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

 It is currently 21 Aug 2018, 01:30

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

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

If x is an integer, what is the value of x?

Author Message
TAGS:

Hide Tags

CEO
Joined: 12 Sep 2015
Posts: 2710
If x is an integer, what is the value of x?  [#permalink]

Show Tags

13 Oct 2016, 08:22
1
Top Contributor
2
00:00

Difficulty:

85% (hard)

Question Stats:

44% (01:22) correct 56% (01:37) wrong based on 138 sessions

HideShow timer Statistics

If x is an integer, what is the value of x?

1) x² - 4x + 3 < 0
2) |2x - 4| < 1

NOTE: Kudos for all correct solutions.

_________________

Brent Hanneson – Founder of gmatprepnow.com

SC Moderator
Joined: 13 Apr 2015
Posts: 1710
Location: India
Concentration: Strategy, General Management
GMAT 1: 200 Q1 V1
GPA: 4
WE: Analyst (Retail)
Re: If x is an integer, what is the value of x?  [#permalink]

Show Tags

13 Oct 2016, 09:53
1
x = ?

St1: x^2 - 4x + 3 < 0
x^2 - 3x - x + 3 < 0
x(x - 3) -1(x - 3) < 0
(x - 3)(x - 1) < 0
x < 3 and x > 1
Since x is an integer, value of x = 2
Sufficient

St2: |2x - 4| < 1
|2x - 4| is non negative and x is an integer
2x - 4 = 0
x = 2
Sufficient

Math Expert
Joined: 02 Aug 2009
Posts: 6558
Re: If x is an integer, what is the value of x?  [#permalink]

Show Tags

13 Oct 2016, 09:59
1
GMATPrepNow wrote:
If x is an integer, what is the value of x?

1) x² - 4x + 3 < 0
2) |2x - 4| < 1
NOTE: Kudos for all correct solutions.

Hi
(1)
$$x^2-4x+3<0......x^2-4x+4-1<0......x^2-4x+4<1.....(x-2)^2<1..$$
Since (x-2)^2 cannot be NEGATIVE, only possible value is 0..
So x-2=0...x=2
Sufficient

(2)
|2x-4|<1....
Since MOD cannot be NEGATIVE, 2x-4=0...x=2
Sufficient

D
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Intern
Joined: 01 Nov 2011
Posts: 9
Location: India
WE: Sales (Computer Software)
Re: If x is an integer, what is the value of x?  [#permalink]

Show Tags

12 Dec 2017, 12:42
Vyshak wrote:
x = ?

St1: x^2 - 4x + 3 < 0
x^2 - 3x - x + 3 < 0
x(x - 3) -1(x - 3) < 0
(x - 3)(x - 1) < 0
x < 3 and x > 1
Since x is an integer, value of x = 2
Sufficient

St2: |2x - 4| < 1
|2x - 4| is non negative and x is an integer
2x - 4 = 0
x = 2
Sufficient

Can you explain the following:-
ST1: How do you derive the following 2 inferences (x<3 and x>1) from such an equation?
Math Expert
Joined: 02 Sep 2009
Posts: 48074
Re: If x is an integer, what is the value of x?  [#permalink]

Show Tags

12 Dec 2017, 21:13
goelanu wrote:
Vyshak wrote:
x = ?

St1: x^2 - 4x + 3 < 0
x^2 - 3x - x + 3 < 0
x(x - 3) -1(x - 3) < 0
(x - 3)(x - 1) < 0
x < 3 and x > 1
Since x is an integer, value of x = 2
Sufficient

St2: |2x - 4| < 1
|2x - 4| is non negative and x is an integer
2x - 4 = 0
x = 2
Sufficient

Can you explain the following:-
ST1: How do you derive the following 2 inferences (x<3 and x>1) from such an equation?

There are several methods possible. The links below should help.

9. Inequalities

For more check Ultimate GMAT Quantitative Megathread

_________________
Re: If x is an integer, what is the value of x? &nbs [#permalink] 12 Dec 2017, 21:13
Display posts from previous: Sort by

Events & Promotions

 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®.