BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Integral Solutions

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Legendary Member
Posts: 1132
Joined: Mon Jul 20, 2009 3:38 am
Location: India
Thanked: 64 times
Followed by:6 members
GMAT Score:760

Integral Solutions

by harsh.champ » Wed Feb 17, 2010 6:16 am
The integral solutions of the inequality (5x-1) < (x+1) ^2 < (7x-3) are


A. 2
B. 3
C. 2 , 3
D. 2 , 3 , 4
E. 3 , 4
It takes time and effort to explain, so if my comment helped you please press Thanks button :)



Just because something is hard doesn't mean you shouldn't try,it means you should just try harder.

"Keep Walking" - Johnny Walker :P
Top
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 1022
Joined: Mon Jul 20, 2009 11:49 pm
Location: Gandhinagar
Thanked: 41 times
Followed by:2 members

by shashank.ism » Wed Feb 17, 2010 7:07 am
harsh.champ wrote:The integral solutions of the inequality (5x-1) < (x+1) ^2 < (7x-3) are


A. 2
B. 3
C. 2 , 3
D. 2 , 3 , 4
E. 3 , 4
(5x-1) < (x+1) ^2 < (7x-3) -->(5x-1) < ( x ^2+1 +2x) < (7x-3)
--> 3x-2<x ^2<5x-4
3x-2<x ^2 --> x ^2-3x+2>0 -->(x-2)(x-1)>0 --> x<1 or x>2 ------(i)

x ^2<5x-4 --> x ^2-5x+4<0 --> (x-4)(x-1)<0 --> 1<x<4 -------(ii)
from (i) & (ii), we get 2<x<4 so integral [spoiler]soln is 3 Ans . B
[/spoiler]
My Websites:
www.mba.webmaggu.com - India's social Network for MBA Aspirants

www.deal.webmaggu.com -India's online discount, coupon, free stuff informer.

www.dictionary.webmaggu.com - A compact free online dictionary with images.

Nothing is Impossible, even Impossible says I'm possible.
Top
GMAT Instructor
Posts: 1578
Joined: Thu May 28, 2009 8:02 am
Thanked: 128 times
Followed by:34 members
GMAT Score:760

by Osirus@VeritasPrep » Wed Feb 17, 2010 7:09 am
shashank.ism wrote:
harsh.champ wrote:The integral solutions of the inequality (5x-1) < (x+1) ^2 < (7x-3) are


A. 2
B. 3
C. 2 , 3
D. 2 , 3 , 4
E. 3 , 4
(5x-1) < (x+1) ^2 < (7x-3) -->(5x-1) < ( x ^2+1 +2x) < (7x-3)
--> 3x-2<x ^2<5x-4
3x-2<x ^2 --> x ^2-3x+2>0 -->(x-2)(x-1)>0 --> x<1 or x>2 ------(i)

x ^2<5x-4 --> x ^2-5x+4<0 --> (x-4)(x-1)<0 --> 1<x<4 -------(ii)
from (i) & (ii), we get 2<x<4 so integral [spoiler]soln is 3 Ans . B
[/spoiler]
So is this the part of the program where you come and post the solutions from complore?
https://www.beatthegmat.com/the-retake-o ... 51414.html

Brandon Dorsey
GMAT Instructor
Veritas Prep

Buy any Veritas Prep book(s) and receive access to 5 Practice Cats for free! Learn More.
Top
User avatar
Legendary Member
Posts: 1022
Joined: Mon Jul 20, 2009 11:49 pm
Location: Gandhinagar
Thanked: 41 times
Followed by:2 members

by shashank.ism » Wed Feb 17, 2010 7:21 am
osirus0830 wrote:
shashank.ism wrote:
harsh.champ wrote:The integral solutions of the inequality (5x-1) < (x+1) ^2 < (7x-3) are


A. 2
B. 3
C. 2 , 3
D. 2 , 3 , 4
E. 3 , 4
(5x-1) < (x+1) ^2 < (7x-3) -->(5x-1) < ( x ^2+1 +2x) < (7x-3)
--> 3x-2<x ^2<5x-4
3x-2<x ^2 --> x ^2-3x+2>0 -->(x-2)(x-1)>0 --> x<1 or x>2 ------(i)

x ^2<5x-4 --> x ^2-5x+4<0 --> (x-4)(x-1)<0 --> 1<x<4 -------(ii)
from (i) & (ii), we get 2<x<4 so integral [spoiler]soln is 3 Ans . B
[/spoiler]
So is this the part of the program where you come and post the solutions from complore?
I have solved the problems myself if in any case u are able to find answer on complore be happy
My Websites:
www.mba.webmaggu.com - India's social Network for MBA Aspirants

www.deal.webmaggu.com -India's online discount, coupon, free stuff informer.

www.dictionary.webmaggu.com - A compact free online dictionary with images.

Nothing is Impossible, even Impossible says I'm possible.
Top
User avatar
Legendary Member
Posts: 2109
Joined: Sun Apr 19, 2009 10:25 pm
Location: New Jersey
Thanked: 109 times
Followed by:79 members
GMAT Score:640

by money9111 » Wed Feb 17, 2010 8:23 am
I think the answer is B only! i plugged in the numbers for each one starting with 2... quickly ruled that out in the first step becayse i got 9<9 and thats false... so i eliminated ACD, and then just tried 4 and got 25<25 as the 2nd half... and that's wrong... so B it is...
My goal is to make MBA applicants take onus over their process.

My story from Pre-MBA to Cornell MBA - New Post in Pre-MBA blog

Me featured on Poets & Quants

Free Book for MBA Applicants

Top
User avatar
Legendary Member
Posts: 1022
Joined: Mon Jul 20, 2009 11:49 pm
Location: Gandhinagar
Thanked: 41 times
Followed by:2 members

by shashank.ism » Wed Feb 17, 2010 8:46 am
money9111 wrote:I think the answer is B only! i plugged in the numbers for each one starting with 2... quickly ruled that out in the first step becayse i got 9<9 and thats false... so i eliminated ACD, and then just tried 4 and got 25<25 as the 2nd half... and that's wrong... so B it is...
ok plugin and elimination is a bit faster method for this problem . Good approach money 1119.
My Websites:
www.mba.webmaggu.com - India's social Network for MBA Aspirants

www.deal.webmaggu.com -India's online discount, coupon, free stuff informer.

www.dictionary.webmaggu.com - A compact free online dictionary with images.

Nothing is Impossible, even Impossible says I'm possible.
Top
User avatar
Legendary Member
Posts: 1132
Joined: Mon Jul 20, 2009 3:38 am
Location: India
Thanked: 64 times
Followed by:6 members
GMAT Score:760

by harsh.champ » Thu Feb 18, 2010 12:23 am
osirus0830 wrote:
shashank.ism wrote:
harsh.champ wrote:The integral solutions of the inequality (5x-1) < (x+1) ^2 < (7x-3) are


A. 2
B. 3
C. 2 , 3
D. 2 , 3 , 4
E. 3 , 4
(5x-1) < (x+1) ^2 < (7x-3) -->(5x-1) < ( x ^2+1 +2x) < (7x-3)
--> 3x-2<x ^2<5x-4
3x-2<x ^2 --> x ^2-3x+2>0 -->(x-2)(x-1)>0 --> x<1 or x>2 ------(i)

x ^2<5x-4 --> x ^2-5x+4<0 --> (x-4)(x-1)<0 --> 1<x<4 -------(ii)
from (i) & (ii), we get 2<x<4 so integral [spoiler]soln is 3 Ans . B
[/spoiler]
So is this the part of the program where you come and post the solutions from complore?
Hey osirus,
This is a very common type of math question and can be found in various sources.I don't know whether it is there in complore also.

As for the soln. approach ,we can find that the plugging technique is better suited for the question and it can be solved easily.


Another approach is plotting the lines y=5x-1 and y=7x-3 and the quadratic curve:(x+1)^2 and then solving it through the graph.
[This method is only for those people who are very well conversant with the graphical approach.In case ,you are not,don't use this method on the exam.It can backfire also if you don't have adequate practice of graphical approach]
It takes time and effort to explain, so if my comment helped you please press Thanks button :)



Just because something is hard doesn't mean you shouldn't try,it means you should just try harder.

"Keep Walking" - Johnny Walker :P
Top
Post new topic Post Reply
• Page 1 of 1