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

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SVP
Joined: 11 Sep 2015
Posts: 1999

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If x is an integer, what is the value of x? [#permalink]

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13 Oct 2016, 07:22
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Difficulty:

85% (hard)

Question Stats:

44% (01:27) correct 56% (01:41) wrong based on 124 sessions

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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.

[Reveal] Spoiler: OA

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Brent Hanneson – Founder of gmatprepnow.com

Kudos [?]: 2877 [0], given: 364

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Joined: 13 Apr 2015
Posts: 1540

Kudos [?]: 1295 [1], given: 913

Location: India
Concentration: Strategy, General Management
WE: Information Technology (Consulting)
Re: If x is an integer, what is the value of x? [#permalink]

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13 Oct 2016, 08:53
1
KUDOS
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

Kudos [?]: 1295 [1], given: 913

Math Expert
Joined: 02 Aug 2009
Posts: 5536

Kudos [?]: 6450 [1], given: 122

Re: If x is an integer, what is the value of x? [#permalink]

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13 Oct 2016, 08:59
1
KUDOS
Expert's post
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
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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Re: If x is an integer, what is the value of x? [#permalink]

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12 Dec 2017, 11:42
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?

Kudos [?]: 5 [0], given: 18

Math Expert
Joined: 02 Sep 2009
Posts: 43348

Kudos [?]: 139706 [0], given: 12794

Re: If x is an integer, what is the value of x? [#permalink]

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12 Dec 2017, 20:13
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

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Kudos [?]: 139706 [0], given: 12794

Re: If x is an integer, what is the value of x?   [#permalink] 12 Dec 2017, 20:13
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