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

It is currently 20 Jul 2018, 11:14

Close

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
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.

Close

Request Expert Reply

Confirm Cancel

M04-11

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47157
M04-11  [#permalink]

Show Tags

New post 16 Sep 2014, 00:22
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

58% (00:50) correct 42% (00:41) wrong based on 200 sessions

HideShow timer Statistics

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47157
Re M04-11  [#permalink]

Show Tags

New post 16 Sep 2014, 00:22
Official Solution:


(1) \(|j| = j^{-1}\). Rewrite as \(|j|*j=1\). From that we have \(j=1\) (here \(j\) cannot be a negative number, since in this case we would have \(|j|*j=\text{positive}*\text{negative}=\text{negative} \ne 1\)). Sufficient.

(2) \(j^j = 1\). Again only one solution: \(j=1\). Sufficient.


Answer: D
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Current Student
User avatar
Joined: 06 Mar 2014
Posts: 257
Location: India
GMAT Date: 04-30-2015
Reviews Badge
Re: M04-11  [#permalink]

Show Tags

New post 19 Sep 2014, 01:57
As per ii) j^j = 1.

So 1 can also be equal to j^0.

Therefore, j^j = j^0. so same base power is equated which brings us to: j=0.

But 0^0 = 0 so that is not our solution.

hence j=1, as any number raised to same power if = 1 then that number is 1.

Am i right in assuming the following rule (highlighted one) based on the above calculations ?

Kindly shed some light on it.
Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47157
Re: M04-11  [#permalink]

Show Tags

New post 19 Sep 2014, 02:06
2
earnit wrote:
As per ii) j^j = 1.

So 1 can also be equal to j^0.

Therefore, j^j = j^0. so same base power is equated which brings us to: j=0.

But 0^0 = 0 so that is not our solution.

hence j=1, as any number raised to same power if = 1 then that number is 1.

Am i right in assuming the following rule (highlighted one) based on the above calculations ?

Kindly shed some light on it.


Sorry, but not following you...

Anyway, 0^0, in some sources equals to 1, some mathematicians say it's undefined. But you won't need this for the GMAT because the case of 0^0 is not tested on the GMAT. So on the GMAT the possibility of 0^0 is always ruled out (in our question it's also rules out, notice that we are given that j is not 0).
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
Joined: 17 Mar 2014
Posts: 140
Location: United States
Concentration: Entrepreneurship, Leadership
GPA: 3.97
GMAT ToolKit User Reviews Badge
Re: M04-11  [#permalink]

Show Tags

New post 19 Sep 2014, 03:07
Bunuel wrote:
earnit wrote:
As per ii) j^j = 1.

So 1 can also be equal to j^0.

Therefore, j^j = j^0. so same base power is equated which brings us to: j=0.

But 0^0 = 0 so that is not our solution.

hence j=1, as any number raised to same power if = 1 then that number is 1.

Am i right in assuming the following rule (highlighted one) based on the above calculations ?

Kindly shed some light on it.


Sorry, but not following you...

Anyway, 0^0, in some sources equals to 1, some mathematicians say it's undefined. But you won't need this for the GMAT because the case of 0^0 is not tested on the GMAT. So on the GMAT the possibility of 0^0 is always ruled out (in our question it's also rules out, notice that we are given that j is not 0).


Thanks for pointing that out. Yes, I was confused because 0^0 = 1 (actually several answers to this solution), some say its 0, some say its undefined.

But, yes the question says "j is not equal to 0".
_________________

KUDOS!!!, I need them too :)

Intern
Intern
avatar
Joined: 30 Aug 2014
Posts: 1
Location: United States
Concentration: Accounting
GPA: 3.9
WE: Accounting (Consumer Products)
Premium Member
Re: M04-11  [#permalink]

Show Tags

New post 13 Apr 2015, 17:02
What if J=-1?
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47157
Re: M04-11  [#permalink]

Show Tags

New post 14 Apr 2015, 04:41
Senior Manager
Senior Manager
avatar
D
Joined: 06 Jan 2015
Posts: 399
Location: India
Concentration: Operations, Finance
GPA: 3.35
WE: Information Technology (Computer Software)
Re: M04-11  [#permalink]

Show Tags

New post 18 Feb 2016, 22:12
Hi Bunuel,

Not getting where am I going wrong with statement 1

|j|=j^-1

j=1/j

j^2=1

And j=-(1/j)

j^2=-1

Can you please help me.
_________________

आत्मनॊ मोक्षार्थम् जगद्धिताय च

Resource: GMATPrep RCs With Solution

Expert Post
3 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47157
Re: M04-11  [#permalink]

Show Tags

New post 19 Feb 2016, 01:55
3
NandishSS wrote:
Hi Bunuel,

Not getting where am I going wrong with statement 1

|j|=j^-1

j=1/j

j^2=1

And j=-(1/j)

j^2=-1

Can you please help me.


j^2=-1 has no real solutions.

j^2=1 has two solutions j=-1 and j=1 but j=-1 does not satisfy |j|=j^(-1), so we are left with j=1 only.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Senior Manager
Senior Manager
avatar
D
Joined: 06 Jan 2015
Posts: 399
Location: India
Concentration: Operations, Finance
GPA: 3.35
WE: Information Technology (Computer Software)
Re: M04-11  [#permalink]

Show Tags

New post 20 Feb 2016, 03:25
Thanks a lot Bunuel!!!:-)
_________________

आत्मनॊ मोक्षार्थम् जगद्धिताय च

Resource: GMATPrep RCs With Solution

Manager
Manager
avatar
B
Joined: 27 Aug 2014
Posts: 82
Re: M04-11  [#permalink]

Show Tags

New post 25 Feb 2016, 09:59
Bunuel wrote:
If \(j \ne 0\), what is the value of \(j\) ?


(1) \(|j| = j^{-1}\)

(2) \(j^j = 1\)


Hi

For stmt 1, what I did was I squared both sides to get rid of the mod sign. So :

j^2=1/j^2

j^4=1
Hence j takes both 1 0r -1. not sufficient.

Pls advise. tx
1 KUDOS received
Current Student
avatar
S
Joined: 20 Mar 2014
Posts: 2641
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Premium Member Reviews Badge
M04-11  [#permalink]

Show Tags

New post 25 Feb 2016, 10:21
1
sinhap07 wrote:
Bunuel wrote:
If \(j \ne 0\), what is the value of \(j\) ?


(1) \(|j| = j^{-1}\)

(2) \(j^j = 1\)


Hi

For stmt 1, what I did was I squared both sides to get rid of the mod sign. So :

j^2=1/j^2

j^4=1
Hence j takes both 1 0r -1. not sufficient.

Pls advise. tx


When you square any equation, you are invariably increasing the number of solutions to twice the actual number of solution. A linear equation has 1 solution while a quadratic equation has 2 etc.

Statement 1 is linear in j and hence only 1 solution should be possible. When you square, make sure to check back the solutions by plugging them into the main equation and see which one actually satisfies the original linear equation.

After you got 1 and -1 as your solutions, -1 is rejected as it does not satisfy \(|j| = j^{-1}\). Thus, only j=1 satisfies the given conditions.

Hope this helps.
Intern
Intern
avatar
Joined: 23 Mar 2016
Posts: 14
Re: M04-11  [#permalink]

Show Tags

New post 17 Sep 2016, 04:59
can u please explain me where i m wrong?
if j=-1
|j|=-1 as if |x|=-x if x<0
then |j|*j=1(-1*-1)
-1 also satisfies this
:roll: :roll:
Intern
Intern
avatar
B
Joined: 04 Jun 2017
Posts: 2
CAT Tests
Re M04-11  [#permalink]

Show Tags

New post 08 Jun 2017, 20:37
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. how j^j = 1 results in j=1
Manager
Manager
avatar
G
Joined: 12 Jun 2016
Posts: 220
Location: India
Concentration: Technology, Leadership
WE: Sales (Telecommunications)
GMAT ToolKit User
Re: M04-11  [#permalink]

Show Tags

New post 23 Sep 2017, 06:15
Hello Bunuel,

Though I agree with the solution, I am not able to see where I am going wrong when solving for S1.Can you please check my work and suggest where I am going wrong?

S1: \(|J| = J^{-1}\)

Opening the Modulus we have

Case 1:

\(J = J^{-1}\)

\(J^2 = 1\)

\(J = ± 1\)

Case 2 :

\(-J = j^{-1}\)

\(-J^2 = 1\) (Undefined on GMAT).

Substituting Both J = 1 and J = -1 into the equation we can also see the equation is satisfied.

So, should we not conclude that J = ± 1 ?
_________________

My Best is yet to come!

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47157
Re: M04-11  [#permalink]

Show Tags

New post 23 Sep 2017, 07:19
1
susheelh wrote:
Hello Bunuel,

Though I agree with the solution, I am not able to see where I am going wrong when solving for S1.Can you please check my work and suggest where I am going wrong?

S1: \(|J| = J^{-1}\)

Opening the Modulus we have

Case 1:

\(J = J^{-1}\)

\(J^2 = 1\)

\(J = ± 1\)

Case 2 :

\(-J = j^{-1}\)

\(-J^2 = 1\) (Undefined on GMAT).

Substituting Both J = 1 and J = -1 into the equation we can also see the equation is satisfied.

So, should we not conclude that J = ± 1 ?


j = -1 does NOT satisfy |j| = j^(-1):

LHS = |-1| = 1 while RHS = (-1)^(-1) = -1.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
G
Joined: 12 Jun 2016
Posts: 220
Location: India
Concentration: Technology, Leadership
WE: Sales (Telecommunications)
GMAT ToolKit User
Re: M04-11  [#permalink]

Show Tags

New post 23 Sep 2017, 07:27
How silly of me! :roll: <Slapping myself now!>

Thank you so much Bunuel for correcting me!!

Bunuel wrote:
susheelh wrote:
Hello Bunuel,

Though I agree with the solution, I am not able to see where I am going wrong when solving for S1.Can you please check my work and suggest where I am going wrong?

S1: \(|J| = J^{-1}\)

Opening the Modulus we have

Case 1:

\(J = J^{-1}\)

\(J^2 = 1\)

\(J = ± 1\)

Case 2 :

\(-J = j^{-1}\)

\(-J^2 = 1\) (Undefined on GMAT).

Substituting Both J = 1 and J = -1 into the equation we can also see the equation is satisfied.

So, should we not conclude that J = ± 1 ?


j = -1 does NOT satisfy |j| = j^(-1):

LHS = |-1| = 1 while RHS = (-1)^(-1) = -1.

_________________

My Best is yet to come!

Intern
Intern
avatar
B
Joined: 22 Jan 2017
Posts: 34
GMAT ToolKit User
Re: M04-11  [#permalink]

Show Tags

New post 21 Oct 2017, 14:40
I understand that when you square both sides of an equation you create another solution that is potentially invalid due to some other parameter (equation, stipulation etc). But how is that happening here? I just multiplied both sides by j, I didn't square anything.

|j| = 1\j
|j| * j = 1

I then considered both cases to remove the modulus and found j = +/- 1.

Now, I am sure the best practice here is just always to check too see that both solutions work, but can someone explain to me here why I ended up with two solutions (one of which does not hold) without squaring both sides of the equation?

Thanks!
Intern
Intern
avatar
B
Joined: 09 Sep 2015
Posts: 25
Re: M04-11  [#permalink]

Show Tags

New post 05 Apr 2018, 22:57
Hi Guys

statement 1 : |j| * j = 1

Doesn't this equation have two solutions that is

-j * j = 1 (eq 1) & j * j = 1 (eq 2)

if j=1 then eq 2 satisfies not eq 1
but if j=-1 then eq 2 satisfies but not eq 1

We have two values of "j" here. Then Statement 1 must not be sufficient.

Am i missing something here ?
Any help is appreciated

Thanks.
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47157
Re: M04-11  [#permalink]

Show Tags

New post 06 Apr 2018, 02:12
amargad0391 wrote:
Hi Guys

statement 1 : |j| * j = 1

Doesn't this equation have two solutions that is

-j * j = 1 (eq 1) & j * j = 1 (eq 2)

if j=1 then eq 2 satisfies not eq 1
but if j=-1 then eq 2 satisfies but not eq 1

We have two values of "j" here. Then Statement 1 must not be sufficient.

Am i missing something here ?
Any help is appreciated

Thanks.


\(j = -1\) does NOT satisfy \(|j| = j^{(-1)}\):

\(LHS = |-1| = 1\) while \(RHS = (-1)^{(-1)} = -1\).
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Re: M04-11 &nbs [#permalink] 06 Apr 2018, 02:12

Go to page    1   2    Next  [ 24 posts ] 

Display posts from previous: Sort by

M04-11

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

Moderators: chetan2u, Bunuel

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

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®.