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# If x is an integer, what is the value of x? (1) x^2 - 4x + 3

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Math Expert
Joined: 02 Sep 2009
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Re: If x is an integer, what is the value of x? (1) x^2 - 4x + 3 [#permalink]

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03 Jul 2015, 01:02
abani wrote:
Bunuel wrote:
dimitri92 wrote:
If x is an integer, what is the value of x?

(1) x2 - 4x + 3 < 0
(2) x2 + 4x +3 > 0

Given: $$x=integer$$.

(1) $$x^2-4x+3<0$$ --> $$1<x<3$$ --> as $$x$$ is an integer then $$x=2$$. Sufficient.

(2) $$x^2+4x+3>0$$ --> $$x<-3$$ or $$x>-1$$ --> multiple values are possible for integer $$x$$. Not sufficient.

Answer: A.

I understand this but I have problem when I start plugging values in 1.
when x =0 => 0 -0+ 3 < 0 implies NO
when x=1 => 1-4 +3 < 0 NO
when x =2 => 4 -8 +3 =-1 < 0 is YES
since we can have multiple values of x, isn't that statement should be insufficient.

Haw are 0 and 1 satisfying x^2 - 4x + 3 < 0? You wrote yourself that they din't. Only 2 does.
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Re: If x is an integer, what is the value of x? (1) x^2 - 4x + 3 [#permalink]

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04 Jul 2015, 05:35
I understand this but I have problem when I start plugging values in 1.
when x =0 => 0 -0+ 3 < 0 implies NO
when x=1 => 1-4 +3 < 0 NO
when x =2 => 4 -8 +3 =-1 < 0 is YES
since we can have multiple values of x, isn't that statement should be insufficient.[/quote]

Haw are 0 and 1 satisfying x^2 - 4x + 3 < 0? You wrote yourself that they din't. Only 2 does.[/quote][/quote]

Right! I was out of my mind . Thanks Bunuel
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Joined: 07 Jul 2015
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Re: If x is an integer, what is the value of x? (1) x^2 - 4x + 3 [#permalink]

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30 Aug 2015, 12:59
Hi Can anybody please explain me how did we comclude 1<x<3 ?
I still did not get this part!
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Re: If x is an integer, what is the value of x? (1) x^2 - 4x + 3 [#permalink]

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30 Aug 2015, 23:24
rads2400 wrote:
Hi Can anybody please explain me how did we comclude 1<x<3 ?
I still did not get this part!

Have you read previous TWO pages of the discussion? There are many posts explaining this.
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Re: If x is an integer, what is the value of x? (1) x^2 - 4x + 3 [#permalink]

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31 Aug 2015, 02:49
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Expert's post
Product of 2 terms <0 , then the variable lies between the given points.

(x-a) (x-b)<0, (considering a<b, in the number line)

1st Condition

Either x-a<0 i.e x<a or x-b>0 i.e x>b - NO common region

2nd Condition

Either x-a>0 i.e x>a or x-b<0 i.e x<b - a<x<b

Hope this helps.
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Re: If x is an integer, what is the value of x? (1) x^2 - 4x + 3 [#permalink]

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17 Nov 2015, 17:49
good question...design to get you in C trap.

a can be rewritten as (x-1)(x-3)<0
that can be only in one case, when x-1 is positive and x-3 is negative. The only option that works is x=2.

Statement 2:
(x+1)(x+3)>0 well, there are an infinity choices for X, thus, statement 2 alone is not sufficient.

A.
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Re: If x is an integer, what is the value of x? (1) x^2 - 4x + 3 [#permalink]

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13 Mar 2016, 07:21
Finding the range of x we get that x=2 is the only integer value => A is sufficient
but for statement 2 => x can have ∞ many values
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Re: If x is an integer, what is the value of x? (1) x^2 - 4x + 3 [#permalink]

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30 Jul 2016, 02:36
Hi!
would like to share what answer i got:
st1) x>1 , 1<x<3 , x>3
(using that curve and line plotting way)
st2) x<-3 , -3<x<-1, x>-1

inequalities-trick-91482.html

please help me on this..
thnks
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Re: If x is an integer, what is the value of x? (1) x^2 - 4x + 3 [#permalink]

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30 Jul 2016, 02:38
AryamaDuttaSaikia wrote:
Product of 2 terms <0 , then the variable lies between the given points.

(x-a) (x-b)<0, (considering a<b, in the number line)

1st Condition

Either x-a<0 i.e x<a or x-b>0 i.e x>b - NO common region

2nd Condition

Either x-a>0 i.e x>a or x-b<0 i.e x<b - a<x<b

Hope this helps.

what if product of two terms is greater than 0?
please help on this too
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Re: If x is an integer, what is the value of x? (1) x^2 - 4x + 3 [#permalink]

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Re: If x is an integer, what is the value of x? (1) x^2 - 4x + 3   [#permalink] 04 Aug 2017, 12:09

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# If x is an integer, what is the value of x? (1) x^2 - 4x + 3

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