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

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Re: If x is an integer, what is the value of x? (1) x^2 - 4x + 3 [#permalink] New post 17 Jan 2013, 07:11
Statement 1: If x has to be an integer only x=2 would yield a number that is less than 0. Sufficient.
Statement 2: x can take on any number of integers that would yield a number greater than 0. Not Sufficient.
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Re: If x is an integer, what is the value of x? (1) x^2 - 4x + 3 [#permalink] New post 05 Jul 2013, 01:44
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Re: If x is an integer, what is the value of x? (1) x^2 - 4x + 3 [#permalink] New post 07 Jul 2013, 21:20
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(1) reduces to (x-3)(x-1) < 0 which is possible only when x-3 and x-1 are of the opposite signs which => 1<x<3. Since x is an integer, we have a solution for x=2.

(2) reduces to (x+3)(x+1) > 0 which is possible for x < -3 or x > -1 which has many solutions, Not sufficient.

Thus (A) is the answer.
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Re: If x is an integer, what is the value of x? (1) x^2 - 4x + 3 [#permalink] New post 17 May 2014, 01:05
Bunuel, very useful approach, thanks again

in the first equation,we wrote

(x-1)(x-3)<0 , so we know both terms have opposite signs, i.e

x>1 or x<3, since x is an integer, x has to be 2

However the other set is (x-1)<0 & (x-3)>0, or , x<1 or x>3, which can have many values, hence i marked statement 1 as insufficient,

for ex- x= -2 and y =4, equations becomes -3 * 1 = -3 , and it is still less than zero, hence satisfied.

Where am i going wrong?
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Re: If x is an integer, what is the value of x? (1) x^2 - 4x + 3 [#permalink] New post 17 May 2014, 04:45
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gaurav1418z wrote:
Bunuel, very useful approach, thanks again

in the first equation,we wrote

(x-1)(x-3)<0 , so we know both terms have opposite signs, i.e

x>1 or x<3, since x is an integer, x has to be 2

However the other set is (x-1)<0 & (x-3)>0, or , x<1 or x>3, which can have many values, hence i marked statement 1 as insufficient,

for ex- x= -2 and y =4, equations becomes -3 * 1 = -3 , and it is still less than zero, hence satisfied.

Where am i going wrong?


How can x be simultaneously less than 1 and more than 3 for (x-1)(x-3)<0 ?

One of the ways of solving quadratic inequalities is given here: if-x-is-an-integer-what-is-the-value-of-x-1-x-2-4x-94661.html#p731476


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Re: If x is an integer, what is the value of x? (1) x^2 - 4x + 3 [#permalink] New post 16 Jun 2014, 03:15
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] New post 16 Jun 2014, 04:36
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Re: If x is an integer, what is the value of x? (1) x^2 - 4x + 3 [#permalink] New post 22 Jun 2014, 05:17
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] New post 22 Jun 2014, 06:24
Expert's post
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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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If x is an integer, what is the value of x? (1) x^2 - 4x + 3 [#permalink] New post 22 Jun 2014, 12:52
Bunuel wrote:
gauravsoni wrote:
gurpreetsingh 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 ?[/quote]


Thanks Bunuel, The second link with the graphical approach made everything very clear. I have been struggling to figure out how this works. Thanks again.
Re: If x is an integer, what is the value of x? (1) x^2 - 4x + 3   [#permalink] 22 Jun 2014, 12:52
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