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

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Joined: 22 Mar 2014
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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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16 Jun 2014, 04:15
hi.
Just wondering whether 1/0 will be an integer?
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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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16 Jun 2014, 05:36
Vvt316 wrote:
hi.
Just wondering whether 1/0 will be an integer?

Division by 0 is not allowed, thus 1/0 is undefined. So the answer to your question is - no.
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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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22 Jun 2014, 06:17
gurpreetsingh wrote:
Hussain15 wrote:
If $$x$$ is an integer, what is the value of $$x$$ ?

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

IMO A

1st equation gives (x-1)*(x-3) <0 which is only possible when x=2

2nd gives (x+1)*(x+3) > 0 which is possible when x< -3 and x> -1 thus multiple values.

Thus A

OA pls.

Hi Gurpreet ,

Can you please explain how did you did you say from the second statement that x <- 3and x> -1 ?

The factors of the equation would be -1 and -3 how how do we know the sign for x ... (I have read many forms but can't understand)
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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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22 Jun 2014, 07:24
gauravsoni wrote:
gurpreetsingh wrote:
Hussain15 wrote:
If $$x$$ is an integer, what is the value of $$x$$ ?

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

IMO A

1st equation gives (x-1)*(x-3) <0 which is only possible when x=2

2nd gives (x+1)*(x+3) > 0 which is possible when x< -3 and x> -1 thus multiple values.

Thus A

OA pls.

Hi Gurpreet ,

Can you please explain how did you did you say from the second statement that x <- 3and x> -1 ?

The factors of the equation would be -1 and -3 how how do we know the sign for x ... (I have read many forms but can't understand)

Have you checked this post: if-x-is-an-integer-what-is-the-value-of-x-1-x-2-4x-94661.html#p731476 and this: if-x-is-an-integer-what-is-the-value-of-x-1-x-2-4x-94661-20.html#p1365336 ?
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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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24 Aug 2014, 13:19
Hi Bunuel,
Can I safely deduce the following

When (x+3)(x+1) = 0 , There are exactly two solutions

When (x+3) (x+1)> 0 , there are multiple solutions. Because by putting any positive value of x I can get >0

When (x+3) (x+1)<0, Either (x+3) or (x+1) has to be negative and obviously none can be Zero. In that case to make negative I can take only one value which is -2.

I don't want to concentrate on graphical method. Will the approach work for these types of questions always?
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Posts: 58117
Re: If x is an integer, what is the value of x? (1) x^2 - 4x + 3  [#permalink]

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24 Aug 2014, 13:24
Raihanuddin wrote:
Hi Bunuel,
Can I safely deduce the following

When (x+3)(x+1) = 0 , There are exactly two solutions

When (x+3) (x+1)> 0 , there are multiple solutions. Because by putting any positive value of x I can get >0

When (x+3) (x+1)<0, Either (x+3) or (x+1) has to be negative and obviously none can be Zero. In that case to make negative I can take only one value which is -2.

I don't want to concentrate on graphical method. Will the approach work for these types of questions always?

That's not correct.

(x + 3)(x + 1) > 0 means that x < -3 or x > -1.
(x + 3)(x + 1) < 0 means that -3 < x < -1.
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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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09 Oct 2014, 05:54
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.

Hello Bunuel, I am not sure if I followed your explanation all that clearly. I was able to get to the factors of the equation but after that, you mention about "<" symbol and as a result you arrive at $$1<x<3$$. How come? I tried to grasp your graphical approach but that did sit well either. Could you please elaborate? Thank you in advance!
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Posts: 58117
Re: If x is an integer, what is the value of x? (1) x^2 - 4x + 3  [#permalink]

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09 Oct 2014, 05:58
Blackbox 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.

Hello Bunuel, I am not sure if I followed your explanation all that clearly. I was able to get to the factors of the equation but after that, you mention about "<" symbol and as a result you arrive at $$1<x<3$$. How come? I tried to grasp your graphical approach but that did sit well either. Could you please elaborate? Thank you in advance!

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

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09 Oct 2014, 12:36
Blackbox 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.

Hello Bunuel, I am not sure if I followed your explanation all that clearly. I was able to get to the factors of the equation but after that, you mention about "<" symbol and as a result you arrive at $$1<x<3$$. How come? I tried to grasp your graphical approach but that did sit well either. Could you please elaborate? Thank you in advance!

After spending long time on this topic, I have come to an easy solution for me. You may like it

(1) (x-3)(x-1)<0. Now use the logic. To get negative result Either (x-3) or (x-1) has to be negative and the other has to +ve

Here, (x-3) can't be positive, Because if x-3>0 then x>3 and if x>3 then x-1 will become +ve. So (x-3)(x-1) will become +ve.

Therefore, (x-3) has to be negative,x-3<0 or x<3 and and as I said earlier x-1>0 or x>1

Finally we get, 1<x<3. Sufficient because 2 is the only integer between 1 and 3.

(2) we don't need to find equation. Just by putting multiple positive values we can satisfy statement 2. So Not sufficient

Ans. A
Hopefully my thinking is correct. I expect expert reply. Can I get more such question to practice?
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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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10 Oct 2014, 05:03
Bunuel 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.

With reference to your statement $$1<x<3$$ above, I calculated the range as $$x<1$$ or $$x<3$$
What I did wrong?[/quote]

How to solve quadratic inequalities - Graphic approach.

$$x^2-4x+3<0$$ is the graph of parabola and it look likes this:
Attachment:
en.plot (1).png

Intersection points are the roots of the equation $$x^2-4x+3=0$$, which are $$x_1=1$$ and $$x_2=3$$. "<" sign means in which range of $$x$$ the graph is below x-axis. Answer is $$1<x<3$$ (between the roots).

If the sign were ">": $$x^2-4x+3>0$$. First find the roots ($$x_1=1$$ and $$x_2=3$$). ">" sign means in which range of $$x$$ the graph is above x-axis. Answer is $$x<1$$ and $$x>3$$ (to the left of the smaller root and to the right of the bigger root).

This approach works for any quadratic inequality. For example: $$-x^2-x+12>0$$, first rewrite this as $$x^2+x-12<0$$ (so that the coefficient of x^2 to be positive. It's possible to solve without rewriting, but easier to master one specific pattern).

$$x^2+x-12<0$$. Roots are $$x_1=-4$$ and $$x_1=3$$ --> below ("<") the x-axis is the range for $$-4<x<3$$ (between the roots).

Again if it were $$x^2+x-12>0$$, then the answer would be $$x<-4$$ and $$x>3$$ (to the left of the smaller root and to the right of the bigger root).

Hope it helps.[/quote]

I am fond of your explanations !!
++++kudos
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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, 03:49
1
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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02 Aug 2019, 22:34
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.

How are you getting X is greater than 1 in the first eqn. Shouldn't it be X is less than 1? The two factors are -3 & -1.
Am I going wrong somewhere?
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Re: If x is an integer, what is the value of x? (1) x^2 - 4x + 3   [#permalink] 02 Aug 2019, 22:34

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