For any non-zero a and b that satisfy |ab| = ab and |a| = -a : Problem Solving (PS)

kannn

Intern

Joined: 26 Mar 2007

Posts: 49

Concentration: General Management, Leadership

Schools: Thunderbird '15

For any non-zero a and b that satisfy |ab| = ab and |a| = -a [#permalink]

08 May 2011, 05:59

1

Kudos

25

Bookmarks

00:00

A

B

C

D

E

Difficulty:

65% (hard)

Question Stats:

55% (01:58) correct

45% (02:07) wrong

based on 486 sessions

Hide Show timer Statistics

For any non-zero a and b that satisfy |ab| = ab and |a| = -a

|b - 4| + |ab - b| = ?

a) ab - 4
b) 2b - ab - 4
c) ab + 4
d) ab - 2b + 4
e) 4 - ab

Show Answer

Official Answer

Official Answer and Stats are available only to registered users. Register/Login.

beyondgmatscore

Manager

Joined: 14 Feb 2011

Posts: 103

Re: For any non-zero a and b that satisfy |ab| = ab and |a| = -a [#permalink]

08 May 2011, 07:08

11

Kudos

4

Bookmarks

kannn wrote:

For any non-zero a and b that satisfy |ab| = ab and |a| = -a

|b - 4| + |ab - b| = ?

a) ab - 4
b) 2b - ab - 4
c) ab + 4
d) ab - 2b + 4
e) 4 - ab

Since $|a| = -a$, a is negative. Similarly, since $|ab| = ab$, a and b are the same sign so b is also negative.

Lets see $|b - 4|$, since b and -4 are both negative $|b - 4|$ will actually equal $|b| + 4$

Similarly, $|ab-b|$ would equal $ab + |b|$, so expression becomes $ab + 2|b| + 4$

Since $|b| = -b$, the expression reduces to $ab -2b + 4$

So, D is the answer

L

GMATinsight

GMAT Club Legend

Joined: 08 Jul 2010

Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator

Posts: 5951

Location: India

GMAT: QUANT+DI EXPERT

Schools: IIM (A) ISB '24

GMAT 1: 750 Q51 V41

WE:Education (Education)

Re: For any non-zero a and b that satisfy |ab| = ab and |a| = -a [#permalink]

21 Jul 2015, 10:04

4

Kudos

5

Bookmarks

Expert Reply

kannn wrote:

For any non-zero a and b that satisfy |ab| = ab and |a| = -a

|b - 4| + |ab - b| = ?

a) ab - 4
b) 2b - ab - 4
c) ab + 4
d) ab - 2b + 4
e) 4 - ab

|a| = -a Suggests that 'a' is Negative

|ab| = ab Suggests that 'ab' is Positive

'ab' is Positive Suggests that 'a' and 'b' have same Sign i.e. either both positive or both negative

But since 'a' is Negative therefore 'b' is Negative too.

Since b is negative so |b - 4| = -b+4

Since ab is Positive and b is Negative so |ab - b| = ab - b

i.e. |b - 4| + |ab - b| = -b+4 + ab - b = ab - 2b + 4

Answer: Option D

gmat1220

Senior Manager

Joined: 03 Feb 2011

Status:Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.

Affiliations: University of Chicago Booth School of Business

Posts: 472

Re: For any non-zero a and b that satisfy |ab| = ab and |a| = -a [#permalink]

Updated on: 15 May 2011, 21:28

I tried two values

a is negative bcos of the constraint |a| = -a. Since a is negative b is negative bcos of absolute value |ab| = ab constraint. Absolute value is non negative.

Now put a = -1 and b = -2. Only D is left.

Hence the answer is D. I will like to see some algebraic explanations though.

kannn wrote:

For any non-zero a and b that satisfy |ab| = ab and |a| = -a

|b - 4| + |ab - b| = ?

a) ab - 4
b) 2b - ab - 4
c) ab + 4
d) ab - 2b + 4
e) 4 - ab

Originally posted by gmat1220 on 08 May 2011, 06:25.
Last edited by gmat1220 on 15 May 2011, 21:28, edited 1 time in total.

B

subhashghosh

Retired Moderator

Joined: 16 Nov 2010

Posts: 909

Location: United States (IN)

Concentration: Strategy, Technology

Re: For any non-zero a and b that satisfy |ab| = ab and |a| = -a [#permalink]

08 May 2011, 07:30

3

Kudos

|ab| = ab and |a| = -a

=> b is also negative.

So

|b-4| + |ab -b|

= -(b-4) (as b-4 is negative, so expression is totally negative) + ab - b ( as ab is positive and -b is positive, so expression is totally positive)

= 4 - b + ab - b

= ab - 2b + 4

Answer - D
_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

Signature Read More

amit2k9

Director

Joined: 08 May 2009

Status:There is always something new !!

Affiliations: PMI,QAI Global,eXampleCG

Posts: 553

Re: For any non-zero a and b that satisfy |ab| = ab and |a| = -a [#permalink]

08 May 2011, 09:18

using values as both a and b are negative.

a = -1 and b = -2 also a = -2 and b = -3.

gives d.

PallavTandon

Intern

Joined: 29 Mar 2011

Posts: 9

Re: For any non-zero a and b that satisfy |ab| = ab and |a| = -a [#permalink]

08 May 2011, 13:01

Given that |a|=-a which means a is -ve
Also |ab|=ab which means both a,b are either both -ve or both +ve
since a is negative, b is also negative.

Considering this
|b-4| will always be a -ve expression. So if we remove mod signs, it becomes 4-b
|ab-b| will always be a +ve expression since ab is +ve and b is -ve. To remove mod signs it will be +ve expression. ab-b

So |b-4| + |ab-b| = 4-b+ab-b
= 4-2b+ ab
= D

Spidy001

Senior Manager

Joined: 01 Feb 2011

Posts: 309

Re: For any non-zero a and b that satisfy |ab| = ab and |a| = -a [#permalink]

08 May 2011, 14:11

slight variation of @beyondgmatscore approach

|a| = -a => a<0

ab>0 => a<0, b<0

now we have |b-4| + |ab-b|

as b<0, we know |b|=-b =>b= -|b|

given expression = |-|b|-4| +|ab +|b||

=|b|+4+ab+|b|= ab-2b+4 ( as |b|= -b)

Answer is D.

RussianDude

Intern

Joined: 11 Apr 2015

Posts: 28

Location: Germany

Concentration: General Management, Entrepreneurship

Schools: INSEAD Jan '17 (S) HEC '18 IE '18 (I)

GPA: 3.1

WE:Project Management (Energy and Utilities)

Re: For any non-zero a and b that satisfy |ab| = ab and |a| = -a [#permalink]

04 Aug 2015, 11:30

hey guys, I think I am missing something here...

howcome |a| = -a? I thought that an absolute value can never be negative?

G

ENGRTOMBA2018

SVP

Joined: 20 Mar 2014

Posts: 2363

Concentration: Finance, Strategy

Schools: Kellogg '18 (M)

GMAT 1: 750 Q49 V44 Verified score

GPA: 3.7

WE:Engineering (Aerospace and Defense)

Re: For any non-zero a and b that satisfy |ab| = ab and |a| = -a [#permalink]

04 Aug 2015, 11:45

1

Kudos

RussianDude wrote:

hey guys, I think I am missing something here...

howcome |a| = -a? I thought that an absolute value can never be negative?

There are 3 things when we talk about "absolute values"

1. They can not be negative. Example, |-6| = 6 and |7| = 7, |0| =0 etc.
2. |a| = -a ONLY IF a <0 . So lets say, a =-6, then |-6| = 6 (a POSITIVE) value.
3. |a| = a for a $\geq$0

What you are saying is correct that |a| can never be NEGATIVE but as per #2 above, |a| = -a when a < 0 . Thus when a <0 then -a will be >0 (positive).

Hope this helps.
_________________

Signature Read More

L

GMATinsight

GMAT Club Legend

Joined: 08 Jul 2010

Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator

Posts: 5951

Location: India

GMAT: QUANT+DI EXPERT

Schools: IIM (A) ISB '24

GMAT 1: 750 Q51 V41

WE:Education (Education)

Re: For any non-zero a and b that satisfy |ab| = ab and |a| = -a [#permalink]

04 Aug 2015, 11:49

1

Kudos

Expert Reply

RussianDude wrote:

hey guys, I think I am missing something here...

howcome |a| = -a? I thought that an absolute value can never be negative?

-a will be positive for negative values of a

E.g. if a=-2, then |a| = 2= -(-2) = -a

I.e. if|a| = -a then a must be negative

RussianDude

Intern

Joined: 11 Apr 2015

Posts: 28

Location: Germany

Concentration: General Management, Entrepreneurship

Schools: INSEAD Jan '17 (S) HEC '18 IE '18 (I)

GPA: 3.1

WE:Project Management (Energy and Utilities)

Re: For any non-zero a and b that satisfy |ab| = ab and |a| = -a [#permalink]

04 Aug 2015, 12:08

thanks guys, it is clear now. Kudos for you :-)

P

mvictor

Board of Directors

Joined: 17 Jul 2014

Posts: 2164

Location: United States (IL)

Concentration: Finance, Economics

Schools: Stanford '20 (WD)

GMAT 1: 650 Q49 V30 Verified score

GPA: 3.92

WE:General Management (Transportation)

Re: For any non-zero a and b that satisfy |ab| = ab and |a| = -a [#permalink]

25 Nov 2015, 19:18

solved it as well through assigning variables
if |a| = -a that means that a is negative and the only case when |ab|=ab is when b is negative as well
suppose b=-3 and a=-2

by plugging in numbers, only D works

B

sharankotagiri

Intern

Joined: 10 Jun 2019

Posts: 7

Re: For any non-zero a and b that satisfy |ab| = ab and |a| = -a [#permalink]

21 Jun 2019, 00:03

S

wizmaverick

Intern

Joined: 22 May 2019

Posts: 17

Location: India

Schools: Darden '23 (A) ISB'22 (A) IESE'23 (D) Haas '23 (WL) Anderson '23 (I) Tepper '23 (A$) McCombs '23 (A$) Fuqua '23 (D)

GMAT 1: 760 Q50 V42 Verified score

Re: For any non-zero a and b that satisfy |ab| = ab and |a| = -a [#permalink]

21 Jun 2019, 00:45

If you read the question carefully

Quote:

For any non-zero a and b that satisfy

The underlined part of the above statement tells us that plugging in values for a and b, which satisfy the below conditions, into the five options will reveal the correct answer.

Quote:

|ab| = ab and |a| = -a

Since |a| = -a, a is a negative quantity. Since |ab| = ab, and a is a negative quantity, b must be a negative quantity as well.
The question setter will definitely anticipate a lot of students using this approach, and using -1 and -1. Luckily plugging in [-1,-1] does reveal that option (D) is correct. I'd go (and went) with [-2,-2]

bumpbot

Non-Human User

Joined: 09 Sep 2013

Posts: 32535

Re: For any non-zero a and b that satisfy |ab| = ab and |a| = -a [#permalink]

06 Jun 2023, 00:08

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.
_________________

Signature Read More

gmatclubot

Re: For any non-zero a and b that satisfy |ab| = ab and |a| = -a [#permalink]

06 Jun 2023, 00:08

GMAT Problem Solving (PS) Questions

For any non-zero a and b that satisfy |ab| = ab and |a| = -a

GMAT Question Banks