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

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CEO
Joined: 11 Sep 2015
Posts: 3237
If x is an integer, what is the value of x?  [#permalink]

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13 Oct 2016, 07:22
1
Top Contributor
2
00:00

Difficulty:

85% (hard)

Question Stats:

46% (02:01) correct 54% (02:12) wrong based on 140 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.

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Joined: 13 Apr 2015
Posts: 1687
Location: India
Concentration: Strategy, General Management
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Re: If x is an integer, what is the value of x?  [#permalink]

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13 Oct 2016, 08:53
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: 7106
Re: If x is an integer, what is the value of x?  [#permalink]

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13 Oct 2016, 08:59
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
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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

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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?
Math Expert
Joined: 02 Sep 2009
Posts: 51185
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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Re: If x is an integer, what is the value of x? &nbs [#permalink] 12 Dec 2017, 20:13
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