if x^2-x-6<0, what is the value of x?

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ch0719: Senior | Next Rank: 100 Posts; Posts: 45; Joined: Mon May 26, 2008 4:12 pm

by ch0719 » Sat Jan 03, 2009 3:13 pm

if x^2-x-6<0, what is the value of x?

1. x is an positive integer
2. -2<x<2

I found this somewhere on the web, the answer given is A but I thought it should be E, what do you think?

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Source: Beat The GMAT — Data Sufficiency | Sat Jan 03, 2009 3:13 pm

logitech: Legendary Member; Posts: 2134; Joined: Mon Oct 20, 2008 11:26 pmFollowed by: 25 members; Thanked: 237 times; GMAT Score:730

Re: if x^2-x-6<0, what is the value of x?

by logitech » Sat Jan 03, 2009 4:13 pm

ch0719 wrote:if x^2-x-6<0, what is the value of x?

1. x is an positive integer
2. -2<x<2

I found this somewhere on the web, the answer given is A but I thought it should be E, what do you think?

x^2-x-6<0 only when -2 < X < 3

So Statement 1 can not be sufficient. TRY 100 and you wont get a negative number

Statement 2 is a subset of -2 < X < 3 and sufficient.

So I would go with B

LGTCH
---------------------
"DON'T LET ANYONE STEAL YOUR DREAM!"

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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Sat Jan 03, 2009 6:20 pm

Let me add to the confusion more

How abt C)???

x^2-x-6<0
x^2-x<6
x(x-1)<6

or

(x+2) (x-3) < 0

Stmt I

x could be 1,2. No need to analayze any further analysis multiple values x INSUFF

Stmt II

-2<x<2

x could have multiple value satisfying (x+2) (x-3) < 0

-1,0,1.... (just considering integers(not anydecimal values) wihtin this range)

Highly INSUFF

Stmt I and II together

x has to be 1

SUFF

Choose C)

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logitech: Legendary Member; Posts: 2134; Joined: Mon Oct 20, 2008 11:26 pmFollowed by: 25 members; Thanked: 237 times; GMAT Score:730

Re: if x^2-x-6<0, what is the value of x?

by logitech » Sat Jan 03, 2009 6:24 pm

So Cramya you really think that -1,0 wont satisfy the equation?

For 0 it is -6 <0

For -1 it is -4 < 0

So I guess PUFF PUFF PASS

Oh by the way, what is HIGHLY INSUFF ?

LGTCH
---------------------
"DON'T LET ANYONE STEAL YOUR DREAM!"

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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Sat Jan 03, 2009 6:27 pm

Oh by the way, what is HIGHLY INSUFF

->

One that opens up a world of POSSIBILTIES.

Since x did not have to be an integer based on stm II imagine if we had considered all the decimal values between the given range that satisfied the conditions...

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logitech: Legendary Member; Posts: 2134; Joined: Mon Oct 20, 2008 11:26 pmFollowed by: 25 members; Thanked: 237 times; GMAT Score:730

by logitech » Sat Jan 03, 2009 6:31 pm

Cramya,

Did you study Math in the college ? If not, here is the Calculus 101

In fact, if you learn how to construct this tables you will really like them!

Attachments

LGTCH
---------------------
"DON'T LET ANYONE STEAL YOUR DREAM!"

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logitech: Legendary Member; Posts: 2134; Joined: Mon Oct 20, 2008 11:26 pmFollowed by: 25 members; Thanked: 237 times; GMAT Score:730

by logitech » Sat Jan 03, 2009 6:53 pm

what is the value of x ?

Okay - End of misunderstanding.

Cramya, I thought that you are saying that -1 and 0 will not satisfy the equation. My bad.

And yes the answer is C because we are looking for a VALUE not a RANGE so

any numbers within the range given in B will satisfy the equation but the only POSITIVE integer is + 1, since +2 is not included.

LGTCH
---------------------
"DON'T LET ANYONE STEAL YOUR DREAM!"

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ch0719: Senior | Next Rank: 100 Posts; Posts: 45; Joined: Mon May 26, 2008 4:12 pm

by ch0719 » Sat Jan 03, 2009 7:23 pm

thanks

given the statement 1 and 2, we can already conclude that the only possible outcome of x is 1, because x has to be a positive int and it has to be lower than a 2, then it got to be 1 regardless of what the question is asking

therefore i guess the question may be not too legit

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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Sat Jan 03, 2009 7:42 pm

therefore i guess the question may be not too legit

What website is the source?

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vivek.kapoor83: Legendary Member; Posts: 833; Joined: Mon Aug 04, 2008 1:56 am; Thanked: 13 times

by vivek.kapoor83 » Sun Jan 04, 2009 1:55 am

cramya wrote:

Cramya
(x+2) (x-3

cramya,
vaulue of X here would be x<-2 and x<3 isnt it but acc to u ..it is
between -2 <x<3 , how cm

if u put x+2<0
u ll get x<-2
or x>-2
Pls explain

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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Sun Jan 04, 2009 2:00 am

cramya,
vaulue of X here would be x<-2 and x<3 isnt it but acc to u ..it is
between -2 <x<3 , how cm

if u put x+2<0
u ll get x<-2
or x>-2

I dont think I said -2 <x<3 in my post. I am missing something. Let em know.

(x+2) (x-3) < 0 is from the whats given

I was telling -2<x<2 (stmt 2) is insuffcient since -1,0,1 all fit the bill

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vivek.kapoor83: Legendary Member; Posts: 833; Joined: Mon Aug 04, 2008 1:56 am; Thanked: 13 times

by vivek.kapoor83 » Sun Jan 04, 2009 3:06 am

sorry, it was said by Logitech but if logitech has done this, this is not correct...am i rite.
it is basic but i am not confident of my inequality skills
so,
x+2 <0
means x< -2..
am i rite...this is my ques.

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rajataga: Senior | Next Rank: 100 Posts; Posts: 87; Joined: Tue Dec 23, 2008 11:06 pm; Thanked: 2 times

by rajataga » Sun Jan 04, 2009 3:12 am

Hello Vivek,

It is -2<x<3 because, because when you factorize,

(x-3)(x+2)<0

so, only one of the two factors can be negative, and the other one has to positive.

hence, x-3 will be negative only when x<3, and x+2 will be negative, only when x>-2...

hence, we get

-2 < x< 3

even i think that the answer will be C,

since only A and B just narrow down this range, however both combined limit the answer to just 1.

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tanviet: Legendary Member; Posts: 1404; Joined: Tue May 20, 2008 6:55 pmFollowed by: 2 members; Thanked: 18 times

by tanviet » Sun Jan 04, 2009 6:01 am

x^2 -x-6<0

(x+2)(x-3)<0

-2<x<3

a, not enough

b, not enouth

c, 0<x<2 and x positive interger

x must be 1

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