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

It is currently 18 Oct 2019, 02:14

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

What is the value of integer x ?

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

Hide Tags

Find Similar Topics 
Current Student
avatar
Joined: 31 Mar 2010
Posts: 165
Schools: Tuck Class of 2013
GMAT ToolKit User
What is the value of integer x ?  [#permalink]

Show Tags

New post 20 Apr 2010, 07:04
6
20
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

44% (02:21) correct 56% (02:09) wrong based on 533 sessions

HideShow timer Statistics

What is the value of integer x ?

(1) 4 < (x-1)*(x-1) < 16
(2) 4 < (x+1)*(x-1) < 16
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58435
Re: Tough Inequation DS: What is the value of integer x ?  [#permalink]

Show Tags

New post 20 Apr 2010, 08:00
10
13
MBAUncle wrote:
What is the value of integer x ?

(1) 4 < (x-1)*(x-1) < 16
(2) 4 < (x+1)*(x-1) < 16

OA is C

If it is asking for the value of X, should an interval be enough to answer the question ?


Note: \(x\) is an integer.

(1) \(4<(x-1)*(x-1)<16\) --> \(4<(x-1)^2<16\) --> \((x-1)^2\) is a perfect square between 4 and 16 --> there is only one perfect square: 9 --> \((x-1)^2=9\) --> \(x-1=3\) or \(x-1=-3\) --> \(x=4\) or \(x=-2\). Two answers, not sufficient.

(2) \(4<(x+1)*(x-1)<16\) --> \(4<x^2-1<16\) --> \(5<x^2<17\) --> \(x^2\) is a perfect square between 5 and 17 --> there are two perfect squares : 9 and 16 --> \(x^2=9\) or \(x^2=16\) --> \(x=3\) or \(x=-3\) or \(x=4\) or \(x=-4\). Four answers, not sufficient.

(1)+(2) Intersection of values from (1) and (2) is \(x=4\). Sufficient.

Answer: C.
_________________
General Discussion
Retired Moderator
User avatar
Status: The last round
Joined: 18 Jun 2009
Posts: 1171
Concentration: Strategy, General Management
GMAT 1: 680 Q48 V34
GMAT ToolKit User
Re: Tough Inequation DS: What is the value of integer x ?  [#permalink]

Show Tags

New post 20 Apr 2010, 08:50
Manager
Manager
avatar
Joined: 27 Dec 2009
Posts: 129
Re: Tough Inequation DS: What is the value of integer x ?  [#permalink]

Show Tags

New post 24 Apr 2010, 10:23
Good question with a great explanation... Bunnel you are the champ :-)
Manager
Manager
User avatar
Joined: 27 Feb 2010
Posts: 81
Location: Denver
Re: Tough Inequation DS: What is the value of integer x ?  [#permalink]

Show Tags

New post 24 Apr 2010, 17:06
Bunuel, Just excellent!!!.
Manager
Manager
avatar
Status: SC SC SC SC SC.... Concentrating on SC alone.
Joined: 20 Dec 2010
Posts: 165
Location: India
Concentration: General Management
GMAT Date: 12-30-2011
What is the value of integer x ? (1) 4 < (x-1)*(x-1) < 16  [#permalink]

Show Tags

New post 07 Nov 2011, 01:36
I have a doubt with that of choosing option 1.

4 < (x-1)*(x-1) < 16

4 < (x-1)^2 < 16

Taking square root.

2 < (x-1) < 4

This gives 2 scenarios. x>3 and x< 5

Since x is an integer, the option must be 4.

So the answer must be A rite .

Any inputs ??
_________________
D- Day December 30 2011. Hoping for the happiest new year celebrations !

Aiming for 700+

Kudo me if the post is worth it
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 9706
Location: Pune, India
Re: DS question from 700 level DS qstns by Bunnel  [#permalink]

Show Tags

New post 07 Nov 2011, 03:54
3
ksp wrote:
Question source :
tough-inequation-ds-what-is-the-value-of-integer-x-93008.html

The question is

What is the value of integer x ?

(1) 4 < (x-1)*(x-1) < 16
(2) 4 < (x+1)*(x-1) < 16

I have a doubt with that of choosing option 1.

4 < (x-1)*(x-1) < 16

4 < (x-1)^2 < 16

Taking square root.

2 < (x-1) < 4



When you take the square root (which you can because all terms are positive), you get
2 < |x - 1| < 4
If x is to be an integer, |x - 1| = 3
x can be 4 or -2

Remember, \(\sqrt{x^2}\neq x\)
Instead, \(\sqrt{x^2}\) = |x|
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58435
Re: What is the value of integer x ?  [#permalink]

Show Tags

New post 17 Jun 2013, 05:05
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE


_________________
Manager
Manager
avatar
B
Joined: 31 Mar 2013
Posts: 60
Location: India
GPA: 3.02
Re: What is the value of integer x ?  [#permalink]

Show Tags

New post 28 Sep 2013, 06:41
I tried solving the first inequality and got this:
Statement 1:
4 < (x-1)*(x-1) < 16

--> \(x^2 -2x -3 < 12\)

--> \(x^2 - 2x - 15<0\)

--> \((x+3) (x-5)<0\)

If x is an integer it means the function will be negative for the values \(x= -2, -1, 0, 1, 2, 3, 4.\)

What is the mistake here?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58435
Re: What is the value of integer x ?  [#permalink]

Show Tags

New post 28 Sep 2013, 06:52
emailmkarthik wrote:
I tried solving the first inequality and got this:
Statement 1:
4 < (x-1)*(x-1) < 16

--> \(x^2 -2x -3 < 12\)

--> \(x^2 - 2x - 15<0\)

--> \((x+3) (x-5)<0\)

If x is an integer it means the function will be negative for the values \(x= -2, -1, 0, 1, 2, 3, 4.\)

What is the mistake here?


Why would you expand and manipulate 4 < (x-1)^2 < 16, when its already in its simplest form?

Anyway:
\(4 < (x-1)^2 < 16\);
\(0 < x^2-2x-3 < 12\) or \(-12 < x^2-2x-15 < 0\);
\(-3<x<-1\) or \(3<x<5\) --> \(x=-2\) or \(x=4\).

Hope this helps.
_________________
Senior Manager
Senior Manager
User avatar
P
Joined: 29 Jun 2017
Posts: 424
GPA: 4
WE: Engineering (Transportation)
GMAT ToolKit User Reviews Badge
Re: What is the value of integer x?  [#permalink]

Show Tags

New post 08 Sep 2017, 14:18
robertops wrote:
What is the value of integer x?

(1) 4<(x-1)(x-1)<16
(2) 4<(x+1)(x-1)<16




1) 4<(x-1)^2<16
3<x<5 or -3<x<-1
X=-2 or 4
A D eliminated

2) 4<x^2-1<16
5<x^2<16
x= -3,3,-4,4
B eliminated

Combine 1&2

X=4 is the answer

C is ANSWER

Posted from my mobile device
_________________
Give Kudos for correct answer and/or if you like the solution.
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13241
Re: What is the value of integer x ?  [#permalink]

Show Tags

New post 23 Oct 2018, 08:47
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.
_________________
GMAT Club Bot
Re: What is the value of integer x ?   [#permalink] 23 Oct 2018, 08:47
Display posts from previous: Sort by

What is the value of integer x ?

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





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