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

It is currently 23 Oct 2018, 13:26

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

What is the value of x?

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

Hide Tags

Manager
Manager
avatar
Joined: 08 Dec 2012
Posts: 62
Location: United Kingdom
WE: Engineering (Consulting)
What is the value of x?  [#permalink]

Show Tags

New post 06 Oct 2013, 10:01
14
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

53% (01:08) correct 47% (01:01) wrong based on 361 sessions

HideShow timer Statistics

What is the value of x?

(1) 4 < x < 6

(2) |x| = 4x − 15
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50058
Re: What is the value of x? (1) 4 < x < 6 (2) |x|=4x−15  [#permalink]

Show Tags

New post 06 Oct 2013, 10:05
4
1
What is the value of x?

(1) 4 < x < 6. Clearly insufficient, x can be any number from 4 to 6, not inclusive.

(2) |x| = 4x − 15. LHS is an absolute value, which is always non negative, hence RHS must also be non-negative: \(4x-15\geq{0}\) --> \(x\geq{\frac{15}{4}}\) --> \(x\) is positive, thus \(|x|=x\) --> \(x=4x-15\) --> \(x=5\). Sufficient

Answer: B.

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

Most Helpful Community Reply
Senior Manager
Senior Manager
User avatar
Joined: 28 Apr 2012
Posts: 287
Location: India
Concentration: Finance, Technology
GMAT 1: 650 Q48 V31
GMAT 2: 770 Q50 V47
WE: Information Technology (Computer Software)
Re: Algebra  [#permalink]

Show Tags

New post 22 Mar 2014, 14:48
4
1
derek123 wrote:
According to me there are 2 solutions for x for option 2 and multiple solutions for option 1 as well (as x can be a non-integer ex. 4.5 or 5 or 5.5) So i think it should be E.
But its not. Can someone please explain why?

Source: Babson Practise Test

Data Sufficiency -

What is the value of x?

(1) 4 < x < 6

(2) |x|=4x−15


A statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;

B statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;

C BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked;

D EACH statement ALONE is sufficient to answer the question asked;

E statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.


you are confused for option 2:

|x|=4x−15

X can be +ve / -ve.
for X = +ve

x = 4x - 15 , hence x = 5

For X = -ve

-x =4x - 15, hence x=3 , however this contradicts your assumption that x is -ve. So this solution is ruled out, leaving x=5 as unique solution.
Hence answer is B.
_________________

"Appreciation is a wonderful thing. It makes what is excellent in others belong to us as well."
― Voltaire


Press Kudos, if I have helped.
Thanks!

General Discussion
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50058
Re: What is the value of x? (1) 4 < x < 6 (2) |x|=4x−15  [#permalink]

Show Tags

New post 06 Oct 2013, 10:06
Bunuel wrote:
What is the value of x?

(1) 4 < x < 6. Clearly insufficient, x can be any number from 4 to 6, not inclusive.

(2) |x| = 4x − 15. LHS is an absolute value, which is always non negative, hence RHS must also be non-negative: \(4x-15\geq{0}\) --> \(x\geq{\frac{15}{4}}\) --> \(x\) is positive, thus \(|x|=x\) --> \(x=4x-15\) --> \(x=5\). Sufficient

Answer: B.

Hope it's clear.


Similar questions to practice: what-is-x-126874.html
_________________

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: 12 May 2013
Posts: 67
Re: What is the value of x? (1) 4 < x < 6 (2) |x|=4x−15  [#permalink]

Show Tags

New post 06 Oct 2013, 12:32
bunuel , m still confused that why B
i got the point rhs and lhs being positive , but why 5 , there can be other possibilities as well such as 4(6)-15=9
so won't the ans be "c" ??? plz correct me ,where i m wrong
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50058
Re: What is the value of x? (1) 4 < x < 6 (2) |x|=4x−15  [#permalink]

Show Tags

New post 06 Oct 2013, 12:35
adymehta29 wrote:
bunuel , m still confused that why B
i got the point rhs and lhs being positive , but why 5 , there can be other possibilities as well such as 4(6)-15=9
so won't the ans be "c" ??? plz correct me ,where i m wrong


Does x=6 satisfy |x| = 4x − 15?
_________________

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: 12 May 2013
Posts: 67
Re: What is the value of x? (1) 4 < x < 6 (2) |x|=4x−15  [#permalink]

Show Tags

New post 06 Oct 2013, 12:43
thankz , bunuel it was a silly mistake :oops:
Intern
Intern
avatar
Joined: 16 Mar 2014
Posts: 3
Algebra  [#permalink]

Show Tags

New post 22 Mar 2014, 10:45
According to me there are 2 solutions for x for option 2 and multiple solutions for option 1 as well (as x can be a non-integer ex. 4.5 or 5 or 5.5) So i think it should be E.
But its not. Can someone please explain why?

Source: Babson Practise Test

Data Sufficiency -

What is the value of x?

(1) 4 < x < 6

(2) |x|=4x−15


A statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;

B statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;

C BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked;

D EACH statement ALONE is sufficient to answer the question asked;

E statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Intern
Intern
avatar
Joined: 06 Sep 2013
Posts: 12
Re: Algebra  [#permalink]

Show Tags

New post 22 Mar 2014, 12:47
Hey to answer your question:

Regarding to option 2, how x can be 4.5 or 5.5 ? try to let x=4.5 or 5.5, do you think the equation will be correct?
no i do not think so, the only answer is x=5
Manager
Manager
User avatar
Joined: 20 Jan 2014
Posts: 149
Location: India
Concentration: Technology, Marketing
GMAT ToolKit User
What is the value of x?  [#permalink]

Show Tags

New post 18 Sep 2014, 12:41
Bunuel wrote:
Bunuel wrote:
What is the value of x?

(1) 4 < x < 6. Clearly insufficient, x can be any number from 4 to 6, not inclusive.

(2) |x| = 4x − 15. LHS is an absolute value, which is always non negative, hence RHS must also be non-negative: \(4x-15\geq{0}\) --> \(x\geq{\frac{15}{4}}\) --> \(x\) is positive, thus \(|x|=x\) --> \(x=4x-15\) --> \(x=5\). Sufficient

Answer: B.

Hope it's clear.


Similar questions to practice: what-is-x-126874.html


Hello Bunuel,
I am confused that why B is answer. I still don't understand that why in this case we did not taken two cases for mod.

I solved by taking two condition for LHS, one is positive and one is negative.
|x|=4x−15

X can be +ve / -ve.
for X = +ve
x = 4x - 15 , hence x = 5

For X = -ve
-x =4x - 15, hence x=3

Why we rejected answer choice with -ve X. Also can u please help me understand that in which cases we should take both +ve and -ve values for MOD and in which cases should not. Absolute Value is a weak pint for me in DS :(

Thanks
_________________

Consider +1 Kudos Please :)

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50058
Re: What is the value of x?  [#permalink]

Show Tags

New post 18 Sep 2014, 13:18
1
him1985 wrote:
Bunuel wrote:
Bunuel wrote:
What is the value of x?

(1) 4 < x < 6. Clearly insufficient, x can be any number from 4 to 6, not inclusive.

(2) |x| = 4x − 15. LHS is an absolute value, which is always non negative, hence RHS must also be non-negative: \(4x-15\geq{0}\) --> \(x\geq{\frac{15}{4}}\) --> \(x\) is positive, thus \(|x|=x\) --> \(x=4x-15\) --> \(x=5\). Sufficient

Answer: B.

Hope it's clear.


Similar questions to practice: what-is-x-126874.html


Hello Bunuel,
I am confused that why B is answer. I still don't understand that why in this case we did not taken two cases for mod.

I solved by taking two condition for LHS, one is positive and one is negative.
|x|=4x−15

X can be +ve / -ve.
for X = +ve
x = 4x - 15 , hence x = 5

For X = -ve
-x =4x - 15, hence x=3

Why we rejected answer choice with -ve X. Also can u please help me understand that in which cases we should take both +ve and -ve values for MOD and in which cases should not. Absolute Value is a weak pint for me in DS :(

Thanks


When you consider the case when x is negative and get x = 3 = positive, you should reject it, as x is not negative. Also, plug x = 3 into the equation, does it hold true?

Below links might help.
Theory on Abolute Values: math-absolute-value-modulus-86462.html
Absolute value tips: absolute-value-tips-and-hints-175002.html
_________________

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

CEO
CEO
User avatar
D
Joined: 12 Sep 2015
Posts: 3037
Location: Canada
Re: What is the value of x?  [#permalink]

Show Tags

New post 10 Oct 2017, 09:12
Top Contributor
nave wrote:
What is the value of x?

(1) 4 < x < 6

(2) |x| = 4x − 15


Target question: What is the value of x?

Statement 1: 4 < x < 6
ASIDE: Some students will assume that x is an integer and incorrectly conclude that x must equal 5. This is a common mistake on the GMAT.
The truth of the matter is that there are infinitely many values of x that satisfy statement 1.
For example x could equal 4.1, or x could equal 4.132 or 4.54 or 5 or 5.4211 etc
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: |x| = 4x − 15
There are 3 steps to solving equations involving ABSOLUTE VALUE:
1. Apply the rule that says: If |x| = k, then x = k and/or x = -k
2. Solve the resulting equations
3. Plug solutions into original equation to check for extraneous roots

Given: |x| = 4x − 15
So, there are two possible cases to examine:
Case a: x = 4x − 15. When we solve this equation, we get: x = 5
Case b: x = -(4x − 15). When we solve this equation, we get: x = 3
At this point, it LOOKS LIKE there are two possible values of x. However, we haven't performed step 3 yet: Plug solutions into original equation to check for extraneous roots

Let's do that.
Case a: Plug x = 5 into original equation to get: |5| = 4(5) − 15
Simplify right side of equation to get: |5| = 5
This works, so x = 5 IS a possible value of x

Case b: Plug x = 3 into original equation to get: |3| = 4(3) − 15
Simplify right side of equation to get: |3| = -3
This DOES NOT work, so x = 3 is NOT a possible value of x

Since there is only ONE possible value of x (x = 5), statement 2 is SUFFICIENT

Answer:

Cheers,
Brent
_________________

Brent Hanneson – GMATPrepNow.com
Image
Sign up for our free Question of the Day emails

Intern
Intern
User avatar
B
Joined: 07 Feb 2017
Posts: 7
Location: India
GPA: 4
WE: Sales (Manufacturing)
Re: What is the value of x?  [#permalink]

Show Tags

New post 06 Dec 2017, 06:15
Hi Bunuel,

I don't understand why ans should B?

Question does not say anything about 'X'. Therefore X can be integer or non-integer number.
So if X =3.75 then |X|= 4X-15 satisfies the condition.
Further if I combine Condition 2 (i.e |X|= 4X-15) with Condition 1 (i.e. 4<x<6) then also we will not get the exact value of X.

According to me Ans. should be E.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50058
Re: What is the value of x?  [#permalink]

Show Tags

New post 06 Dec 2017, 06:23
TarunKB wrote:
Hi Bunuel,

I don't understand why ans should B?

Question does not say anything about 'X'. Therefore X can be integer or non-integer number.
So if X =3.75 then |X|= 4X-15 satisfies the condition.
Further if I combine Condition 2 (i.e |X|= 4X-15) with Condition 1 (i.e. 4<x<6) then also we will not get the exact value of X.

According to me Ans. should be E.


x = 3.75 does not satisfy |x| = 4x − 15. If x = 3.75, then 4*3.75 − 15 = 0, not 3.75.

There are several solution above explaining why the answer is B. Please read them carefully.

Finally, before attempting questions one should go through the basics:

10. Absolute Value



For more check Ultimate GMAT Quantitative Megathread



Hope it helps.
_________________

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

Intern
Intern
User avatar
B
Joined: 07 Feb 2017
Posts: 7
Location: India
GPA: 4
WE: Sales (Manufacturing)
Re: What is the value of x?  [#permalink]

Show Tags

New post 06 Dec 2017, 06:29
Yup Bunnel,
You are right. Made the same mistake as done by Derek123.
Thank you :)
GMAT Club Bot
Re: What is the value of x? &nbs [#permalink] 06 Dec 2017, 06:29
Display posts from previous: Sort by

What is the value of x?

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


Copyright

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®.