GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Dec 2018, 07:51

Expecting Soon:

R1 Admission Decisions from McCombs - Join Chat Room for Latest Updates

GMAT Club Daily Prep

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

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

Events & Promotions

Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• Happy Christmas 20% Sale! Math Revolution All-In-One Products!

December 20, 2018

December 20, 2018

10:00 PM PST

11:00 PM PST

This is the most inexpensive and attractive price in the market. Get the course now!
• Key Strategies to Master GMAT SC

December 22, 2018

December 22, 2018

07:00 AM PST

09:00 AM PST

Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.

If ab ≠ 0, is ab > a/b ?

Author Message
TAGS:

Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6661
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If ab ≠ 0, is ab > a/b ?  [#permalink]

Show Tags

05 Jan 2016, 21:45
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If ab ≠ 0, is ab > a/b ?

(1) |b| > 1

(2) ab + a/b > 0

Modify the original condition and the question and multiply b^2 on the both equations, which becomes ab^3>ab? --> ab^3-ab>0? -->ab(b^2-1)>0?. There are 2 variables(a,b), which should match with the number of equations. So you need 2 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make C the answer.
When 1) &2), |b|>1 -> b^2>1, ab and a/b get to have the same sign in 2). That is, ab>0 -> a/b>0(this is divided by b^2 and as b^2 is a positive number, direction of the sign doesn’t change.) So, 2) becomes ab>0, which is yes and sufficient. Therefore, the answer is C.

 For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Intern
Joined: 22 Oct 2015
Posts: 17
If ab ≠ 0, is ab > a/b ?  [#permalink]

Show Tags

09 Jan 2016, 09:01
Bunuel wrote:
If ab ≠ 0, is ab > a/b ?

Is $$ab > \frac{a}{b}$$? --> is $$ab - \frac{a}{b}>0$$? --> $$\frac{a(b^2-1)}{b}>0$$? --> $$\frac{a}{b}*(b^2-1)>0$$?

(1) |b| > 1 --> both sides are non-negative, thus we can square: $$b^2>1$$ --> $$b^2-1>0$$. We need to know the sign of a/b. Not sufficient.

(2) ab + a/b > 0. Notice that ab and a/b have the same sign. Both of them cannot be negative, because in this case their sum would also be negative, therefore both are positive: a/b > 0. We need to know the sign of b^2-1. Not sufficient.

(1)+(2) $$b^2-1>0$$ and $$\frac{a}{b} > 0$$, thus their product $$\frac{a}{b}*(b^2-1)>0$$. Sufficient.

Hope it's clear.

$$ab > \frac{a}{b}$$

Could someone explain if instead of moving the a/b to the left side, we multiple by b on both sides?

$$ab > \frac{a}{b}$$ Multiple by b on both sides
$$ab^2 > a$$ Then divide by a
$$b^2 > 1$$

I assume this operation is not allowed, by can someone explain to me why? Could it be because we do not know the sign of b?
CEO
Joined: 20 Mar 2014
Posts: 2631
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: If ab ≠ 0, is ab > a/b ?  [#permalink]

Show Tags

09 Jan 2016, 09:13
ZaydenBond wrote:

Could someone explain if instead of moving the a/b to the left side, we multiple by b on both sides?

$$ab > \frac{a}{b}$$ Multiple by b on both sides
$$ab^2 > a$$ Then divide by a
$$b^2 > 1$$

I assume this operation is not allowed, by can someone explain to me why? Could it be because we do not know the sign of b?

Its because of the most important rule in inequalities. You need to reverse the sign of the inequality when you multiple by a negative quantity.

In the question at hand, you do not know whether b>0. If it is, then yes you can multiply the inequality by 'b' but if b<0 then you must reverse the sign of inequalilty. You can also remember this rule by the following example.

You know 2>1 but what about -2 and -1? -2<-1 or in the other words, when you are given 2>1 and you want to multiple throughout by -1, you get -2 < -1 (with reversed sign).

This is the reason why it is much less time consuming to bring a/b to the other side than to multiply throughout by 'b' as you do not know the sign of 'b'

Hope this helps.
Senior SC Moderator
Joined: 14 Nov 2016
Posts: 1324
Location: Malaysia
Re: If ab ≠ 0, is ab > a/b ?  [#permalink]

Show Tags

02 Feb 2017, 16:49
gmatquant25 wrote:
If $$ab ≠ 0$$, is $$ab > \frac{a}{b}$$?

(1) $$|b| > 1$$

(2) $$ab + \frac{a}{b} > 0$$

Solution from "Thursdays With Ron"
Attachments

Untitled.jpg [ 181.2 KiB | Viewed 584 times ]

_________________

"Be challenged at EVERY MOMENT."

“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”

"Each stage of the journey is crucial to attaining new heights of knowledge."

Non-Human User
Joined: 09 Sep 2013
Posts: 9208
Re: If ab ≠ 0, is ab > a/b ?  [#permalink]

Show Tags

24 Sep 2018, 06:54
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: If ab ≠ 0, is ab > a/b ? &nbs [#permalink] 24 Sep 2018, 06:54

Go to page   Previous    1   2   [ 25 posts ]

Display posts from previous: Sort by