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

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

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

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New post 13 Oct 2016, 09:53
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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

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

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New post 13 Oct 2016, 09:59
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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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Re: If x is an integer, what is the value of x? [#permalink]

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New post 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

Answer: D


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

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New post 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

Answer: D


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



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Re: If x is an integer, what is the value of x?   [#permalink] 12 Dec 2017, 21:13
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