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:

If a and b are integers, and |a| > |b|, is a · |b| < a – b?

(1) a < 0

(2) ab >= 0

anybody have a solution for this (under 2 minute). testing value takes way too long here.

E

Given: \(|a|>|b|\) Question: is \(a*|b|<a-b\)?

(1) \(a<0\). If \(a=-3\) and \(b=0\), then \(a*|b|=0>a-b=-3\) and the answer is NO but if \(a=-3\) and \(b=-1\), then \(a*|b|=-3<a-b=-2\) and the answer is YES. Two different answers. Not sufficient.

(2) \(ab\geq{0}\)

Above example works here as well: \(a=-3\) and \(b=0\) --> \(a*|b|=0>a-b=-3\) --> answer NO; \(a=-3\) and \(b=-1\) --> \(a*|b|=-3<a-b=-2\) --> answer YES. Two different answers. Not sufficient.

(1)+(2) Again the same example satisfies the stem and both statements and gives two different answers to the question whether \(a*|b|<a-b\). Hence not sufficient.

1&2) Combined, if a is negative, and ab>=0, this means that b is either 0 or also negative. 3*|-2|<-3-(-2).... YES -3*|0|<-3-0............NO --->INSUFFICIENT

Re: If a and b are integers, and |a| > |b|, is a |b| < a [#permalink]

Show Tags

28 Jul 2010, 10:11

utfan2424 wrote:

Is this really a 700+ question?

I got the question from MHGMAT; maybe it is a 700+ category question under stressed condition, especially given the test conditions required to establish a precise position.
_________________

KUDOS me if you feel my contribution has helped you.

Re: If a and b are integers, and |a| > |b|, is a |b| < a [#permalink]

Show Tags

28 Jul 2010, 15:50

Bunuel wrote:

Bunuel wrote:

thailandvc wrote:

If a and b are integers, and |a| > |b|, is a · |b| < a – b?

(1) a < 0

(2) ab >= 0

anybody have a solution for this (under 2 minute). testing value takes way too long here.

E

Given: \(|a|>|b|\) Question: is \(a*|b|<a-b\)?

(1) \(a<0\). If \(a=-3\) and \(b=0\), then \(a*|b|=0>a-b=-3\) and the answer is NO but if \(a=-3\) and \(b=-1\), then \(a*|b|=-3<a-b=-2\) and the answer is YES. Two different answers. Not sufficient.

(2) \(ab\geq{0}\)

Above example works here as well: \(a=-3\) and \(b=0\) --> \(a*|b|=0>a-b=-3\) --> answer NO; \(a=-3\) and \(b=-1\) --> \(a*|b|=-3<a-b=-2\) --> answer YES. Two different answers. Not sufficient.

(1)+(2) Again the same example satisfies the stem and both statements and gives two different answers to the question whether \(a*|b|<a-b\). Hence not sufficient.

Answer E.

Please tell me if my reasonning is bad

|a| > |b|, is a · |b| < a – b?

(1) a < 0 ==> a · |b|<0 since nothing about b we can not conclude ==> not sufficient (2) ab >= 0

==> a&b neg or a and b neg but no information abt a relatif to b

1 +2 a<0 ==> b <0 not suff

Nevetheless if ab was neg then the ans would be C is tit correct?

Re: If a and b are integers, and |a| > |b|, is a |b| < a [#permalink]

Show Tags

01 Aug 2010, 08:34

If a and b are integers, and |a| > |b|, is a · |b| < a – b? (1) a < 0 (2) ab >= 0 (1) since |a| > |b| => -a < b < a now a<0 : if b<0 then a.|b| < a also a - b > a so clearly a.|b|< a - b but if b=0 then a.|b| =0 and a - b = a thus a.|b| > a - b (0>a) --- so here itself we see that for two diff ranges of b , a<0 is insufficient to determine the inequality completely. So 1 is insuff

(2) ab>=0 --- this means either both a and b are negative (as seen above) OR b = 0 since a cannot be 0 because it is stated that |a|>|b| so a must be non-zero OR both a and b are greater than 0. As we have seen in (1) we get two different values for a<0, b<0 AND a<0 b=0 combo. So 2 also is insuff

combining 1 and 2 changes nothing - still the same conditon remains. So insufficient.

It's a damned tough problem. I wish I had the brains of Bunuel to pick up relevant numbers quickly and solve the problem as he has shown in his solution.

Re: If a and b are integers, and |a| > |b|, is a |b| < a [#permalink]

Show Tags

29 Sep 2010, 02:23

is a - |b| < a - b canceling a from both sides , the eqn becomes |b| > b so basically the eqn is asking if b is -ve or not . Therefore , we will check for that

1 . a < 0 , does not talk about b 2. ab >= 0 implies a>=0 and b>=0 or a<=0 and b<=0

therefore not sufficient

combining both we get b<=0 which is also not sufficient since b=0 does not satisfy the main question . I hope doing this way you feel faster. Also I think that the condition |a| > |b| is irrelevant to the question.

Re: If a and b are integers, and |a| > |b|, is a |b| < a [#permalink]

Show Tags

24 Aug 2012, 12:53

Nice explanation Chris. But I don't think that picking up numbers is the best strategy. Can you tell how to decide which method , mathematics or picking numbers , to be chosen after seeing the question. Moreover can you tell me my mistake in the post just before your post.
_________________

Re: If a and b are integers, and |a| > |b|, is a |b| < a [#permalink]

Show Tags

24 Aug 2012, 14:00

1

This post was BOOKMARKED

siddharthasingh wrote:

Nice explanation Chris. But I don't think that picking up numbers is the best strategy. Can you tell how to decide which method , mathematics or picking numbers , to be chosen after seeing the question. Moreover can you tell me my mistake in the post just before your post.

Hi siddharthasingh,

I think choosing between solving a problem conceptually, algebraically, or by picking numbers is really up to what you are comfortable with. For myself, when it comes to these types of questions with lots of absolute values, equations, and , I know I figure it out quicker either conceptually or by picking numbers. It's basically the best strategy for myself. I basically came to this conclusion after doing lots of practice problems with the help of my error log.

Now, keep in mind I probably would not have done ALL those calculations in my post. I'm not aiming to solve the question, I just want to see if I have enough information to solve the question. Once I came up with a "yes" AND a "no" for each statement, I would have stopped. I just wrote it all out to explain.

|a|>|b| => either i)a>b ii)a<-b Actually, there is a multitude of possibilities. What this statement means is that a is farther away from 0 than b is. Both positive: a>b both negative: a<b a neg, b pos: a<b where 0-a>b-0 a pos, b neg: a>b where a-0>0-b So I personally think it would be easier to view the statement conceptually, knowing that |a|>|b| means the distance of a is greater than the distance of b.

Now, please keep in mind that the above scenarios are POSSIBILITIES. Only 1 is true. We want to figure out if they're both positive or not. 1) a<0 On combining i and 1, b<a<0. Therefore a-b is positive. a|b| is negative. On combining ii and 1) Two cases are emerging. a-------0-------(-b) a-------(-b)------0

We don't know if b<a. we only know that |a|>|b|. knowing that a is a NEGATIVE gets rid of a few possiblities above. A<0, and be can be EITHER neg, pos, or both.

i) b=pos while |a|>|b| (neg)|pos|<(neg)-(pos)....neg<pos... YES ii)b=neg while |a|>|b| (neg)|neg|<(neg)-(neg)....neg<neg....YES Keep in mind that in this case a|b| will be a bigger negative than a-b iii)b=0 (neg)|0|<(neg)-0....0<neg.... NO.

Re: If a and b are integers, and |a| > |b|, is a |b| < a [#permalink]

Show Tags

24 Sep 2013, 05:47

Thank you so much for the explanation. I completely ruled out the possibility for a and b to be equivalent to zero. I will keep that in mind for my future questions. Helps a lot! thanks

Re: If a and b are integers, and |a| > |b|, is a |b| < a [#permalink]

Show Tags

13 Feb 2015, 06:38

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.
_________________

It’s quickly approaching two years since I last wrote anything on this blog. A lot has happened since then. When I last posted, I had just gotten back from...

Since my last post, I’ve got the interview decisions for the other two business schools I applied to: Denied by Wharton and Invited to Interview with Stanford. It all...

Marketing is one of those functions, that if done successfully, requires a little bit of everything. In other words, it is highly cross-functional and requires a lot of different...