Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 18 Oct 2011
Posts: 87
Location: United States
Concentration: Entrepreneurship, Marketing
GMAT Date: 01302013
GPA: 3.3

Re: If x is an integer, what is the value of x? (1) x^2  4x + 3 [#permalink]
Show Tags
17 Jan 2013, 08:11
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.



Math Expert
Joined: 02 Sep 2009
Posts: 45219

Re: If x is an integer, what is the value of x? (1) x^2  4x + 3 [#permalink]
Show Tags
05 Jul 2013, 02:44



Intern
Joined: 05 May 2013
Posts: 23
GRE 1: 1480 Q800 V680

Re: If x is an integer, what is the value of x? (1) x^2  4x + 3 [#permalink]
Show Tags
07 Jul 2013, 22:20
1
This post received KUDOS
(1) reduces to (x3)(x1) < 0 which is possible only when x3 and x1 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.



Intern
Joined: 25 Jan 2014
Posts: 45
Concentration: Strategy, International Business
GMAT 1: 600 Q44 V29 GMAT 2: 710 Q48 V38
GPA: 3.35
WE: Analyst (Computer Software)

Re: If x is an integer, what is the value of x? (1) x^2  4x + 3 [#permalink]
Show Tags
17 May 2014, 02:05
Bunuel, very useful approach, thanks again
in the first equation,we wrote
(x1)(x3)<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 (x1)<0 & (x3)>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?



Math Expert
Joined: 02 Sep 2009
Posts: 45219

Re: If x is an integer, what is the value of x? (1) x^2  4x + 3 [#permalink]
Show Tags
17 May 2014, 05:45
gaurav1418z wrote: Bunuel, very useful approach, thanks again
in the first equation,we wrote
(x1)(x3)<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 (x1)<0 & (x3)>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 (x1)(x3)<0 ? One of the ways of solving quadratic inequalities is given here: ifxisanintegerwhatisthevalueofx1x24x94661.html#p731476
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 22 Mar 2014
Posts: 1

Re: If x is an integer, what is the value of x? (1) x^2  4x + 3 [#permalink]
Show Tags
16 Jun 2014, 04:15
hi. Just wondering whether 1/0 will be an integer?



Math Expert
Joined: 02 Sep 2009
Posts: 45219

Re: If x is an integer, what is the value of x? (1) x^2  4x + 3 [#permalink]
Show Tags
16 Jun 2014, 05:36



Intern
Joined: 05 Feb 2014
Posts: 45

Re: If x is an integer, what is the value of x? (1) x^2  4x + 3 [#permalink]
Show Tags
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 (x1)*(x3) <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)



Math Expert
Joined: 02 Sep 2009
Posts: 45219

Re: If x is an integer, what is the value of x? (1) x^2  4x + 3 [#permalink]
Show Tags
22 Jun 2014, 07:24



Intern
Joined: 05 Feb 2014
Posts: 45

Re: If x is an integer, what is the value of x? (1) x^2  4x + 3 [#permalink]
Show Tags
22 Jun 2014, 13:52
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 (x1)*(x3) <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: ifxisanintegerwhatisthevalueofx1x24x94661.html#p731476 and this: ifxisanintegerwhatisthevalueofx1x24x9466120.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.



Manager
Joined: 11 Sep 2013
Posts: 150
Concentration: Finance, Finance

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



Math Expert
Joined: 02 Sep 2009
Posts: 45219

Re: If x is an integer, what is the value of x? (1) x^2  4x + 3 [#permalink]
Show Tags
24 Aug 2014, 13:24



Manager
Joined: 11 Sep 2013
Posts: 150
Concentration: Finance, Finance

Re: If x is an integer, what is the value of x? (1) x^2  4x + 3 [#permalink]
Show Tags
24 Aug 2014, 13:42
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.



Manager
Joined: 30 May 2012
Posts: 215
Location: United States (TX)
Concentration: Finance, Marketing
GPA: 3.3
WE: Information Technology (Consulting)

Re: If x is an integer, what is the value of x? (1) x^2  4x + 3 [#permalink]
Show Tags
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) \(x^24x+3<0\) > \(1<x<3\) > 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. 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!



Math Expert
Joined: 02 Sep 2009
Posts: 45219

Re: If x is an integer, what is the value of x? (1) x^2  4x + 3 [#permalink]
Show Tags
09 Oct 2014, 05:58



Manager
Joined: 11 Sep 2013
Posts: 150
Concentration: Finance, Finance

If x is an integer, what is the value of x? (1) x^2  4x + 3 [#permalink]
Show Tags
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) \(x^24x+3<0\) > \(1<x<3\) > 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. 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) (x3)(x1)<0. Now use the logic. To get negative result Either (x3) or (x1) has to be negative and the other has to +veHere, (x3) can't be positive, Because if x3>0 then x>3 and if x>3 then x1 will become +ve. So (x3)(x1) will become +ve.Therefore, (x3) has to be negative,x3<0 or x<3 and and as I said earlier x1>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?



Manager
Joined: 30 May 2012
Posts: 215
Location: United States (TX)
Concentration: Finance, Marketing
GPA: 3.3
WE: Information Technology (Consulting)

Re: If x is an integer, what is the value of x? (1) x^2  4x + 3 [#permalink]
Show Tags
09 Oct 2014, 21:03
Bunuel wrote: Thanks bub. I am good with the method to solve inequalities. Do you by any chance have more questions related to Q. Inequalities, please? I've come across four such questions so far on this forum, but again, I have not done a search for them yet ... which I will do now. For those who struggle(d) like me  try this explanation from VeritasPrepKarishma, I think she hit the nail square on the head. inequalitiestrick91482.html#p804990inequalitiestrick9148220.html#p890041Here's to Bunuel, VeritasPrepKarishma and a whole bunch of others that contribute to making Maths easier for people like me



Math Expert
Joined: 02 Sep 2009
Posts: 45219

Re: If x is an integer, what is the value of x? (1) x^2  4x + 3 [#permalink]
Show Tags
10 Oct 2014, 02:03



Intern
Joined: 09 Jul 2014
Posts: 35

Re: If x is an integer, what is the value of x? (1) x^2  4x + 3 [#permalink]
Show Tags
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) \(x^24x+3<0\) > \( 1<x<3\)> 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.[/quote] 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.\(x^24x+3<0\) is the graph of parabola and it look likes this: Attachment: en.plot (1).png Intersection points are the roots of the equation \(x^24x+3=0\), which are \(x_1=1\) and \(x_2=3\). "<" sign means in which range of \(x\) the graph is below xaxis. Answer is \(1<x<3\) (between the roots). If the sign were ">": \(x^24x+3>0\). First find the roots (\(x_1=1\) and \(x_2=3\)). ">" sign means in which range of \(x\) the graph is above xaxis. 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: \(x^2x+12>0\), first rewrite this as \(x^2+x12<0\) (so that the coefficient of x^2 to be positive. It's possible to solve without rewriting, but easier to master one specific pattern). \(x^2+x12<0\). Roots are \(x_1=4\) and \(x_1=3\) > below ( "<") the xaxis is the range for \(4<x<3\) (between the roots). Again if it were \(x^2+x12>0\), 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



Intern
Joined: 20 Sep 2011
Posts: 18
Concentration: Operations, International Business

Re: If x is an integer, what is the value of x? (1) x^2  4x + 3 [#permalink]
Show Tags
02 Jul 2015, 12:34
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) \(x^24x+3<0\) > \(1<x<3\) > 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 => 14 +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.




Re: If x is an integer, what is the value of x? (1) x^2  4x + 3
[#permalink]
02 Jul 2015, 12:34



Go to page
Previous
1 2 3
Next
[ 50 posts ]



