(b=8.\) (D) \(b-a=ab\) or \(b=a(b+1)\). Since \(a\geq{1}\) and \(b>0,\) \(\, \, b=a(b+1)\geq{1}\cdot{(b+1)}=b+1\), impossible. Or, \(b-a<b\) but \(ab>b,\) because \(a\geq{1}.\) So, this equality CANNOT hold.

(E) \(ab=ab,\) no problem for any pair of positive integers \(a\) and \(b.\)

Answer D
_________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

If we pick b = -2 and a = 2 then for d we get -4 which is same as ab....

a and b need to be positive integers.

That is where the trick in this question lies. a and b are distinct positive integers. So their product must be equal to or greater than the greater number. Considering b - a, b will be greater than a (so that the result is positive) and b - a will be smaller than b. Hence, (b - a) can never be the product of 'b' and 'a'.
_________________

Please help me in understanding this question. I am confused between C and D.

Thanks & Regards Vinni

In these questions it is best to take an example as if something is true for all positive integers than it as to be true for the smallest and the easiest integers to work with take a = 1 and b = 2 and work with the options ab = 2 A) a take a =2, b = 1 B) b take a = 1 b = 2 C) 3b + 2a Seems tricky, lets see other options and then come back to it. D) b - a take b = 1 and a = 2 --> b - a = -1 .. How the hell can product of two positive integers be negative ?? or less than each of them? E) ba Always true

Please help me in understanding this question. I am confused between C and D.

Thanks & Regards Vinni

In these questions it is best to take an example as if something is true for all positive integers than it as to be true for the smallest and the easiest integers to work with take a = 1 and b = 2 and work with the options ab = 2 A) a take a =2, b = 1 B) b take a = 1 b = 2 C) 3b + 2a Seems tricky, lets see other options and then come back to it. D) b - a take b = 1 and a = 2 --> b - a = -1 .. How the hell can product of two positive integers be negative ?? or less than each of them? E) ba Always true

You don't even have to worry what C is !

Choosing a specific value for \(b\) for which there is no \(a\) which fulfills the condition is not a proof. There are infinitely many other possible values for \(b.\) The statement is CANNOT be true, not that it MUST be true for any \(a\) and \(b.\) You have to prove/justify that there is no pair \((a,b)\) of positive integers for which the equality holds.
_________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

Please help me in understanding this question. I am confused between C and D.

Thanks & Regards Vinni

In these questions it is best to take an example as if something is true for all positive integers than it as to be true for the smallest and the easiest integers to work with take a = 1 and b = 2 and work with the options ab = 2 A) a take a =2, b = 1 B) b take a = 1 b = 2 C) 3b + 2a Seems tricky, lets see other options and then come back to it. D) b - a take b = 1 and a = 2 --> b - a = -1 .. How the hell can product of two positive integers be negative ?? or less than each of them? E) ba Always true

You don't even have to worry what C is !

Choosing a specific value for \(b\) for which there is no \(a\) which fulfills the condition is not a proof. There are infinitely many other possible values for \(b.\) The statement is CANNOT be true, not that it MUST be true for any \(a\) and \(b.\) You have to prove/justify that there is no pair \((a,b)\) of positive integers for which the equality holds.

Ohk, i didnt understand your point first yes you are right ! i probably didnt phrase my solution correctly but i just wanted to show that product of two +ve integers can never be less that either of them.

Re: Which of the following CANNOT be a product of two distinct [#permalink]

Show Tags

03 Dec 2014, 02:54

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Re: Which of the following CANNOT be a product of two distinct [#permalink]

Show Tags

08 Dec 2015, 10:23

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Campus visits play a crucial role in the MBA application process. It’s one thing to be passionate about one school but another to actually visit the campus, talk...

Its been long time coming. I have always been passionate about poetry. It’s my way of expressing my feelings and emotions. And i feel a person can convey...

Marty Cagan is founding partner of the Silicon Valley Product Group, a consulting firm that helps companies with their product strategy. Prior to that he held product roles at...

Written by Scottish historian Niall Ferguson , the book is subtitled “A Financial History of the World”. There is also a long documentary of the same name that the...