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

It is currently 18 Aug 2018, 13:03

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

M18-01

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47983
M18-01  [#permalink]

Show Tags

New post 16 Sep 2014, 01:02
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

97% (00:22) correct 3% (00:18) wrong based on 145 sessions

HideShow timer Statistics

If \(\frac{1}{2 + \frac{1}{x}} = 1\), what is the value of \(x\)?

A. \(-1\)
B. \(-\frac{1}{2}\)
C. \(\frac{1}{2}\)
D. \(1 \frac{1}{2}\)
E. \(2 \frac{1}{2}\)

_________________

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

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47983
Re M18-01  [#permalink]

Show Tags

New post 16 Sep 2014, 01:02
Official Solution:

If \(\frac{1}{2 + \frac{1}{x}} = 1\), what is the value of \(x\)?

A. \(-1\)
B. \(-\frac{1}{2}\)
C. \(\frac{1}{2}\)
D. \(1 \frac{1}{2}\)
E. \(2 \frac{1}{2}\)

\(\frac{1}{2 + \frac{1}{x}} = 1\) simplifies to \(2 + \frac{1}{x} = 1\) or \(\frac{1}{x} = -1\) from where \(x = -1\).

Answer: A
_________________

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

Director
Director
User avatar
S
Joined: 08 Jun 2015
Posts: 529
Location: India
GMAT 1: 640 Q48 V29
GMAT 2: 700 Q48 V38
Premium Member CAT Tests
Re: M18-01  [#permalink]

Show Tags

New post 01 Jun 2017, 05:29
Solving we get x/(2x+1) = 1 ; i.e., x=-1. The answer is option A
_________________

" The few , the fearless "

Intern
Intern
avatar
B
Joined: 05 Sep 2016
Posts: 12
Location: Argentina
GMAT 1: 650 Q43 V36
GPA: 3.4
GMAT ToolKit User Premium Member
  [#permalink]

Show Tags

New post 01 Jun 2017, 06:29
What am I doing wrong?

If 1/(2+1x)=1
1/2 + 1/(1/x) = 1
1/2 + x/1 = 1
Then x/1 must equal 1/2 in order to maintain the equality.
Thx in advance.

Posted from my mobile device
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47983
Re: M18-01  [#permalink]

Show Tags

New post 01 Jun 2017, 06:35
cocojiz wrote:
What am I doing wrong?

If 1/(2+1x)=1
1/2 + 1/(1/x) = 1
1/2 + x/1 = 1
Then x/1 must equal 1/2 in order to maintain the equality.
Thx in advance.

Posted from my mobile device


\(\frac{1}{a+b}\neq \frac{1}{a} + \frac{1}{b}\).

Does \(\frac{1}{1+1}=\frac{1}{2}\) equal to \(\frac{1}{1}+\frac{1}{1}=2\)?
_________________

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
User avatar
B
Joined: 16 Jan 2013
Posts: 91
Location: Bangladesh
GMAT 1: 490 Q41 V18
GMAT 2: 610 Q45 V28
GPA: 2.75
Premium Member
Re M18-01  [#permalink]

Show Tags

New post 29 Nov 2017, 08:34
I think this is a high-quality question and I agree with explanation.
_________________

Heading towards perfection>>

Study Buddy Forum Moderator
User avatar
D
Joined: 04 Sep 2016
Posts: 1167
Location: India
WE: Engineering (Other)
Premium Member CAT Tests
M18-01  [#permalink]

Show Tags

New post 17 Dec 2017, 05:48
Bunuel

Quote:
\(\frac{1}{2 + \frac{1}{x}} = 1\) simplifies to \(2 + \frac{1}{x} = 1\) or \(\frac{1}{x} = -1\) from where \(x = -1\).


I agree with OE but ended up simplifying \(\frac{1}{2 + \frac{1}{x}} = 1\) to \(\frac{1}{ \frac{2x+1}{x}} = 1\) finally ending up with same answer in
form of : 2x + 1 = x
or
x=-1.

Is this correct too?

Let me know if you assumed x to be positive integer in your approach?
_________________

It's the journey that brings us happiness not the destination.

PS Forum Moderator
avatar
D
Joined: 25 Feb 2013
Posts: 1201
Location: India
GPA: 3.82
GMAT ToolKit User Premium Member Reviews Badge
Re: M18-01  [#permalink]

Show Tags

New post 17 Dec 2017, 05:56
1
adkikani wrote:
Bunuel

Quote:
\(\frac{1}{2 + \frac{1}{x}} = 1\) simplifies to \(2 + \frac{1}{x} = 1\) or \(\frac{1}{x} = -1\) from where \(x = -1\).


I agree with OE but ended up simplifying \(\frac{1}{2 + \frac{1}{x}} = 1\) to \(\frac{1}{ \frac{2x+1}{x}} = 1\) finally ending up with same answer in
form of : 2x + 1 = x
or
x=-1.

Is this correct too?

Let me know if you assumed x to be positive integer in your approach?


Hi adkikani

Your approach is perfectly correct. :thumbup:

as this is an "Equality" and not an "Inequality" so you need not worry about of x being positive or negative while cross-multiplying variables. In case of inequality sign changes when you cross-multiply with negative number.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47983
Re: M18-01  [#permalink]

Show Tags

New post 17 Dec 2017, 05:58
adkikani wrote:
Bunuel

Quote:
\(\frac{1}{2 + \frac{1}{x}} = 1\) simplifies to \(2 + \frac{1}{x} = 1\) or \(\frac{1}{x} = -1\) from where \(x = -1\).


I agree with OE but ended up simplifying \(\frac{1}{2 + \frac{1}{x}} = 1\) to \(\frac{1}{ \frac{2x+1}{x}} = 1\) finally ending up with same answer in
form of : 2x + 1 = x
or
x=-1.

Is this correct too?

Let me know if you assumed x to be positive integer in your approach?


Yes, that's correct. Why do you think that I assumed that x is a positive integer? Why should I've assumed that? How could I assumed that if I got x = -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

Study Buddy Forum Moderator
User avatar
D
Joined: 04 Sep 2016
Posts: 1167
Location: India
WE: Engineering (Other)
Premium Member CAT Tests
M18-01  [#permalink]

Show Tags

New post 17 Dec 2017, 06:24
Bunuel

Quote:
Yes, that's correct.Why do you think that I assumed that x is a positive integer? Why should I've assumed that? How could I assumed that if I got x = -1?


Let me take numbers show two different results for LHS of \(\frac{1}{2 + \frac{1}{x}} = 1\)

x = 1 the fraction becomes 1/3 (overall fraction is now positive)

x = 0 (fraction is not a positive integer)

What I inferred from your OE is that you reversed the fraction but I also need to know the sign of denominator.

I think this Q can be solved using simple common sense w/o touching a pen and paper:

1. I need the ratio to be positive.
2. Denominator has to be positive since 1 is positive
3. To satisfy LHS = RHS I need x = -1

I think my original query was based more on ratio than equating LHS and RHS.
_________________

It's the journey that brings us happiness not the destination.

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47983
Re: M18-01  [#permalink]

Show Tags

New post 17 Dec 2017, 06:33
1
adkikani wrote:
Bunuel

Quote:
Yes, that's correct.Why do you think that I assumed that x is a positive integer? Why should I've assumed that? How could I assumed that if I got x = -1?


Let me take numbers show two different results for LHS of \(\frac{1}{2 + \frac{1}{x}} = 1\)

x = 1 the fraction becomes 1/3 (overall fraction is now positive)

x = -3 fraction becomes -1 (overall fraction is now negative)

What I inferred from your OE is that you reversed the fraction but I also need to know the sign of denominator.

I think this Q can be solved using simple common sense w/o touching a pen and paper:

1. I need the ratio to be positive.
2. Denominator has to be positive since 1 is positive
3. To satisfy LHS = RHS I need x = -1

I think my original query was based more on ratio than equating LHS and RHS.


I do not follow you...

1. What does x = 1 and x = -3 has to do here? Neither of them satisfy the equation.

2. You did not understand the solution. \(\frac{1}{2 + \frac{1}{x}} = 1\), from here we cross multiply to get \(1=2 + \frac{1}{x}\).

3. We have an EQUATION not INEQUALITY. The signs of denominator/numerator are absolutely irrelevant when we manipulate the equations.
_________________

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

Study Buddy Forum Moderator
User avatar
D
Joined: 04 Sep 2016
Posts: 1167
Location: India
WE: Engineering (Other)
Premium Member CAT Tests
Re: M18-01  [#permalink]

Show Tags

New post 17 Dec 2017, 06:40
Bunuel

I understood my mistake. I over complicated simple proportion by taking reciprocals
instead of cross-multiplication. :-)
_________________

It's the journey that brings us happiness not the destination.

Re: M18-01 &nbs [#permalink] 17 Dec 2017, 06:40
Display posts from previous: Sort by

M18-01

  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®.