|
Author |
Message |
|
TAGS:
|
|
|
SVP
Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
Joined: 04 Oct 2009
Posts: 1756
Location: Peru
Schools: Harvard, Stanford, Wharton, MIT & HKS (Government)
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs
Followers: 50
Kudos [?]:
145
[0], given: 108
|
Re: If x is positive, which of the following could be correct [#permalink]
 27 Jun 2012, 14:11
Bunuel, please check my reasoning about statement III: Statement III says 2x < x^2 < \frac{1}{x}So, we analyze part by part of this compound inequality: a) 2x < x^2then, x>2b) x^2 < \frac{1}{x}then, x^3<1 ==> x < 1So, we have x>2 and x<1. That's impossible! if x>2, x cannot be less than 1 at the same time. Statement III could not be correct! Please, confirm.
_________________
"Life’s battle doesn’t always go to stronger or faster men; but sooner or later the man who wins is the one who thinks he can."
My Integrated Reasoning Logbook / Diary: my-ir-logbook-diary-133264.html
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11506
Followers: 1791
Kudos [?]:
9526
[0], given: 826
|
Re: If x is positive, which of the following could be correct [#permalink]
28 Jun 2012, 02:15
|
|
|
|
|
|
Intern
Joined: 18 Jun 2012
Posts: 31
Followers: 1
Kudos [?]:
1
[0], given: 11
|
Re: If x is positive, which of the following could be correct [#permalink]
28 Jul 2012, 20:24
The question asked "what could be the correct ordering" means it asked for the possibilities.
What is question asked "what must be the correct ordering" ? In that case would we be required to choose an option which is true for all scenarios ?
|
|
|
|
|
|
Director
Joined: 22 Mar 2011
Posts: 608
WE: Science (Education)
Followers: 43
Kudos [?]:
266
[0], given: 43
|
Re: If x is positive, which of the following could be correct [#permalink]
29 Jul 2012, 01:37
Please, refer to the attached drawing, in which the three graphs y=1/x, y=2x, and y=x^2 are depicted for x>0. The exact values for A, B, and C can be worked out, but they are not important to establish the order of the three algebraic expressions. So, the correct orderings are: If x between 0 and A: x^2<2x<1/xIf x between A and B: x^2<1/x<2xIf x between B and C: 1/x<x^2<2xIf x greater than C: 1/x<2x<x^2We can see that only the first two of the above options are listed as answers (I and II). Answer: D.
Attachments
3Graphs.jpg [ 15.15 KiB | Viewed 1218 times ]
_________________
PhD in Applied Mathematics
Love GMAT Quant questions and running.
|
|
|
|
|
|
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 3104
Location: Pune, India
Followers: 567
Kudos [?]:
1994
[1] , given: 92
|
Re: If x is positive, which of the following could be correct [#permalink]
29 Jul 2012, 22:58
1
This post received
KUDOS
smartmanav wrote: The question asked "what could be the correct ordering" means it asked for the possibilities.
What is question asked "what must be the correct ordering" ? In that case would we be required to choose an option which is true for all scenarios ? The ordering will be different for different values of x so the question cannot ask for a single correct ordering.
_________________
Karishma
Veritas Prep | GMAT Instructor
My Blog
Save 10% on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.
Veritas Prep Reviews
|
|
|
|
|
|
Senior Manager
Joined: 23 Oct 2010
Posts: 335
Location: Azerbaijan
Followers: 6
Kudos [?]:
68
[0], given: 67
|
Re: If x is positive, which of the following could be correct [#permalink]
08 Aug 2012, 00:50
given that x>0 1 ) x^2 < 2X<1/X lets just check x^2 < 2X => 0 <x<2 ; 2X<1/X => 0<x<1/\sqrt{2} these 2 inequities do not conradict each other. so, 1) is ok 2) x^2 <1/X< 2X check them - x^2 <1/X => 0<x<1 ; 1/X< 2X => x> 1/\sqrt{2} these 2 inequities do not conradict each other. so, 2) is ok 3) 2X< x^2 <1/X check them - 2X< x^2 => x>2 ; x^2 <1/X => x<1 these 2 inequities conradict each other. so, 3) is not ok p.s. dont know why such symbols as sqroot , fraction ets dont work. 
_________________
Happy are those who dream dreams and are ready to pay the price to make them come true
|
|
|
|
|
|
SVP
Joined: 01 Sep 2010
Posts: 1738
Followers: 55
Kudos [?]:
564
[0], given: 467
|
Re: If x is positive, which of the following could be correct [#permalink]
13 Dec 2012, 07:28
picking numbers, both integers and not and only positive. In all cases only the 3 case doesn't work, so pretty fast you can reach D in this question youhave to be really comfortable with theory to solve it, otherwise is best and safe picking number .
_________________
KUDOS is the good manner to help the entire community.
|
|
|
|
|
|
Intern
Joined: 13 Dec 2012
Posts: 4
Followers: 0
Kudos [?]:
0
[0], given: 0
|
Re: If x is positive, which of the following could be correct [#permalink]
13 Dec 2012, 23:41
if x = 1/2, then 1/1/2 = 2 which is greater than 2(1/2)
|
|
|
|
|
|
Senior Manager
Joined: 09 Jun 2010
Posts: 456
Followers: 0
Kudos [?]:
14
[0], given: 39
|
Re: If x is positive, which of the following could be correct [#permalink]
14 Dec 2012, 00:30
positiveness or negativeness is important to inequalit
because x is positive we can multiple both sides of inequality with x and keep the same mark.for example
x^2<2x<1/x
is the same as
x^3<2x^2<1
(if x is negative we have to change the mark of the inequality. this question is not relevant to that cases)
now solve 2 inequality independently . this can be done quick.
this questions can be done in less than 3 minutes. Other method takes longer time and in fact is not good.
pls, comment.
|
|
|
|
|
|
Intern
Joined: 28 Aug 2012
Posts: 9
Followers: 0
Kudos [?]:
0
[0], given: 3
|
Re: If x is positive, which of the following could be correct [#permalink]
11 May 2013, 02:05
Hey Karishma, I feel below highlighted part is not correct. Please check. If I am wrong, please explain. thanks. VeritasPrepKarishma wrote: Vavali wrote: If x is positive, which of the following could be correct ordering of \frac{1}{x}, 2x, and x^2?
(I) x^2 < 2x < \frac{1}{x}
(II) x^2 < \frac{1}{x} < 2x
(III) 2x < x^2 < \frac{1}{x}
(a) none
(b) I only
(c) III only
(d) I and II
(e) I, II and III Let's look at this question logically. There will be some key takeaways here so don't focus on the question and the (long) solution. Focus on the logic. First of all, we are just dealing with positives so life is simpler. To compare two terms e.g. x^2 and 2x, we should focus on the points where they are equal. x^2 = 2x holds when x = 2. When x < 2, x^2 < 2xWhen x > 2, x^2 > 2xSimilarly 1/x = x^2 when x = 1When x < 1, 1/x > x^2. When x > 1, 1/x > x^2 Are you sure this is correct? I think.. we can use x=4 here, then 1/4>16 .. which is not correct. Going on, 1/x = 2x when x = 1/\sqrt{2}When x < 1/\sqrt{2}, 1/x > 2xWhen x > 1/\sqrt{2}, 1/x < 2xSo now you know that: If x < 1/\sqrt{2}, 1/x > 2x, 1/x > x^2 and x^2 < 2xSo x^2 < 2x < 1/x is possible. If 1/\sqrt{2} < x < 11/x < 2x, 1/x > x^2So x^2 < 1/x < 2x is possible. If x > 11/x < 2x, 1/x > x^2So x^2 < 1/x < 2x is possible. (Same as above) For no positive values of x is the third relation possible. |
|
|
|
|
|
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 3104
Location: Pune, India
Followers: 567
Kudos [?]:
1994
[0], given: 92
|
Re: If x is positive, which of the following could be correct [#permalink]
11 May 2013, 03:12
yogirb8801 wrote: Hey Karishma, I feel below highlighted part is not correct. Please check. If I am wrong, please explain. thanks. VeritasPrepKarishma wrote: Vavali wrote: If x is positive, which of the following could be correct ordering of \frac{1}{x}, 2x, and x^2?
(I) x^2 < 2x < \frac{1}{x}
(II) x^2 < \frac{1}{x} < 2x
(III) 2x < x^2 < \frac{1}{x}
(a) none
(b) I only
(c) III only
(d) I and II
(e) I, II and III Let's look at this question logically. There will be some key takeaways here so don't focus on the question and the (long) solution. Focus on the logic. First of all, we are just dealing with positives so life is simpler. To compare two terms e.g. x^2 and 2x, we should focus on the points where they are equal. x^2 = 2x holds when x = 2. When x < 2, x^2 < 2xWhen x > 2, x^2 > 2xSimilarly 1/x = x^2 when x = 1When x < 1, 1/x > x^2. When x > 1, 1/x > x^2 Are you sure this is correct? I think.. we can use x=4 here, then 1/4>16 .. which is not correct. Going on, 1/x = 2x when x = 1/\sqrt{2}When x < 1/\sqrt{2}, 1/x > 2xWhen x > 1/\sqrt{2}, 1/x < 2xSo now you know that: If x < 1/\sqrt{2}, 1/x > 2x, 1/x > x^2 and x^2 < 2xSo x^2 < 2x < 1/x is possible. If 1/\sqrt{2} < x < 11/x < 2x, 1/x > x^2So x^2 < 1/x < 2x is possible. If x > 11/x < 2x, 1/x > x^2So x^2 < 1/x < 2x is possible. (Same as above) For no positive values of x is the third relation possible. That is a typo. If you notice, for every case, the relation is opposite on the opposite sides of the equality value. So the relation that holds in x < 1 will be opposite to the relation that holds when x > 1. That did mess up the entire explanation. Good you pointed it out. I have edited the original post.
_________________
Karishma
Veritas Prep | GMAT Instructor
My Blog
Save 10% on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.
Veritas Prep Reviews
|
|
|
|
|
|
|
Re: If x is positive, which of the following could be correct
[#permalink]
11 May 2013, 03:12
|
|
|
|
|
|
|
|
|
|
|
close
