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

It is currently 14 Nov 2018, 09:43

Stanford R1 Interview Decisions:

Join Chat Room for Live Updates


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
Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • $450 Tuition Credit & Official CAT Packs FREE

     November 15, 2018

     November 15, 2018

     10:00 PM MST

     11:00 PM MST

    EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299)
  • Free GMAT Strategy Webinar

     November 17, 2018

     November 17, 2018

     07:00 AM PST

     09:00 AM PST

    Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

If x is an integer and it satisfies the inequalities, x^2 – 6x - 7...

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

Hide Tags

e-GMAT Representative
User avatar
P
Joined: 04 Jan 2015
Posts: 2191
If x is an integer and it satisfies the inequalities, x^2 – 6x - 7...  [#permalink]

Show Tags

New post Updated on: 31 Oct 2018, 22:40
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

77% (01:39) correct 23% (01:35) wrong based on 56 sessions

HideShow timer Statistics

If x is an integer and it satisfies the inequalities, \(x^2 – 6x - 7 < 0\) and \(2x – x^2 + 3 < 0\), then which of the following can be the value of x?

    A. -1
    B. 0
    C. 1
    D. 2
    E. 5

To read all our articles: Must read articles to reach Q51

Image

_________________








Register for free sessions
Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Must Read Articles
Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com


Originally posted by EgmatQuantExpert on 31 Oct 2018, 03:34.
Last edited by EgmatQuantExpert on 31 Oct 2018, 22:40, edited 1 time in total.
CEO
CEO
User avatar
P
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2698
Location: India
GMAT: INSIGHT
WE: Education (Education)
Reviews Badge
Re: If x is an integer and it satisfies the inequalities, x^2 – 6x - 7...  [#permalink]

Show Tags

New post 31 Oct 2018, 04:59
EgmatQuantExpert wrote:
If x is an integer and it satisfies the inequalities, \(x^2 – 6x - 7 < 0\) and \(2x – x^2 + 3 < 0\), then which of the following can be the value of x?

    A. -1
    B. 0
    C. 1
    D. 2
    E. 5



\(x^2 – 6x - 7 < 0\)
i.e. \(x^2 – 7x + x - 7 < 0\)

i.e.\((x-7)*(x+1) < 0\)

Product of two things is less than zero i.e. one of them must be positive and other must be Negative. Also since (X-7) is smaller than (x+1) therefore (X-7) must be negative

i.e. \((x-7) < 0\) and \((x+1) > 0\)

i.e. \(-1 < x < 7\)

Now, \(2x – x^2 + 3 < 0\)

i.e. \(x^2 - 2x - 3 > 0\)

i.e. \(x^2 - 3x +x - 3 > 0\)

i.e. \((x-3)*(x+1) > 0\)

i.e. \(x > 3 or x < -1\)

Looking at both blue results we can infer that

\(3 < x < 7\)

i.e. x can only be 5 out of given option choices

Answer: Option E
_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Manager
Manager
User avatar
B
Joined: 04 Jun 2018
Posts: 60
CAT Tests
Re: If x is an integer and it satisfies the inequalities, x^2 – 6x - 7...  [#permalink]

Show Tags

New post 31 Oct 2018, 05:19
While I could solve the question by finding out the range of individual equations and then finding out the common value, I have a doubt.

Why can't I add the equations and still get the same result?

If we were to try add these equations ,we would get:

-4x-4<0
i.e x<-1

Why would this method not work?
I know there is a conceptual gap here because x<-1 is not a valid range.

Can some expert help out?
gmatbusters
EgmatQuantExpert
Gladiator59
CEO
CEO
User avatar
P
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2698
Location: India
GMAT: INSIGHT
WE: Education (Education)
Reviews Badge
Re: If x is an integer and it satisfies the inequalities, x^2 – 6x - 7...  [#permalink]

Show Tags

New post 31 Oct 2018, 06:30
1
nitesh50 wrote:
While I could solve the question by finding out the range of individual equations and then finding out the common value, I have a doubt.

Why can't I add the equations and still get the same result?

If we were to try add these equations ,we would get:

-4x-4<0
i.e x<-1

Why would this method not work?
I know there is a conceptual gap here because x<-1 is not a valid range.

Can some expert help out?
gmatbusters
EgmatQuantExpert
Gladiator59



nitesh50

Addition of inequalities is valid for Linear inequalities with same inequation signs.

Here we are dealing with quadratic inequations hence we can not simply add to get the solution

I hope this helps!!!
_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Senior DS Moderator
User avatar
D
Joined: 27 Oct 2017
Posts: 995
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Premium Member CAT Tests
Re: If x is an integer and it satisfies the inequalities, x^2 – 6x - 7...  [#permalink]

Show Tags

New post 31 Oct 2018, 06:50
Dear nitesh50

Adding the quadratic inequalities/equations might lead to loss of some roots, and you can get a larger Set as other conditions get lost with the loss of quadratic term.

Please note that there is a mistake in your solution which seems to show invalid range

Adding you get,
-4x-4<0
or, -4<4x
or x>-1

note that the actual answer x = 5 also satisfy this condition.

nitesh50 wrote:
While I could solve the question by finding out the range of individual equations and then finding out the common value, I have a doubt.

Why can't I add the equations and still get the same result?

If we were to try add these equations ,we would get:

-4x-4<0
i.e x<-1

Why would this method not work?
I know there is a conceptual gap here because x<-1 is not a valid range.

Can some expert help out?
gmatbusters
EgmatQuantExpert
Gladiator59

_________________

Win GMAT CLUB Test- Weekly Quant Quiz Contest
Weekly Quant Quiz Questions- Direct Download
SC: Confusable words

All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory
Error log/Key Concepts
Combination Concept: Division into groups
Question of the Day (QOTD)
Free GMAT CATS

Manager
Manager
User avatar
B
Joined: 04 Jun 2018
Posts: 60
CAT Tests
Re: If x is an integer and it satisfies the inequalities, x^2 – 6x - 7...  [#permalink]

Show Tags

New post 31 Oct 2018, 07:38
gmatbusters wrote:
Dear nitesh50

Adding the quadratic inequalities/equations might lead to loss of some roots, and you can get a larger Set as other conditions get lost with the loss of quadratic term.

Please note that there is a mistake in your solution which seems to show invalid range

Adding you get,
-4x-4<0
or, -4<4x
or x>-1

note that the actual answer x = 5 also satisfy this condition.

nitesh50 wrote:
While I could solve the question by finding out the range of individual equations and then finding out the common value, I have a doubt.

Why can't I add the equations and still get the same result?

If we were to try add these equations ,we would get:

-4x-4<0
i.e x<-1

Why would this method not work?
I know there is a conceptual gap here because x<-1 is not a valid range.

Can some expert help out?
gmatbusters
EgmatQuantExpert
Gladiator59




Hi gmatbusters
Thank you for correcting my mistake.
this might be a stupid question, but
Why is that when we are adding 2 inequalities, it leads to loss of a certain range.
I guess What I am still looking for is a bit of a conceptual understanding to it.

Looking forward to you reply!

Regards
Nitesh
Senior DS Moderator
User avatar
D
Joined: 27 Oct 2017
Posts: 995
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Premium Member CAT Tests
Re: If x is an integer and it satisfies the inequalities, x^2 – 6x - 7...  [#permalink]

Show Tags

New post 31 Oct 2018, 07:44
1
Hi
Since on adding you are loosing the quadratic term, leads to loss of roots/a certain range.

See this example

if x^2 = 2x
and we cancel out x from both sides ( it leads to loss of root, x = 0)
We get x = 2.

Whereas,
x^2 = 2x
or, x(x-2) = 0
or x = 0 or 2

By cancelling some terms you are loosing roots.


nitesh50 wrote:
gmatbusters wrote:
Dear nitesh50

Adding the quadratic inequalities/equations might lead to loss of some roots, and you can get a larger Set as other conditions get lost with the loss of quadratic term.

Please note that there is a mistake in your solution which seems to show invalid range

Adding you get,
-4x-4<0
or, -4<4x
or x>-1

note that the actual answer x = 5 also satisfy this condition.

nitesh50 wrote:
While I could solve the question by finding out the range of individual equations and then finding out the common value, I have a doubt.

Why can't I add the equations and still get the same result?

If we were to try add these equations ,we would get:

-4x-4<0
i.e x<-1

Why would this method not work?
I know there is a conceptual gap here because x<-1 is not a valid range.

Can some expert help out?
gmatbusters
EgmatQuantExpert
Gladiator59




Hi gmatbusters
Thank you for correcting my mistake.
this might be a stupid question, but
Why is that when we are adding 2 inequalities, it leads to loss of a certain range.
I guess What I am still looking for is a bit of a conceptual understanding to it.

Looking forward to you reply!

Regards
Nitesh

_________________

Win GMAT CLUB Test- Weekly Quant Quiz Contest
Weekly Quant Quiz Questions- Direct Download
SC: Confusable words

All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory
Error log/Key Concepts
Combination Concept: Division into groups
Question of the Day (QOTD)
Free GMAT CATS

e-GMAT Representative
User avatar
P
Joined: 04 Jan 2015
Posts: 2191
If x is an integer and it satisfies the inequalities, x^2 – 6x - 7...  [#permalink]

Show Tags

New post 02 Nov 2018, 03:50

Solution


Given:
    • We are given that x is an integer, and
    • We are also given two inequalities,
      o \(x^2 – 6x - 7 < 0\)
      o \(2x – x^2 + 3 < 0\)

To find:
    • We need to find out which among the given answer choices can be a possible value of x that satisfies the given information

Approach and Working:
    • We need to solve both the quadratic inequalities to arrive at the answer.
    • Let’s solve the first inequality, \(x^2 - 6x – 7 < 0\)
      o Implies, (x - 7)(x + 1) < 0

Approach 1: Wavy-line method

Image

    • Thus, the expression is negative for -1 < x < 7
    • The values of x that satisfy this inequality are, x = {0, 1, 2, 3, 4, 5, 6}

Now, let’s solve the second inequality, \(2x - x^2 - 3 < 0\)
    o Multiplying by -1, we get, \(x^2 – 2x - 3 > 0\)
    o Implies, (x - 3)(x + 1) > 0

Image

    • Thus, the expression is positive for x < -1 and x > 3

Combining both the results, -1 < x < 7, and (x < -1 or x > 3), we can say that the values of x that satisfy this inequality are, 3 < x < 7
    • Since, x is an integer, x = {4 , 5 , 6}

Approach 2: Number-line method

Number- line for the expression (x + 1)(x - 7) < 0 is,

Image

    • Thus, the expression is negative for -1 < x < 7

Now, let’s draw the number-line for the expression, (x + 1)(x - 3) > 0

Image

    • Thus, the expression is positive for x < -1 or x > 3

Combining both these results, we get, 3 < x < 7
    • Since, x is an integer, the values of x that satisfy the given expression are {4, 5, 6}

Hence, the correct answer is option E.

Answer: E

Image

_________________








Register for free sessions
Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Must Read Articles
Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

GMAT Club Bot
If x is an integer and it satisfies the inequalities, x^2 – 6x - 7... &nbs [#permalink] 02 Nov 2018, 03:50
Display posts from previous: Sort by

If x is an integer and it satisfies the inequalities, x^2 – 6x - 7...

  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®.