M14, 33 (If ab≠0 and |a|<|b|, which of the following must) : Retired Discussions [Locked]
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 23 Jan 2017, 13:03

### 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 June
Open Detailed Calendar

# M14, 33 (If ab≠0 and |a|<|b|, which of the following must)

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
Manager
Joined: 12 May 2012
Posts: 83
Location: India
Concentration: General Management, Operations
GMAT 1: 650 Q51 V25
GMAT 2: 730 Q50 V38
GPA: 4
WE: General Management (Transportation)
Followers: 2

Kudos [?]: 91 [0], given: 14

M14, 33 (If ab≠0 and |a|<|b|, which of the following must) [#permalink]

### Show Tags

09 Jun 2012, 07:10
This post is edited to rectify the incorrect choice.

If ab≠0 and |a|<|b|, which of the following must be negative?

A. (a/b)− (b/a)
B. (a−b)/(a+b)
C. a^b−b^a
D. a(b/(a−b))
E. (b−a)/b

[Reveal] Spoiler:
OA: B

OE:
[Reveal] Spoiler:
Solution
|a|<|b| means that a2<b2 → a2−b2<0 → (a−b)(a+b)<0, so a−b and a+b have the opposite signs, which means that a−ba+b will always be negative.

To discard other options consider a=−1 and b=2.

Last edited by manulath on 09 Jun 2012, 07:37, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 36618
Followers: 7099

Kudos [?]: 93556 [1] , given: 10578

Re: M14, 33 (If ab≠0 and |a|<|b|, which of the following must) [#permalink]

### Show Tags

09 Jun 2012, 07:16
1
KUDOS
Expert's post
If $$ab\neq{0}$$ and $$|a|<|b|$$, which of the following must be negative?

A. $$\frac{a}{b} - \frac{b}{a}$$

B. $$\frac{a-b}{a+b}$$

C. $$a^b-b^a$$

D. $$\frac{ab}{a-b}$$

E. $$\frac{b-a}{b}$$

$$|a|<|b|$$ means that $$a^2<b^2$$ --> $$a^2-b^2<0$$ --> $$(a-b)(a+b)<0$$, so $$a-b$$ and $$a+b$$ have the opposite signs, which means that $$\frac{a-b}{a+b}$$ will always be negative.

To discard other options consider $$a=-1$$ and $$b=2$$.
_________________
Manager
Joined: 12 May 2012
Posts: 83
Location: India
Concentration: General Management, Operations
GMAT 1: 650 Q51 V25
GMAT 2: 730 Q50 V38
GPA: 4
WE: General Management (Transportation)
Followers: 2

Kudos [?]: 91 [0], given: 14

Re: M14, 33 (If ab≠0 and |a|<|b|, which of the following must) [#permalink]

### Show Tags

09 Jun 2012, 07:28
manulath wrote:
If ab≠0 and |a|<|b|, which of the following must be negative?

A. (a/b)− (b/b)
B. (a−b)/(a+b)
C. a^b−b^a
D. a(b/(a−b))
E. (b−a)/b

With respect to the Choice A : (a/b)− (b/b)

as ab≠0, what ever the value of b,
b/b is always 1
choice A reduces to a/b-1

as |a|<|b| ......... a/b will always be less than 1

scenario 1: a>0, b>0
clearly a/b <1

scenario 2: a<0, b<0
in a/b, the negative signs will cancel each other
Hence once again a/b<1

scenario 3 and 4: a<0, b>0 or a>0,b<0
in a/b, one value is +ve and other is -ve
Hence a/b will be -ve
that is to say a/b<0
or to say a/b<1

As we see that in all the above cases a/b < 1
in choice A: (a/b)-(b/b) will always be -ve

Where did I went wrong?

Even if I put the values give in OE

manulath wrote:
OE: Solution
|a|<|b| means that a2<b2 → a2−b2<0 → (a−b)(a+b)<0, so a−b and a+b have the opposite signs, which means that a−ba+b will always be negative.

[highlight]To discard other options consider a=−1 and b=2[/highlight]

A. (a/b)− (b/b) => (-1/2) - (2/2) => -1/2 - 1 = -3/2 a negative value
Math Expert
Joined: 02 Sep 2009
Posts: 36618
Followers: 7099

Kudos [?]: 93556 [0], given: 10578

Re: M14, 33 (If ab≠0 and |a|<|b|, which of the following must) [#permalink]

### Show Tags

09 Jun 2012, 07:29
manulath wrote:
manulath wrote:
If ab≠0 and |a|<|b|, which of the following must be negative?

A. (a/b)− (b/b)
B. (a−b)/(a+b)
C. a^b−b^a
D. a(b/(a−b))
E. (b−a)/b

With respect to the Choice A : (a/b)− (b/b)

as ab≠0, what ever the value of b,
b/b is always 1
choice A reduces to a/b-1

as |a|<|b| ......... a/b will always be less than 1

scenario 1: a>0, b>0
clearly a/b <1

scenario 2: a<0, b<0
in a/b, the negative signs will cancel each other
Hence once again a/b<1

scenario 3 and 4: a<0, b>0 or a>0,b<0
in a/b, one value is +ve and other is -ve
Hence a/b will be -ve
that is to say a/b<0
or to say a/b<1

As we see that in all the above cases a/b < 1
in choice A: (a/b)-(b/b) will always be -ve

Where did I went wrong?

Even if I put the values give in OE

manulath wrote:
OE: Solution
|a|<|b| means that a2<b2 → a2−b2<0 → (a−b)(a+b)<0, so a−b and a+b have the opposite signs, which means that a−ba+b will always be negative.

[highlight]To discard other options consider a=−1 and b=2[/highlight]

A. (a/b)− (b/b) => (-1/2) - (2/2) => -1/2 - 1 = -3/2 a negative value

There is a typo in option A. It should read a/b-b/a.
_________________
Manager
Joined: 12 May 2012
Posts: 83
Location: India
Concentration: General Management, Operations
GMAT 1: 650 Q51 V25
GMAT 2: 730 Q50 V38
GPA: 4
WE: General Management (Transportation)
Followers: 2

Kudos [?]: 91 [0], given: 14

Re: M14, 33 (If ab≠0 and |a|<|b|, which of the following must) [#permalink]

### Show Tags

09 Jun 2012, 07:33
Bunuel wrote:
A. $$\frac{a}{b} - \frac{b}{a}$$

Okay it seems that question I got was incorrect.
I have send the screenshot to you as pm.
Intern
Joined: 19 Sep 2011
Posts: 29
WE: Consulting (Consulting)
Followers: 0

Kudos [?]: 5 [0], given: 4

Re: M14, 33 (If ab≠0 and |a|<|b|, which of the following must) [#permalink]

### Show Tags

20 Sep 2012, 10:47
Hi Bunuel,

Could you please explain as to how did you know that a= -1 and b = 2 would make all the other answers invalid?was it just hit and trial or was there any specific reason for choosing these two values?

Thanks.
Math Expert
Joined: 02 Sep 2009
Posts: 36618
Followers: 7099

Kudos [?]: 93556 [0], given: 10578

Re: M14, 33 (If ab≠0 and |a|<|b|, which of the following must) [#permalink]

### Show Tags

20 Sep 2012, 11:37
negative wrote:
Hi Bunuel,

Could you please explain as to how did you know that a= -1 and b = 2 would make all the other answers invalid?was it just hit and trial or was there any specific reason for choosing these two values?

Thanks.

With a certain algebraic manipulations with the expression in the stem we can get that B is the correct answer. So, the example which discard other options are just to illustrate that they are wrong, and yes you can find the proper numbers for that by trial and error.
_________________
Intern
Joined: 29 Jul 2012
Posts: 29
GMAT 1: Q V
Followers: 0

Kudos [?]: 14 [0], given: 7

Re: M14, 33 (If ab≠0 and |a|<|b|, which of the following must) [#permalink]

### Show Tags

29 Apr 2013, 18:28
I thought |x| = \sqrt{x^2}? How do you arrive at |a| = a^2?
Manager
Status: Pushing Hard
Affiliations: GNGO2, SSCRB
Joined: 30 Sep 2012
Posts: 89
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.33
WE: Analyst (Health Care)
Followers: 1

Kudos [?]: 83 [0], given: 11

Re: M14, 33 (If ab≠0 and |a|<|b|, which of the following must) [#permalink]

### Show Tags

29 Apr 2013, 19:58
manulath wrote:
This post is edited to rectify the incorrect choice.

If ab≠0 and |a|<|b|, which of the following must be negative?

A. (a/b)− (b/a)
B. (a−b)/(a+b)
C. a^b−b^a
D. a(b/(a−b))
E. (b−a)/b

[Reveal] Spoiler:
OA: B

OE:
[Reveal] Spoiler:
Solution
|a|<|b| means that a2<b2 → a2−b2<0 → (a−b)(a+b)<0, so a−b and a+b have the opposite signs, which means that a−ba+b will always be negative.

To discard other options consider a=−1 and b=2.

I've also done the way Bunuel explained ........................... as
Given .......... $$|a|<|b|$$ i.e., $$a^2<b^2$$
Therefore, $$a^2-b^2<0$$ & therefore, $$(a-b)(a+b)<0$$ & ultimately divide both sides with $$(a+b)$$
Hence, , I got ... $$\frac{a-b}{a+b}$$ < 0
_________________

If you don’t make mistakes, you’re not working hard. And Now that’s a Huge mistake.

Math Expert
Joined: 02 Sep 2009
Posts: 36618
Followers: 7099

Kudos [?]: 93556 [0], given: 10578

Re: M14, 33 (If ab≠0 and |a|<|b|, which of the following must) [#permalink]

### Show Tags

30 Apr 2013, 00:03
youngkacha wrote:
I thought |x| = \sqrt{x^2}? How do you arrive at |a| = a^2?

$$a^2<b^2$$ is obtained by squaring $$|a|<|b|$$ (we can safely square $$|a|<|b|$$ since both sides of the inequality are non-negative).

Hope it's clear.
_________________
Intern
Joined: 29 Jul 2012
Posts: 29
GMAT 1: Q V
Followers: 0

Kudos [?]: 14 [0], given: 7

Re: M14, 33 (If ab≠0 and |a|<|b|, which of the following must) [#permalink]

### Show Tags

30 Apr 2013, 14:42
Bunuel wrote:
youngkacha wrote:
I thought |x| = \sqrt{x^2}? How do you arrive at |a| = a^2?

$$a^2<b^2$$ is obtained by squaring $$|a|<|b|$$ (we can safely square $$|a|<|b|$$ since both sides of the inequality are non-negative).

Hope it's clear.

Oh okay, I see now. This was a tough one for me.

Thank you.
Re: M14, 33 (If ab≠0 and |a|<|b|, which of the following must)   [#permalink] 30 Apr 2013, 14:42
Similar topics Replies Last post
Similar
Topics:
19 M14#10 19 18 Mar 2009, 12:41
20 M14 #19 19 02 Feb 2009, 21:06
5 M14 #18 19 02 Feb 2009, 20:55
6 M14 #27 19 13 Nov 2008, 16:55
18 M14 #13 25 11 Nov 2008, 20:40
Display posts from previous: Sort by

# M14, 33 (If ab≠0 and |a|<|b|, which of the following must)

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

Moderator: Bunuel

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.