Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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

Re: If x is an integer, what is the value of x? (1) x^2 - 4x + 3 [#permalink]
07 Jul 2013, 21:20

1

This post received KUDOS

(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.

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]
24 Aug 2014, 12:19

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? Please help

Re: If x is an integer, what is the value of x? (1) x^2 - 4x + 3 [#permalink]
24 Aug 2014, 12:24

Expert's post

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? Please help

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. _________________

Re: If x is an integer, what is the value of x? (1) x^2 - 4x + 3 [#permalink]
24 Aug 2014, 12:42

Bunuel wrote:

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? Please help

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.

So for the 1st one value can be -4, -5....... or can be 0, 1, 2,...... and can be fraction also. For the 2nd one only -2 if integer but can any number in between -1 and and -3 if not integer. Actually in the original question I have seen integer. That's why I picked integer. If x is integer, is my reasoning correct to find answer? So far I think I am saying the same thing you have given for the above two.

gmatclubot

Re: If x is an integer, what is the value of x? (1) x^2 - 4x + 3
[#permalink]
24 Aug 2014, 12:42