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Math : Algebra 101

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Director
Status: Final Lap Up!!!
Affiliations: NYK Line
Joined: 21 Sep 2012
Posts: 812
Location: India
GMAT 1: 410 Q35 V11
GMAT 2: 530 Q44 V20
GMAT 3: 630 Q45 V31
GPA: 3.84
WE: Engineering (Transportation)
Re: Math : Algebra 101  [#permalink]

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29 Jan 2013, 05:47
VeritasPrepKarishma wrote:
Archit143 wrote:
Need Help!!! Urgent

What is the difference between the solution of below problems, Is there any difference in the approach:-
1. X^3 > X

soln: -1<X<0 or X>1

If we follow the above principle for solving than the answer to below equation must be:

2. a^3< a^2 + 2a

-1<a<0 or a>2

but the answer as per MGMAt quant book is
0<a<2 or a<-1

Pls help me in getting the right concept.........

Responding to a pm:

2. a^3< a^2 + 2a

a^3 - a^2 - 2a < 0
a(a - 2)(a + 1) < 0

......-1.....0............2.......

Since you want the expression to be negative, the required range is a < -1 or 0 < a < 2 (Notice the sign in the original inequality. It is less than)

The range you have written: -1<a<0 or a>2 is for the expression to be positive.

Check out these posts for further clarification:

http://www.veritasprep.com/blog/2012/06 ... e-factors/
http://www.veritasprep.com/blog/2012/07 ... ns-part-i/
http://www.veritasprep.com/blog/2012/07 ... s-part-ii/
http://www.veritasprep.com/blog/2012/07 ... qualities/

Karishma

You are no less than Ron ...I would rate you above them in Maths
I mean what great explanations.......
can you fw the links of your blog on MODULUS, various type of questions.....
Thanks a trillion....I am sure i have added atleast 1 point to my maths score.......

Was it so simple!!!!!!!!I am thinking now!!!!!!!!!!!!!!!!!!!!

Archit
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Joined: 02 Sep 2009
Posts: 65062
Re: Math : Algebra 101  [#permalink]

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10 Jul 2013, 23:06
Bumping for review*.

*New project from GMAT Club!!! Check HERE

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Re: Math : Algebra 101  [#permalink]

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23 Oct 2013, 06:17
Thank you for the book, it is a very useful one. I have a question on Solving equations of degree 2 : QUADRATIC part.
"The sum is -11 and the product is 30. So numbers are -5,-6". I think there is a typo: the sum is 11 (=b), not -11 as far as the solutions are x1=-5, and x2=-6 (we have 2 binomials (x+5) and (x+6). Please correct if I am wrong.
Thanks again.
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Joined: 02 Sep 2009
Posts: 65062
Re: Math : Algebra 101  [#permalink]

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24 Oct 2013, 01:26
marvas wrote:
Thank you for the book, it is a very useful one. I have a question on Solving equations of degree 2 : QUADRATIC part.
"The sum is -11 and the product is 30. So numbers are -5,-6". I think there is a typo: the sum is 11 (=b), not -11 as far as the solutions are x1=-5, and x2=-6 (we have 2 binomials (x+5) and (x+6). Please correct if I am wrong.
Thanks again.

The sum of the roots is (-5) + (-6) = -11, which is -b/a=-(11/1)=-11.

Hope it's clear.
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Re: Math : Algebra 101  [#permalink]

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07 Jan 2015, 13:17
this post has been really helpful. Thank you
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Joined: 26 Jun 2015
Posts: 2
Concentration: Finance, Strategy
GMAT 1: 740 Q48 V44
GPA: 3.67
Re: Math : Algebra 101  [#permalink]

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29 Jun 2015, 15:05
1
shrouded1 wrote:
Eg. $$x^6 -3x^3 + 2 = 0$$
Here let $$y=x^3$$
$$y^2-3y+2=0$$
$$(y-2)(y-1)=0$$

So the solution is y=1,2 or x^3=1,2 or x=1,cube_root(3)

Hi,

First of all, numerous thanks for all the work on this forum, it is so helpful.

I was going through the Math book and noticed a typo on the solution above. Shouldn't x = 1 & cube_root(2) ? Not a big deal, but always worth mentioning!
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Joined: 02 Sep 2009
Posts: 65062
Re: Math : Algebra 101  [#permalink]

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30 Jun 2015, 03:09
RCM wrote:
shrouded1 wrote:
Eg. $$x^6 -3x^3 + 2 = 0$$
Here let $$y=x^3$$
$$y^2-3y+2=0$$
$$(y-2)(y-1)=0$$

So the solution is y=1,2 or x^3=1,2 or x=1,cube_root(3)

Hi,

First of all, numerous thanks for all the work on this forum, it is so helpful.

I was going through the Math book and noticed a typo on the solution above. Shouldn't x = 1 & cube_root(2) ? Not a big deal, but always worth mentioning!

Edited the typo. Thank you!
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Re: Math : Algebra 101  [#permalink]

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02 Jun 2017, 07:24
Excellent post!

came her to review the basics again!

thank you!
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Re: Math : Algebra 101  [#permalink]

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20 Jun 2020, 22:26
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Math : Algebra 101   [#permalink] 20 Jun 2020, 22:26

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